Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C3 |
| direct product | C7×C17×C3⋊Dic21 |
| unambiguous semidirect product | C3⋊(C7×C17×Dic21) |
| unambiguous semidirect product | C7⋊(C7×C17×C3⋊Dic3) |
| derived | C32×C7 ⋊ C4×C7×C17 |
| Hall | C32×C72×C17 ⋊ C4 |
| Hall | C72×C17 ⋊ C3⋊Dic3 |
| Hall | C32×C72 ⋊ C4×C17 |
| Hall | C32×C17 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C17×C3⋊Dic3 |
| Sylow | C32 ⋊ C7×C17×Dic7 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4284 |
7854 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 331);