Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×(C3⋊D3)⋊D17 |
| unambiguous semidirect product | (C3⋊D3)⋊(C72×D17) |
| unambiguous semidirect product | D51⋊(D3×C72) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C22 |
| derived, Hall | C32×C17 ⋊ C22×C72 |
| Hall | C72×C17 ⋊ D32 |
| Hall | C32×C72 ⋊ C2×D17 |
| Sylow | C17 ⋊ D32×C72 |
| Sylow | C32 ⋊ C2×C72×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | (C3⋊D3)⋊D17 |
| commutator, cosocle, hypocenter | C32×C17 | C22×C72 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C22 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C72 | |
440 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4998 |
2793 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 597);