Finite Group DatabasebetaFinite Group Databasebeta| order | 23718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×D201 |
| unambiguous semidirect product | C3⋊(C59×D67) |
| unambiguous semidirect product | C67⋊(D3×C59) |
| Fitting, socle, Hall | C3×C59×C67 ⋊ C2 |
| derived, Hall | C3×C67 ⋊ C2×C59 |
| Hall | C59×C67 ⋊ D3 |
| Hall | C3×C59 ⋊ D67 |
| Sylow | C67 ⋊ D3×C59 |
| Sylow | C3 ⋊ C59×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | D201 |
| commutator, cosocle, hypocenter | C3×C67 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C3×C59×C67 | C2 |
| LCS | G ▷ C3×C67 | |
| UCS | C1 ◁ C59 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11859 |
6018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23718, 7);