Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#14556975⋊C2 |
| unambiguous semidirect product | #14556975⋊(C2×C5) |
| unambiguous semidirect product | ((C13⋊D13)⋊C7)⋊(C2×C5) |
| Fitting, socle, Hall | C5×C132 ⋊ C2×D7 |
| derived, Hall | C132⋊C7 ⋊ C22×C5 |
| Hall | C5×C132⋊C7 ⋊ C22 |
| Sylow | C132 ⋊ C2×C5×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #14556975⋊C2 |
| commutator, cosocle, hypocenter | C132⋊C7 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C132 | C2×D7 |
| LCS | G ▷ C132⋊C7 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 455 |
170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 55);