Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C4×C31⋊C32 |
| unambiguous semidirect product | (C4×C31×C31⋊C3)⋊C3 |
| unambiguous semidirect product | (C4×#15668332)⋊C3 |
| unambiguous semidirect product | (C4×#15668333)⋊C3 |
| Fitting, Hall | C4×C312 ⋊ C32 |
| derived, Sylow | C312 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | C31⋊C32 |
| commutator, hypocenter | C312 | C32×C4 |
| Frattini | C2 | C2×C31⋊C32 |
| Fitting | C4×C312 | C32 |
| socle, cosocle | C2×C312 | C2×C32 |
| prime radical | C2×C31⋊C32 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C4 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 372 |
676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 102);