Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic61⋊C3 |
| unambiguous semidirect product | Dic61⋊(C3×C13) |
| derived, Sylow | C61 ⋊ C3×C4×C13 |
| Hall | C13×Dic61 ⋊ C3 |
| Hall | C13×C61⋊C3 ⋊ C4 |
| Hall | C13×C61 ⋊ C3×C4 |
| Hall | Dic61 ⋊ C3×C13 |
| Hall | C61⋊C3 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D61⋊C3 |
| commutator, hypocenter | C61 | C3×C4×C13 |
| Frattini | C2 | C13×D61⋊C3 |
| Fitting, socle | C2×C13×C61 | C2×C3 |
| prime radical | C2×C13×C61⋊C3 | C2 |
| cosocle | C2×C61 | C2×C3×C13 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×Dic61⋊C3, C3×C13×Dic61⋊C3, C13×C3⋊(Dic61⋊C3) |
| maximal normal subgroup of | C13⋊C3×Dic61⋊C3, C3×C13×Dic61⋊C3 |
| maximal quotient of | C13×Dic61⋊C9, C3×C13×Dic61⋊C3, C13×C3⋊(Dic61⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 13);