Finite Group DatabasebetaFinite Group Databasebeta| order | 23660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×D7×D169 |
| unambiguous semidirect product | (D7×C169)⋊(C2×C5) |
| unambiguous semidirect product | (C7×D169)⋊(C2×C5) |
| unambiguous semidirect product | D1183⋊(C2×C5) |
| Fitting, Hall | C5×C7×C169 ⋊ C22 |
| derived, Hall | C7×C169 ⋊ C22×C5 |
| Hall | C5×C169 ⋊ C2×D7 |
| Sylow | C169 ⋊ C2×C5×D7 |
| Hall | C5×C7 ⋊ C2×D169 |
| Sylow | C7 ⋊ C2×C5×D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D7×D169 |
| commutator, cosocle, hypocenter | C7×C169 | C22×C5 |
| Frattini | C13 | C5×D7×D13 |
| Fitting | C5×C7×C169 | C22 |
| socle | C5×C7×C13 | C2×D13 |
| LCS | G ▷ C7×C169 | |
| UCS | C1 ◁ C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5915 |
2150 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 22);