Finite Group DatabasebetaFinite Group Databasebeta| order | 23684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2 |
| direct product | C2×C31×D191 |
| unambiguous semidirect product | C191⋊(C22×C31) |
| unambiguous semidirect product | (C2×C191)⋊(C2×C31) |
| Fitting, socle | C2×C31×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C22×C31 |
| Hall | C31×C191 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C31 | D191 |
| commutator, cosocle, hypocenter | C191 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C191 | C2 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C2×C31 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11842 |
6014 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23684, 7);