Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C4×#14558651 |
| Fitting, Hall | C4×C13×C61 ⋊ C3 |
| derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | C4×C61 ⋊ C13⋊C3 |
| Sylow | C61 ⋊ C4×C13⋊C3 |
| Hall | C4×C13 ⋊ C61⋊C3 |
| Sylow | C13 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #14558651 |
| commutator, hypocenter | C13×C61 | C3×C4 |
| Frattini | C2 | C2×#14558651 |
| Fitting | C4×C13×C61 | C3 |
| socle, cosocle | C2×C13×C61 | C2×C3 |
| prime radical | C2×#14558651 | C2 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
1068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C13⋊C3×C61⋊C3, Dic3×#14558651, C3×C4×#14558651 |
| maximal normal subgroup of | C4×C13⋊C3×C61⋊C3, C3×C4×#14558651 |
| maximal quotient of | C4×#20297357, Dic3×#14558651, C3×C4×#14558651 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 5);