Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C5⋊#14556975 |
| unambiguous semidirect product | (C2×C5)⋊#14556975 |
| Fitting, socle | C2×C5×C132 ⋊ D7 |
| derived, Hall | C5×C132⋊C7 ⋊ C22 |
| Hall | C132⋊C7 ⋊ C2×D5 |
| Hall | C5×C132 ⋊ C2×D7 |
| Sylow | C132 ⋊ C2×D35 |
| Sylow | C5 ⋊ C2×#14556975 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#14556975 |
| commutator, cosocle, hypocenter | C5×C132⋊C7 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C132 | D7 |
| LCS | G ▷ C5×C132⋊C7 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 910 |
194 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 72);