Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#64422⋊C2 |
| unambiguous semidirect product | #64422⋊(C2×C17) |
| Fitting, socle, Hall | C72×C17 ⋊ C22×C3 |
| derived, Sylow | C72 ⋊ C22×C3×C17 |
| Hall | D72×C17 ⋊ C3 |
| Hall | C17×#3862 ⋊ C22 |
| Hall | D72 ⋊ C3×C17 |
| Hall | #3862 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #64422⋊C2 |
| commutator, cosocle, hypocenter | C72 | C22×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C17 | |
84 conjugacy classes of subgroups.
323 conjugacy classes — view the full character table.
| maximal subgroup of | C17×AGL(1,𝔽7)2, C3×C17×#64422⋊C2, C17×#64422⋊D3, … |
| maximal normal subgroup of | C17×AGL(1,𝔽7)2, C3×C17×#64422⋊C2 |
| maximal quotient of | C17×#11725075⋊C2, C3×C17×#64422⋊C2, C17×#64422⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 86);