Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×C7⋊#595 |
| derived, Hall | C72×C17 ⋊ C4×C9 |
| Hall | C7×C17×C7⋊C9 ⋊ C4 |
| Hall | C7×C7⋊#595 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ #595 |
| Sylow | C72 ⋊ C9×#595 |
| Sylow | C17 ⋊ Dic7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×C7⋊#595 |
| commutator, hypocenter | C72×C17 | C4×C9 |
| Fitting, socle | C3×C72×C17 | C3×C4 |
| prime radical, cosocle | C3×C72×D17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
570 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 190);