Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C3×#261×C61 |
| Fitting, socle, Hall | C3×C13×C61 ⋊ C4 |
| derived, Sylow | C13 ⋊ C3×C4×C61 |
| Hall | C13×C61 ⋊ C3×C4 |
| Hall | C3×C13 ⋊ C4×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C61 | #261 |
| commutator, hypocenter | C13 | C3×C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C61 | C4 |
| prime radical | C3×D13×C61 | C2 |
| cosocle | D13 | C2×C3×C61 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C61 | |
24 conjugacy classes of subgroups.
1281 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C61×#261⋊C9, #43269650, #43269651, … |
| maximal normal subgroup of | C61×#261⋊C9, #43269650, #43269651, … |
| maximal quotient of | C9×#261×C61, C32×#261×C61, C3×C61×C3⋊#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 67);