Finite Group DatabasebetaFinite Group Databasebeta| order | 936 |
| isoclinism | isoclinic class of A4×C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×A4×C13⋊C3 |
| unambiguous semidirect product | (C23×C13⋊C3)⋊C3 |
| unambiguous semidirect product | (C2×A4×C13)⋊C3 |
| unambiguous semidirect product | (C2×C22⋊(C13⋊C3))⋊C3 |
| Fitting, socle, Hall | C23×C13 ⋊ C32 |
| derived | C22×C13 ⋊ C2×C32 |
| Sylow | C13 ⋊ C2×C3×A4 |
| Sylow | C23 ⋊ C3×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×C13⋊C3 |
| commutator, cosocle, hypocenter | C22×C13 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C23×C13 | C32 |
| LCS | G ▷ C22×C13 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 78 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(936, 174);