Finite Group DatabasebetaFinite Group Databasebeta| order | 29988 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×C3⋊#16809726 |
| unambiguous semidirect product | C3⋊(C3×#16809726) |
| Fitting, socle, Hall | C32×C72×C17 ⋊ C4 |
| derived | C3×C72×C17 ⋊ C3×C4 |
| Hall | C72×C17 ⋊ C3×Dic3 |
| Hall | C32×C72 ⋊ Dic17 |
| Hall | C32×C17 ⋊ #5997 |
| Sylow | C72 ⋊ C3×Dic51 |
| Sylow | C17 ⋊ C3×C3⋊#5997 |
| Sylow | C32 ⋊ #16809726 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#16809726 |
| commutator, hypocenter | C3×C72×C17 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C72×C17 | C4 |
| prime radical | C32×C17×C7⋊D7 | C2 |
| cosocle | C3×C17×C7⋊D7 | C2×C3 |
| LCS | G ▷ C3×C72×C17 | |
| UCS | C1 ◁ C3 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 714 |
1998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29988, 573);