Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D819 |
| unambiguous semidirect product | (C2×C7)⋊(C7×D117) |
| unambiguous semidirect product | (C2×C9)⋊(C7×D91) |
| unambiguous semidirect product | (C2×C13)⋊(C7×D63) |
| Fitting | C2×C72×C9×C13 ⋊ C2 |
| derived | C7×C9×C13 ⋊ C22×C7 |
| Hall | C72×C9×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×D9 |
| Hall | C72×C9 ⋊ C2×D13 |
| Hall | C9×C13 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D117 |
| Sylow | C13 ⋊ C2×C7×D63 |
| Sylow | C9 ⋊ C2×C7×D91 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D819 |
| commutator, cosocle, hypocenter | C7×C9×C13 | C22×C7 |
| Frattini | C3 | C2×C7×D273 |
| Fitting | C2×C72×C9×C13 | C2 |
| socle | C2×C3×C72×C13 | D3 |
| LCS | G ▷ C7×C9×C13 | |
| UCS | C1 ◁ C2×C7 | |
156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3276 |
5754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 560);