Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of A6 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C4×A6 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C4 | A6 |
| commutator, hypocenter | A6 | C4 |
| Frattini, cosocle | C2 | C2×A6 |
| socle, prime radical | C2×A6 | C2 |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C4 | |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
28 conjugacy classes — view the full character table.
| maximal subgroup of | #72209929, #72210859, #72224450, … |
| maximal normal subgroup of | #72210859, #72224450, #72224453, … |
| maximal quotient of | #72210857, C4×SL(2,𝔽9), Dic5×A6, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4596);