Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D959 |
| unambiguous semidirect product | (C2×C137)⋊(C32×D7) |
| Fitting, socle | C2×C32×C7×C137 ⋊ C2 |
| derived, Hall | C7×C137 ⋊ C22×C32 |
| Hall | C32×C7×C137 ⋊ C22 |
| Hall | C32×C137 ⋊ C2×D7 |
| Sylow | C137 ⋊ C2×C32×D7 |
| Hall | C32×C7 ⋊ C2×D137 |
| Sylow | C7 ⋊ C2×C32×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D959 |
| commutator, cosocle, hypocenter | C7×C137 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C7×C137 | C2 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17262 |
8658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 121);