Finite Group DatabasebetaFinite Group Databasebeta| order | 23306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C271 · Schur multiplier (H2) = C1 |
| direct product | D43×C271 |
| unambiguous semidirect product | C43⋊(C2×C271) |
| Fitting, socle, Hall | C43×C271 ⋊ C2 |
| derived, Sylow | C43 ⋊ C2×C271 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C271 | D43 |
| commutator, cosocle, hypocenter | C43 | C2×C271 |
| Frattini | C1 | G |
| Fitting, socle | C43×C271 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C271 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11653 |
6233 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23306, 1);