Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | D7×C3⋊D273 |
| unambiguous semidirect product | (C3×D7)⋊D273 |
| unambiguous semidirect product | (C7×D7)⋊(C3⋊D39) |
| unambiguous semidirect product | (C13×D7)⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C72×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×C3⋊D3 |
| Hall | C32×C72 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ D72 |
| Sylow | C72 ⋊ C2×C3⋊D39 |
| Sylow | C13 ⋊ D7×C3⋊D21 |
| Sylow | C32 ⋊ D7×D91 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C13 | C22 |
| LCS | G ▷ C32×C72×C13 | |
| UCS | C1 | |
312 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1638 |
2055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1583);