Finite Group DatabasebetaFinite Group Databasebeta| order | 23364 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C11×D177 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C11×D59) |
| unambiguous semidirect product | (C2×C59)⋊(C3×D3×C11) |
| Fitting, socle | C2×C32×C11×C59 ⋊ C2 |
| derived | C3×C59 ⋊ C22×C3×C11 |
| Hall | C32×C11×C59 ⋊ C22 |
| Hall | C11×C59 ⋊ C2×C3×D3 |
| Hall | C32×C59 ⋊ C22×C11 |
| Hall | C32×C11 ⋊ C2×D59 |
| Sylow | C59 ⋊ C2×C3×D3×C11 |
| Sylow | C32 ⋊ C2×C11×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C11 | D177 |
| commutator, cosocle, hypocenter | C3×C59 | C22×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11×C59 | C2 |
| LCS | G ▷ C3×C59 | |
| UCS | C1 ◁ C2×C3×C11 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7788 |
5940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23364, 70);