Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #595×#3861 |
| Fitting, socle, derived, Hall | C72×C17 ⋊ C3×C4 |
| Hall | C72×#595 ⋊ C3 |
| Hall | C17×#3861 ⋊ C4 |
| Sylow | C72 ⋊ C3×#595 |
| Sylow | C17 ⋊ C4×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C17 | C3×C4 |
| prime radical | D17×#3861 | C2 |
| cosocle | C72×D17 | C2×C3 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
152 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)2×#595, C3×#595×#3861, #3861×C3⋊#595 |
| maximal normal subgroup of | ΓL(1,𝔽8)2×#595, C3×#595×#3861 |
| maximal quotient of | #595×#89204, C3×#595×#3861, #3861×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 99);