Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C72 · Schur multiplier (H2) = C2×C7 |
| direct product | C2×C3×C72×D51 |
| unambiguous semidirect product | (C2×C3)⋊(C3×C72×D17) |
| unambiguous semidirect product | (C2×C17)⋊(C3×D3×C72) |
| Fitting, socle | C2×C32×C72×C17 ⋊ C2 |
| derived | C3×C17 ⋊ C22×C3×C72 |
| Hall | C32×C72×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×C3×D3 |
| Hall | C32×C72 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C22×C72 |
| Sylow | C17 ⋊ C2×C3×D3×C72 |
| Sylow | C32 ⋊ C2×C72×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C72 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C22×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C72×C17 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C3×C72 | |
440 conjugacy classes of subgroups; only the 220 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 220 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9996 |
7938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 656);