Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D49⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C17 · Schur multiplier (H2) = C2 |
| Fitting | C2×C17×C49 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C22×C3×C17 |
| Hall | C2×C17×D49 ⋊ C3 |
| Hall | C17×C49⋊C3 ⋊ C22 |
| Hall | C17×C49 ⋊ C22×C3 |
| Hall | C2×D49 ⋊ C3×C17 |
| Hall | C49⋊C3 ⋊ C22×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C22×C3×C17 |
| Frattini | C7 | C2×C17×AGL(1,𝔽7) |
| Fitting | C2×C17×C49 | C2×C3 |
| socle | C2×C7×C17 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C2×C17 | |
60 conjugacy classes of subgroups.
476 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C17×D49⋊C3, C2×C3×C17×D49⋊C3, C2×C17×C3⋊(D49⋊C3) |
| maximal normal subgroup of | C2×C3×C17×D49⋊C3 |
| maximal quotient of | C2×C17×D49⋊C9, D3×C17×D49⋊C3, C2×C3×C17×D49⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 18);