Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| isoclinism | isoclinic class of GL(3,𝔽2)2 |
| automorphism | ? |
| homology | Abelianization (H1) = C1 · Schur multiplier (H2) = C22 |
| direct product | GL(3,𝔽2)2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | G | C1 |
| LCS | G | |
| UCS | C1 | |
382 conjugacy classes of subgroups; only the 4 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 4 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
36 conjugacy classes — view the full character table.
| derived subgroup of | #72244493 |
| socle of | #72244493 |
| maximal subgroup of | #72244493 |
| maximal normal subgroup of | #72244493 |
| maximal quotient of | Ω+(4,𝔽7), GL(3,𝔽2)×SL(2,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.