Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×C7⋊#10587739 |
| Fitting, socle, Hall | C32×C7×C137 ⋊ C4 |
| derived, Hall | C7×C137 ⋊ C32×C4 |
| Hall | C32×C137 ⋊ Dic7 |
| Sylow | C137 ⋊ C32×Dic7 |
| Hall | C32×C7 ⋊ #10587739 |
| Sylow | C7 ⋊ C32×#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C7⋊#10587739 |
| commutator, hypocenter | C7×C137 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C137 | C4 |
| prime radical | C32×C7×D137 | C2 |
| cosocle | C7×D137 | C2×C32 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8631 |
2232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 88);