Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×D119 |
| Fitting, socle, Hall | C3×C72×C17 ⋊ C22 |
| derived, Hall | C72×C17 ⋊ C22×C3 |
| Hall | C3×C72 ⋊ C2×D17 |
| Hall | C3×C17 ⋊ D72 |
| Sylow | C72 ⋊ C2×C3×D17 |
| Sylow | C17 ⋊ C3×D72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×D119 |
| commutator, cosocle, hypocenter | C72×C17 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C17 | C22 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
915 conjugacy classes — view the full character table.
| maximal subgroup of | #11725076⋊D17, #11725075⋊D17, D7⋊C9×D119, … |
| maximal normal subgroup of | #11725076⋊D17, #11725075⋊D17, D7⋊C9×D119, … |
| maximal quotient of | C9×D7×D119, C32×D7×D119, C3×D7×D357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 139);