Finite Group DatabasebetaFinite Group Databasebeta| order | 22451 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C157⋊C13 |
| unambiguous semidirect product | C157⋊(C11×C13) |
| unambiguous semidirect product | (C11×C157)⋊C13 |
| Fitting, socle, Hall | C11×C157 ⋊ C13 |
| derived, Sylow | C157 ⋊ C11×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C157⋊C13 |
| commutator, cosocle, hypocenter | C157 | C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C157 | C13 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1727 |
275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22451, 1);