Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C7 |
| direct product | Dic17×#3862 |
| derived, Hall | C72×C17 ⋊ C3×C4 |
| Hall | C72×Dic17 ⋊ C3 |
| Hall | C17×#3862 ⋊ C4 |
| Sylow | C72 ⋊ C3×Dic17 |
| Sylow | C17 ⋊ C4×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D17×#3862 |
| commutator, hypocenter | C72×C17 | C3×C4 |
| Fitting, socle, cosocle | C2×C72×C17 | C2×C3 |
| prime radical | C2×C17×#3862 | C2 |
| LCS | G ▷ C72×C17 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)2×Dic17, C3×Dic17×#3862, #3862×Dic51 |
| maximal normal subgroup of | ΓL(1,𝔽8)2×Dic17, C3×Dic17×#3862 |
| maximal quotient of | Dic17×#89205, C3×Dic17×#3862, #3862×Dic51 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 56);