Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D1071 |
| unambiguous semidirect product | (C7×D7)⋊D153 |
| unambiguous semidirect product | (C9×D7)⋊D119 |
| unambiguous semidirect product | (D7×C17)⋊D63 |
| Fitting, derived, Hall | C72×C9×C17 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D9 |
| Hall | C72×C9 ⋊ C2×D17 |
| Hall | C9×C17 ⋊ D72 |
| Sylow | C72 ⋊ C2×D153 |
| Sylow | C17 ⋊ D7×D63 |
| Sylow | C9 ⋊ D7×D119 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C72×C9×C17 | C22 |
| Frattini | C3 | D7×D357 |
| socle | C3×C72×C17 | C2×D3 |
| LCS | G ▷ C72×C9×C17 | |
| UCS | C1 | |
156 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2142 |
2685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 248);