Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#15691758 |
| Fitting, socle, Hall | C3×C13×C61 ⋊ C4 |
| derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | C3×C61 ⋊ #261 |
| Sylow | C61 ⋊ C3×#261 |
| Hall | C3×C13 ⋊ #6923 |
| Sylow | C13 ⋊ C3×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #15691758 |
| commutator, hypocenter | C13×C61 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C61 | C4 |
| prime radical | C3×D793 | C2 |
| cosocle | D793 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
606 conjugacy classes — view the full character table.
| maximal subgroup of | #43269642, #43269643, #43269648, … |
| maximal normal subgroup of | #43269642, #43269643, #43269648, … |
| maximal quotient of | C9×#15691758, C32×#15691758, C3×C3⋊#15691758 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 68);