Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D21×D51 |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C22 |
| derived | C32×C7×C17 ⋊ C22×C7 |
| Hall | C72×C17 ⋊ D32 |
| Hall | C32×C72 ⋊ C2×D17 |
| Hall | C32×C17 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ D3×D51 |
| Sylow | C17 ⋊ D3×C7×D21 |
| Sylow | C32 ⋊ C7×D7×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D21×D51 |
| commutator, cosocle, hypocenter | C32×C7×C17 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C22 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 ◁ C7 | |
230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1428 |
2268 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 601);