Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C3×C7 |
| direct product | C17×#13183676 |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived, Hall | C32×C72 ⋊ C4×C17 |
| Hall | C72×C17 ⋊ #157 |
| Hall | C32×C17 ⋊ #5997 |
| Sylow | C72 ⋊ C17×#157 |
| Sylow | C32 ⋊ C17×#5997 |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
1938 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 548);