Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C27 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×C22⋊C27 |
| derived | C22 ⋊ C2×C7×C27 |
| Hall | C23×C7 ⋊ C27 |
| Sylow | C23 ⋊ C7×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7×C9 | A4 |
| commutator, hypocenter | C22 | C2×C7×C27 |
| Frattini | C9 | C2×C7×A4 |
| Fitting | C23×C7×C9 | C3 |
| socle, prime radical | C23×C3×C7 | C9 |
| cosocle | C22×C9 | C2×C3×C7 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C2×C7×C9 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 40 |
| 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, 91);