Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2 |
| direct product | C5×C7×D132 |
| unambiguous semidirect product | (C13×D13)⋊(C2×C5×C7) |
| Fitting, socle, Hall | C5×C7×C132 ⋊ C22 |
| derived, Sylow | C132 ⋊ C22×C5×C7 |
| Hall | C7×C132 ⋊ C22×C5 |
| Hall | C5×C132 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D132 |
| commutator, cosocle, hypocenter | C132 | C22×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C132 | C22 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C5×C7 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
2240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 78);