Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C31 |
| direct product | C2×C3×C3⋊(C31⋊D31) |
| unambiguous semidirect product | (C2×C3)⋊(C3×C31⋊D31) |
| Fitting, socle | C2×C32×C312 ⋊ C2 |
| derived | C3×C312 ⋊ C22×C3 |
| Hall | C32×C312 ⋊ C22 |
| Sylow | C312 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×C31⋊D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C3⋊(C31⋊D31) |
| commutator, cosocle, hypocenter | C3×C312 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C312 | C2 |
| LCS | G ▷ C3×C312 | |
| UCS | C1 ◁ C2×C3 | |
748 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11532 |
8658 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 225);