Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C3×C7 |
| direct product | C2×C72×C3⋊D51 |
| unambiguous semidirect product | (C2×C3)⋊(C72×D51) |
| unambiguous semidirect product | (C2×C17)⋊(C72×C3⋊D3) |
| Fitting, socle | C2×C32×C72×C17 ⋊ C2 |
| derived, Hall | C32×C17 ⋊ C22×C72 |
| Hall | C32×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×C3⋊D3 |
| Hall | C32×C72 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×C72×C3⋊D3 |
| Sylow | C32 ⋊ C2×C72×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | C3⋊D51 |
| commutator, cosocle, hypocenter | C32×C17 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C72×C17 | C2 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C2×C72 | |
600 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14994 |
7644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 662);