Finite Group DatabasebetaFinite Group Databasebeta| order | 23177 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C49 · Schur multiplier (H2) = C1 |
| direct product | C11×C43⋊C49 |
| unambiguous semidirect product | C43⋊(C11×C49) |
| unambiguous semidirect product | (C11×C43)⋊C49 |
| derived, Sylow | C43 ⋊ C11×C49 |
| Hall | C11×C43 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C11 | C43⋊C7 |
| commutator, hypocenter | C43 | C11×C49 |
| Frattini | C7 | C11×C43⋊C7 |
| Fitting, socle, prime radical | C7×C11×C43 | C7 |
| cosocle | C7×C43 | C7×C11 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C7×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23177 |
1001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23177, 2);