Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of S4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×C7×S4 |
| unambiguous semidirect product | A4⋊(C2×C32×C7) |
| Fitting, socle | C22×C32×C7 ⋊ D3 |
| derived | A4 ⋊ C2×C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | S4 |
| commutator, cosocle, hypocenter | A4 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C7 | D3 |
| LCS | G ▷ A4 | |
| UCS | C1 ◁ C32×C7 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
315 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 842);