Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C41 |
| direct product | C32×C41⋊D41 |
| unambiguous semidirect product | C41⋊(C32×D41) |
| Fitting, socle, Hall | C32×C412 ⋊ C2 |
| derived, Sylow | C412 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C41⋊D41 |
| commutator, cosocle, hypocenter | C412 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C412 | C2 |
| LCS | G ▷ C412 | |
| UCS | C1 ◁ C32 | |
528 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15129 |
7578 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30258, 28);