Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#15691760 |
| Fitting, socle, derived, Hall | C3×C13×C61 ⋊ C4 |
| Hall | C13×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ #261 |
| Sylow | C61 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic61 |
| Sylow | C13 ⋊ Dic183 |
| Sylow | C3 ⋊ #15691760 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C61 | C4 |
| prime radical, cosocle | C3×D13×C61 | C2 |
| LCS | G ▷ C3×C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,13,61|a^2=b,c^a=c^2,d^a=d^5,e^a=e^60,d^b=d^12735 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#15691760, C3⋊#23748923, C3⋊#23748924, … |
| maximal normal subgroup of | C3⋊#23748923, C3⋊#23748924, C3⋊#23748929, … |
| maximal quotient of | C9⋊#15691760, C3×C3⋊#15691760, C3⋊(C3⋊#15691760) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 78);