Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×#6923 |
| Fitting, socle, Hall | C3×C13×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C3×C4×C13 |
| Hall | C13×C61 ⋊ C3×C4 |
| Hall | C3×C61 ⋊ C4×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | #6923 |
| commutator, hypocenter | C61 | C3×C4×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C61 | C4 |
| prime radical | C3×C13×D61 | C2 |
| cosocle | D61 | C2×C3×C13 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C13 | |
24 conjugacy classes of subgroups.
741 conjugacy classes — view the full character table.
| maximal subgroup of | C13×#6923⋊C9, #43269663, #43269664, … |
| maximal normal subgroup of | C13×#6923⋊C9, #43269663, #43269664, … |
| maximal quotient of | C9×C13×#6923, C32×C13×#6923, C3×C13×C3⋊#6923 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 66);