Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×C17⋊#11725071 |
| unambiguous semidirect product | (C2×C17)⋊#11725071 |
| derived, Hall | C17×#89205 ⋊ C22 |
| Hall | C72×C17 ⋊ C2×D9 |
| Hall | #89205 ⋊ C2×D17 |
| Sylow | C72 ⋊ C2×D153 |
| Sylow | C17 ⋊ C2×#11725071 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C17⋊#11725071 |
| commutator, cosocle, hypocenter | C17×#89205 | C22 |
| Frattini | C3 | C2×C17⋊#64418 |
| Fitting, socle | C2×C3×C72×C17 | D3 |
| LCS | G ▷ C17×#89205 | |
| UCS | C1 ◁ C2 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
990 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 221);