Finite Group DatabasebetaFinite Group Databasebeta| order | 23380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D1169 |
| unambiguous semidirect product | (C2×C7)⋊(C5×D167) |
| unambiguous semidirect product | (C2×C167)⋊(C5×D7) |
| Fitting, socle | C2×C5×C7×C167 ⋊ C2 |
| derived, Hall | C7×C167 ⋊ C22×C5 |
| Hall | C5×C7×C167 ⋊ C22 |
| Hall | C5×C167 ⋊ C2×D7 |
| Sylow | C167 ⋊ C2×C5×D7 |
| Hall | C5×C7 ⋊ C2×D167 |
| Sylow | C7 ⋊ C2×C5×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D1169 |
| commutator, cosocle, hypocenter | C7×C167 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C167 | C2 |
| LCS | G ▷ C7×C167 | |
| UCS | C1 ◁ C2×C5 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11690 |
5860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23380, 23);