Finite Group DatabasebetaFinite Group Databasebeta| order | 22862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D71⋊C7 |
| unambiguous semidirect product | D71⋊(C7×C23) |
| unambiguous semidirect product | (C71⋊C7)⋊(C2×C23) |
| unambiguous semidirect product | (C23×D71)⋊C7 |
| Fitting, socle, Hall | C23×C71 ⋊ C2×C7 |
| derived, Sylow | C71 ⋊ C2×C7×C23 |
| Hall | C23×C71⋊C7 ⋊ C2 |
| Hall | C23×D71 ⋊ C7 |
| Hall | C71⋊C7 ⋊ C2×C23 |
| Hall | D71 ⋊ C7×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D71⋊C7 |
| commutator, cosocle, hypocenter | C71 | C2×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C71 | C2×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1633 |
437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22862, 10);