Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic959 |
| derived, Hall | C7×C137 ⋊ C4×C9 |
| Hall | C7×C9×C137 ⋊ C4 |
| Hall | C9×C137 ⋊ Dic7 |
| Sylow | C137 ⋊ C9×Dic7 |
| Hall | C7×C9 ⋊ Dic137 |
| Sylow | C7 ⋊ C9×Dic137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D959 |
| commutator, hypocenter | C7×C137 | C4×C9 |
| Frattini | C2×C3 | C3×D959 |
| Fitting | C2×C7×C9×C137 | C2 |
| socle, prime radical, cosocle | C2×C3×C7×C137 | C2×C3 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C2×C9 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34524 |
8658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 5);