Finite Group DatabasebetaFinite Group Databasebeta| order | 22876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×D19×C43⋊C7 |
| unambiguous semidirect product | C19⋊(C22×C43⋊C7) |
| unambiguous semidirect product | (C2×C19)⋊(C2×C43⋊C7) |
| unambiguous semidirect product | (C2×D19×C43)⋊C7 |
| Fitting, socle | C2×C19×C43 ⋊ C2×C7 |
| derived, Hall | C19×C43 ⋊ C22×C7 |
| Hall | C19×C43⋊C7 ⋊ C22 |
| Hall | C2×D19×C43 ⋊ C7 |
| Sylow | C43 ⋊ C2×C7×D19 |
| Sylow | C19 ⋊ C22×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D19×C43⋊C7 |
| commutator, cosocle, hypocenter | C19×C43 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C43 | C2×C7 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1634 |
286 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22876, 17);