Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D1681 |
| unambiguous semidirect product | C1681⋊(C2×C32) |
| Fitting, Hall | C32×C1681 ⋊ C2 |
| derived, Sylow | C1681 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D1681 |
| commutator, cosocle, hypocenter | C1681 | C2×C32 |
| Frattini | C41 | C32×D41 |
| Fitting | C32×C1681 | C2 |
| socle | C32×C41 | D41 |
| LCS | G ▷ C1681 | |
| UCS | C1 ◁ C32 | |
36 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, 6);