Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | C3×#16809725 |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C4 |
| derived, Hall | C72×C17 ⋊ C3×C4 |
| Hall | C3×C72 ⋊ #595 |
| Hall | C3×C17 ⋊ #5997 |
| Sylow | C72 ⋊ C3×#595 |
| Sylow | C17 ⋊ C3×#5997 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809725 |
| commutator, hypocenter | C72×C17 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C4 |
| prime radical | C3×C7⋊D119 | C2 |
| cosocle | C7⋊D119 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
56 conjugacy classes of subgroups.
636 conjugacy classes — view the full character table.
| maximal subgroup of | #16809725⋊C9, C9×#16809725, C3×#23756206, … |
| maximal normal subgroup of | #16809725⋊C9, C9×#16809725, C3×#16809725⋊C3, … |
| maximal quotient of | C9×#16809725, C32×#16809725, C3×C3⋊#16809725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 142);