Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C7 |
| direct product | C9×#16809726 |
| Fitting, Hall | C72×C9×C17 ⋊ C4 |
| derived, Hall | C72×C17 ⋊ C4×C9 |
| Hall | C72×C9 ⋊ Dic17 |
| Hall | C9×C17 ⋊ #5997 |
| Sylow | C72 ⋊ C9×Dic17 |
| Sylow | C17 ⋊ C9×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #16809726 |
| commutator, hypocenter | C72×C17 | C4×C9 |
| Frattini | C3 | C3×#16809726 |
| Fitting | C72×C9×C17 | C4 |
| socle | C3×C72×C17 | C3×C4 |
| prime radical, cosocle | C3×C17×C7⋊D7 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C9 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
2016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 232);