Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C4×C13×C61⋊C3 |
| unambiguous semidirect product | (C4×C61)⋊(C3×C13) |
| Fitting, Hall | C4×C13×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C4×C13 |
| Hall | C13×C61 ⋊ C3×C4 |
| Hall | C4×C61 ⋊ C3×C13 |
24 conjugacy classes of subgroups.
1196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C13⋊C3×C61⋊C3, Dic3×C13×C61⋊C3, C3×C4×C13×C61⋊C3 |
| maximal normal subgroup of | C4×C13⋊C3×C61⋊C3, C3×C4×C13×C61⋊C3 |
| maximal quotient of | C4×C13×C61⋊C9, Dic3×C13×C61⋊C3, C3×C4×C13×C61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 2);