Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#6923⋊C3 |
| unambiguous semidirect product | #6923⋊(C3×C13) |
| Fitting, socle, Hall | C13×C61 ⋊ C3×C4 |
| derived, Sylow | C61 ⋊ C3×C4×C13 |
| Hall | C13×#6923 ⋊ C3 |
| Hall | C13×C61⋊C3 ⋊ C4 |
| Hall | #6923 ⋊ C3×C13 |
| Hall | C61⋊C3 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #6923⋊C3 |
| commutator, hypocenter | C61 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C61 | C3×C4 |
| prime radical | C13×D61⋊C3 | C2 |
| cosocle | D61 | C2×C3×C13 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
221 conjugacy classes — view the full character table.
| maximal subgroup of | C13⋊C3×#6923⋊C3, C3×C13×#6923⋊C3, C13×C3⋊(#6923⋊C3) |
| maximal normal subgroup of | C13⋊C3×#6923⋊C3, C3×C13×#6923⋊C3 |
| maximal quotient of | C13×#6923⋊C9, C3×C13×#6923⋊C3, C13×C3⋊(#6923⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 26);