Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #595×C49⋊C3 |
| unambiguous semidirect product | (C49×#595)⋊C3 |
| Fitting, derived, Hall | C17×C49 ⋊ C3×C4 |
| Hall | C49×#595 ⋊ C3 |
| Hall | C17×C49⋊C3 ⋊ C4 |
| Sylow | C49 ⋊ C3×#595 |
| Sylow | C17 ⋊ C4×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C17×C49 | C3×C4 |
| Frattini | C7 | ΓL(1,𝔽8)×#595 |
| socle | C7×C17 | C4×ΓL(1,𝔽8) |
| prime radical | D17×C49⋊C3 | C2 |
| cosocle | D17×C49 | C2×C3 |
| LCS | G ▷ C17×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
152 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#595×C49⋊C3, C49⋊C3×C3⋊#595 |
| maximal normal subgroup of | C3×#595×C49⋊C3 |
| maximal quotient of | #595×C49⋊C9, C3×#595×C49⋊C3, C49⋊C3×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 14);