Finite Group DatabasebetaFinite Group Databasebeta| order | 30654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| Fitting, socle, Hall | C32×C131 ⋊ C2×C13 |
| derived, Sylow | C131 ⋊ C2×C32×C13 |
| Hall | C32×C131⋊C13 ⋊ C2 |
| Hall | C32×D131 ⋊ C13 |
| Hall | C131⋊C13 ⋊ C2×C32 |
| Hall | D131 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D131⋊C13 |
| commutator, cosocle, hypocenter | C131 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C131 | C2×C13 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1179 |
279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30654, 18);