Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C7 · Schur multiplier (H2) = C2×C33 |
| direct product | C2×C32×C7×A4 |
| Fitting, socle | C23×C32×C7 ⋊ C3 |
| derived | C22 ⋊ C2×C33×C7 |
| Hall | C23×C7 ⋊ C33 |
| Sylow | C23 ⋊ C33×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C7 | A4 |
| commutator, cosocle, hypocenter | C22 | C2×C33×C7 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32×C7 | C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C32×C7 | |
272 conjugacy classes of subgroups.
| transitive degree | μt(G) = 378 |
504 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 880);