Finite Group DatabasebetaFinite Group Databasebeta| order | 9516 |
| isoclinism | isoclinic class of C22⋊(C13⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C61 · Schur multiplier (H2) = C2 |
| direct product | C61×C22⋊(C13⋊C3) |
| unambiguous semidirect product | C22⋊(C13⋊C3×C61) |
| unambiguous semidirect product | C13⋊(A4×C61) |
| Fitting, socle, Hall | C22×C13×C61 ⋊ C3 |
| derived, Hall | C22×C13 ⋊ C3×C61 |
| Hall | C13×C61 ⋊ A4 |
| Hall | C22×C61 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ A4×C61 |
| Sylow | C22 ⋊ C13⋊C3×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C22⋊(C13⋊C3) |
| commutator, cosocle, hypocenter | C22×C13 | C3×C61 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13×C61 | C3 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C61 | |
20 conjugacy classes of subgroups.
1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9516, 87);