Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| isoclinism | isoclinic class of D61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2 |
| Fitting, socle | C2×C13×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C22×C3×C13 |
| Hall | C2×C13×D61 ⋊ C3 |
| Hall | C13×C61⋊C3 ⋊ C22 |
| Hall | C13×C61 ⋊ C22×C3 |
| Hall | C2×D61 ⋊ C3×C13 |
| Hall | C61⋊C3 ⋊ C22×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C22×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C13 | |
40 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C13⋊C3×D61⋊C3, D3×C13×D61⋊C3, C2×C3×C13×D61⋊C3, … |
| maximal normal subgroup of | C2×C13⋊C3×D61⋊C3, C2×C3×C13×D61⋊C3 |
| maximal quotient of | C2×C13×D61⋊C9, D3×C13×D61⋊C3, C2×C3×C13×D61⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 54);