Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊(C3⋊(C7⋊#595)) |
| unambiguous semidirect product | C3⋊(C7×C3⋊(C7⋊#595)) |
| unambiguous semidirect product | C7⋊(C7×C3⋊(C3⋊#595)) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived | C32×C7×C17 ⋊ C4×C7 |
| Hall | C72×C17 ⋊ C3⋊Dic3 |
| Hall | C32×C72 ⋊ #595 |
| Hall | C32×C17 ⋊ C7×Dic7 |
| Sylow | C72 ⋊ C3⋊(C3⋊#595) |
| Sylow | C17 ⋊ C7×C3⋊Dic21 |
| Sylow | C32 ⋊ C7×C7⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C3⋊(C7⋊#595)) |
| commutator, hypocenter | C32×C7×C17 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C32×C72×D17 | C2 |
| cosocle | C32×C7×D17 | C2×C7 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 ◁ C7 | |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2142 |
2226 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 624);