Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3×C7 |
| direct product | D13×C3⋊(C3⋊(C7⋊D7)) |
| unambiguous semidirect product | (C3×D13)⋊(C3⋊(C7⋊D7)) |
| unambiguous semidirect product | (C7×D13)⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C72×C13 ⋊ C22 |
| Hall | C72×C13 ⋊ C2×C3⋊D3 |
| Hall | C32×C72 ⋊ C2×D13 |
| Hall | C32×C13 ⋊ C2×C7⋊D7 |
| Sylow | C72 ⋊ C3⋊D3×D13 |
| Sylow | C13 ⋊ C2×C3⋊(C3⋊(C7⋊D7)) |
| Sylow | C32 ⋊ D13×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C72×C13 | C22 |
| LCS | G ▷ C32×C72×C13 | |
| UCS | C1 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5733 |
1776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1590);