Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3×C7 |
| direct product | C32×C7⋊(C7⋊#595) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived, Hall | C72×C17 ⋊ C32×C4 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7⋊Dic7 |
| Sylow | C72 ⋊ C32×#595 |
| Sylow | C17 ⋊ C32×C7⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C7⋊(C7⋊#595) |
| commutator, hypocenter | C72×C17 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C32×C72×D17 | C2 |
| cosocle | C72×D17 | C2×C32 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C32 | |
360 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7497 |
2232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 569);