Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D117 |
| unambiguous semidirect product | (C9×D7)⋊(C7×D13) |
| unambiguous semidirect product | (C13×D7)⋊(C7×D9) |
| Fitting, Hall | C72×C9×C13 ⋊ C22 |
| derived | C7×C9×C13 ⋊ C22×C7 |
| Hall | C72×C13 ⋊ C2×D9 |
| Hall | C72×C9 ⋊ C2×D13 |
| Hall | C9×C13 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D117 |
| Sylow | C13 ⋊ C7×D7×D9 |
| Sylow | C9 ⋊ C7×D7×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D117 |
| commutator, cosocle, hypocenter | C7×C9×C13 | C22×C7 |
| Frattini | C3 | C7×D7×D39 |
| Fitting | C72×C9×C13 | C22 |
| socle | C3×C72×C13 | C2×D3 |
| LCS | G ▷ C7×C9×C13 | |
| UCS | C1 ◁ C7 | |
156 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 156 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) = 1638 |
2100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 520);