Finite Group DatabasebetaFinite Group Databasebeta| order | 30690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C32×ΓL(1,𝔽32)⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | ΓL(1,𝔽32)⋊D11 |
| commutator, cosocle, hypocenter | C11×C31 | C2×C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C31 | C2×C5 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C32 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
612 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30690, 162);