Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| direct product | C9×C7⋊(C7⋊#595) |
| Fitting, Hall | C72×C9×C17 ⋊ C4 |
| derived, Hall | C72×C17 ⋊ C4×C9 |
| Hall | C72×C9 ⋊ #595 |
| Hall | C9×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C9×#595 |
| Sylow | C17 ⋊ C9×C7⋊Dic7 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
2232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 225);