Finite Group DatabasebetaFinite Group Databasebeta| order | 35334 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#26044501 |
| Fitting, socle | C3×C13×C151 ⋊ C2×C3 |
| derived, Hall | C13×C151 ⋊ C2×C32 |
| Hall | C3×#20238114 ⋊ C2 |
| Hall | D13×C151 ⋊ C32 |
| Sylow | C151 ⋊ C3×D13⋊C3 |
| Hall | D13 ⋊ C3×C151⋊C3 |
| Sylow | C13 ⋊ C2×C3×C151⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #26044501 |
| commutator, cosocle, hypocenter | C13×C151 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C151 | C2×C3 |
| LCS | G ▷ C13×C151 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5889 |
1224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35334, 35);