Finite Group DatabasebetaFinite Group Databasebeta| order | 15134 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1081 |
| unambiguous semidirect product | C23⋊(C7×D47) |
| unambiguous semidirect product | C47⋊(C7×D23) |
| Fitting, socle, Hall | C7×C23×C47 ⋊ C2 |
| derived, Hall | C23×C47 ⋊ C2×C7 |
| Hall | C7×C47 ⋊ D23 |
| Hall | C7×C23 ⋊ D47 |
| Sylow | C47 ⋊ C7×D23 |
| Sylow | C23 ⋊ C7×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1081 |
| commutator, cosocle, hypocenter | C23×C47 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C47 | C2 |
| LCS | G ▷ C23×C47 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7567 |
3794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D23×D47, D7×D1081, D161⋊D47, … |
| maximal normal subgroup of | C7×D23×D47, D7×D1081, D161⋊D47, … |
| maximal quotient of | C7×Dic1081, C2×C7×D1081 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15134, 5);