Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A42 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C22×C33 |
| direct product | C9×A42 |
| Fitting | C24×C9 ⋊ C32 |
| derived, Sylow | C24 ⋊ C32×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | A42 |
| commutator, hypocenter | C24 | C32×C9 |
| Frattini | C3 | C3×A42 |
| Fitting | C24×C9 | C32 |
| socle, cosocle | C24×C3 | C33 |
| prime radical | C3×A42 | C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C9 | |
275 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72228707, A42×3−1+2, A4×(C22⋊A4)⋊C9, … |
| maximal normal subgroup of | #72228707, A42×3−1+2, C9×A4⋊S4, … |
| maximal quotient of | #72229281, A4×(C22⋊A4)⋊C9, C2×C9×A42, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2949);