Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C13⋊C3×#6923 |
| Fitting, socle, derived, Hall | C13×C61 ⋊ C3×C4 |
| Hall | C13×#6923 ⋊ C3 |
| Hall | C13⋊C3×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×C13⋊C3 |
| Sylow | C13 ⋊ C3×#6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C61 | C3×C4 |
| prime radical | C13⋊C3×D61 | C2 |
| cosocle | C13×D61 | C2×C3 |
| LCS | G ▷ C13×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
133 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#6923⋊C3, C3×C13⋊C3×#6923, C13⋊C3×C3⋊#6923 |
| maximal normal subgroup of | C13⋊C3×#6923⋊C3, C3×C13⋊C3×#6923 |
| maximal quotient of | C13⋊C9×#6923, C3×C13⋊C3×#6923, C13⋊C3×C3⋊#6923 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 51);