Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| Fitting, socle, derived, Sylow | C312 ⋊ C22×C32 |
| Hall | C31⋊C32 ⋊ C22 |
| Hall | D312 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C312 | C22×C32 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
121 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 136);