Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of A42 |
| automorphism | ? |
| homology | Abelianization (H1) = C92 · Schur multiplier (H2) = C22×C9 |
| direct product | C22⋊C92 |
| derived, Sylow | C24 ⋊ C92 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | A42 |
| commutator, hypocenter | C24 | C92 |
| Fitting, socle, prime radical, cosocle | C24×C32 | C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C32 | |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1795);