Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C7×C13 · Schur multiplier (H2) = C2×C3 |
| direct product | C7×A4×C13×ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×ΓL(1,𝔽8))⋊(C3×C7×C13) |
| unambiguous semidirect product | (C7×A4)⋊(C3×C7×C13) |
| unambiguous semidirect product | (C22⋊ΓL(1,𝔽8))⋊(C3×C7×C13) |
| Fitting, socle, Hall | C22×C72×C13 ⋊ C32 |
| derived | C22×C7 ⋊ C32×C7×C13 |
| Hall | C72×C13 ⋊ C3×A4 |
| Hall | C22×C72 ⋊ C32×C13 |
| Hall | C22×C13 ⋊ C3×C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×A4×C13 |
| Sylow | C22 ⋊ C3×C7×C13×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | A4×ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C7 | C32×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C22×C72×C13 | C32 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C7×C13 | |
132 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1092 |
1820 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1333);