Finite Group DatabasebetaFinite Group Databasebeta| order | 30258 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C41 |
| direct product | C3×(C41⋊D41)⋊C3 |
| unambiguous semidirect product | (C41⋊D41)⋊C32 |
| unambiguous semidirect product | (C3×C41⋊D41)⋊C3 |
| Fitting, socle | C3×C412 ⋊ C2×C3 |
| derived, Sylow | C412 ⋊ C2×C32 |
| Hall | C3×C412⋊C3 ⋊ C2 |
| Hall | C41⋊D41 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C41⋊D41)⋊C3 |
| commutator, cosocle, hypocenter | C412 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C412 | C2×C3 |
| LCS | G ▷ C412 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 369 |
858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30258, 22);