Finite Group DatabasebetaFinite Group Databasebeta| order | 30972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D2581 |
| unambiguous semidirect product | (C2×C29)⋊(C3×D89) |
| unambiguous semidirect product | (C2×C89)⋊(C3×D29) |
| Fitting, socle | C2×C3×C29×C89 ⋊ C2 |
| derived, Hall | C29×C89 ⋊ C22×C3 |
| Hall | C3×C29×C89 ⋊ C22 |
| Hall | C3×C89 ⋊ C2×D29 |
| Sylow | C89 ⋊ C2×C3×D29 |
| Hall | C3×C29 ⋊ C2×D89 |
| Sylow | C29 ⋊ C2×C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D2581 |
| commutator, cosocle, hypocenter | C29×C89 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C29×C89 | C2 |
| LCS | G ▷ C29×C89 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15486 |
7752 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30972, 32);