Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C3 |
| direct product | C41×C3⋊D123 |
| unambiguous semidirect product | C3⋊(C41×D123) |
| unambiguous semidirect product | C41⋊(C3⋊D3×C41) |
| Fitting, socle, Hall | C32×C412 ⋊ C2 |
| derived | C32×C41 ⋊ C2×C41 |
| Sylow | C412 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ C41×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C3⋊D123 |
| commutator, cosocle, hypocenter | C32×C41 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C412 | C2 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C41 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 738 |
7626 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30258, 33);