Sporadic groups and their variants
| Sporadic group | Variants |
|---|
| $\mathrm{M}_{11}$ |
| $\mathrm{M}_{12}$ |
$\mathrm{M}_{12}:2$, $2\cdot \mathrm{M}_{12}$, $2\cdot \mathrm{M}_{12}:2$, $2\cdot \mathrm{M}_{12}.2\text{ (isoclinic)}$ |
| $\mathrm{M}_{22}$ |
${\mathrm{M}_{22}}:2$, $2\cdot \mathrm{M}_{22}$, $2\cdot\mathrm{M}_{22}:2$, $2\cdot\mathrm{M}_{22}.2$ (iso), $3\cdot\mathrm{M}_{22}$, $3\cdot\mathrm{M}_{22}:2$, $4\cdot \mathrm{M}_{22}$, $4\cdot\mathrm{M}_{22}:2$, $4\cdot\mathrm{M}_{22}.2$ (iso), $6\cdot\mathrm{M}_{22}$, $6\cdot\mathrm{M}_{22}:2$, $6\cdot\mathrm{M}_{22}.2$ (iso), $12\cdot \mathrm{M}_{22}$, $12\cdot\mathrm{M}_{22}:2$, $12\cdot\mathrm{M}_{22}.2$ (iso) |
| $\mathrm{M}_{23}$ |
| $\mathrm{M}_{24}$ |
| $\mathrm{J}_{1}$ |
| $\mathrm{J}_{2}$ | $\mathrm{J}_{2}:2$, $2\cdot\mathrm{J}_{2}$, $2\cdot\mathrm{J}_2:2$, $2\cdot\mathrm{J}_2.2$ (iso) |
| $\mathrm{J}_{3}$ | $\mathrm{J}_{3}:2$, $3\cdot\mathrm{J}_3$, $3\cdot\mathrm{J}_3:2$ |
| $\mathrm{J}_{4}$ |
| $\mathrm{Co}_{1}$ | $2\cdot\mathrm{Co}_{1}$ |
| $\mathrm{Co}_{2}$ |
| $\mathrm{Co}_{3}$ |
| $\mathrm{Fi}_{22}$ | $\mathrm{Fi}_{22}:2$, $2\cdot\mathrm{Fi}_{22}$, $2\cdot\mathrm{Fi}_{22}:2$, $2\cdot\mathrm{Fi}_{22}.2$ (iso), $3\cdot\mathrm{Fi}_{22}$, $3\cdot\mathrm{Fi}_{22}:2$, $6\cdot\mathrm{Fi}_{22}$, $6\cdot\mathrm{Fi}_{22}:2$, $6\cdot\mathrm{Fi}_{22}.2$ (iso) |
| $\mathrm{Fi}_{23}$ |
| $\mathrm{Fi'}_{24}$ | $\mathrm{Fi}_{24}=\mathrm{Fi}_{24}':2$, $3\cdot\mathrm{Fi'}_{24}$, $3\cdot\mathrm{Fi'}_{24}:2$ |
| $\mathrm{HS}$ | $\mathrm{HS}:2$, $2\cdot\mathrm{HS}$, $2\cdot\mathrm{HS}:2$, $2\cdot\mathrm{HS}.2$ (iso) |
| $\mathrm{McL}$ | $\mathrm{McL}:2$, $3\cdot\mathrm{McL}$, $3\cdot\mathrm{McL}:2$ |
| $\mathrm{Suz}$ | $\mathrm{Suz}:2$, $2\cdot\mathrm{Suz}$, $2\cdot\mathrm{Suz}:2$, $2\cdot\mathrm{Suz}.2$ (iso), $3\cdot\mathrm{Suz}$, $3\cdot\mathrm{Suz}:2$, $6\cdot\mathrm{Suz}$, $6\cdot\mathrm{Suz}:2$, $6\cdot\mathrm{Suz}.2$ (iso) |
| $\mathrm{He}$ | $\mathrm{He}:2$ |
| $\mathrm{HN}$ | $\mathrm{HN}:2$ |
| $\mathrm{Th}$ |
| $\mathrm{B}$ | $2\cdot\mathrm{B}$ |
| $\mathrm{M}$ |
| $\mathrm{O'N}$ | $\mathrm{O'N}:2$, $3\cdot\mathrm{ON}$, $3\cdot\mathrm{ON}:2$ |
| $\mathrm{Ru}$ | $2\cdot\mathrm{Ru}$ |
| $\mathrm{Ly}$ |
| Group | Standard generators | Conjugacy classes | Character information | Modular information | Permutation representations | Linear representations | Maximal subgroups |
|---|
| $\mathrm{M}_{11}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in all characteristics | All, with SLPs with standard generators if applicable |
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| $\mathrm{M}_{12}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in all characteristics | All, with SLPs with standard generators if applicable |
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| $\mathrm{M}_{22}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{M}_{23}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{M}_{24}$ | Yes | Yes | Complete | Not all Ext1 data | Not largest perm rep | All irreducibles in positive characteristic up to dimension 3000 | All, with SLPs with standard generators if applicable |
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| $\mathrm{J}_{1}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{J}_{2}$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{J}_{3}$ | Yes | Yes | Complete | Little Ext1 data | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| Co3 | Yes | Yes | Complete | No Ext^1 matrices | All primitive up to 500000 | All irreducibles in positive characteristics up to 3000 | All, with SLPs with standard generators for HS and M23 |
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| HS | Yes | Yes | Complete | No 2-cohomology for simple modules in the principal block | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| McL | Yes | Yes | Complete | No Ext1 data | All primitive | All irreducibles in positive characteristic up to dimension 2200 for prime 2, 3000 for other primes, with a few larger | All, with SLPs with standard generators if applicable |
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| Ly | Yes | Yes | Complete | Nothing yet | None | Small-dimensional irreducibles in characteristic 5 | All, with SLPs with standard generators for maximals 1 and 2. |
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| Group | Standard generators | Conjugacy classes | Character information | Modular information | Permutation representations | Linear representations | Maximal subgroups |
|---|
| $\mathrm{M}_{12}:2$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{M}_{22}:2$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable |
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| $\mathrm{J}_{2}:2$ | Yes | Yes | Complete | Complete | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable except for $3.\mathrm{A}_6.2^2$ |
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| $\mathrm{HS}:2$ | Yes | Yes | Complete | No Ext1 for p=2,3,5, no 2-cohomology | All primitive | All irreducibles in positive characteristic | All, with SLPs with standard generators if applicable except for $\mathrm{L}_3(4):2^2$ (no std gens defined yet) |
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