Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C3⋊(C7⋊#261) |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)×C7⋊#261) |
| Fitting, socle, derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ #261 |
| Sylow | C72 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×Dic21 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C3×C4 |
| prime radical | C3×C7×ΓL(1,𝔽8)×D13 | C2 |
| cosocle | C3×C72×D13 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1638 |
435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1182);