Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #261×C61⋊C3 |
| Fitting, socle, derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | #261×C61 ⋊ C3 |
| Hall | C13×C61⋊C3 ⋊ C4 |
| Sylow | C61 ⋊ C3×#261 |
| Sylow | C13 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C3×C4 |
| prime radical | D13×C61⋊C3 | C2 |
| cosocle | D13×C61 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
161 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽13)×C61⋊C3, C3×#261×C61⋊C3, C3⋊#261×C61⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽13)×C61⋊C3, C3×#261×C61⋊C3 |
| maximal quotient of | #261×C61⋊C9, C3×#261×C61⋊C3, C3⋊#261×C61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 48);