Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×C5×#95 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C32×C5 | C22 |
| commutator | C2 | C32×C42×C5 |
| Frattini, cosocle | C23 | C22×C32×C5 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C32×C5 ◁ G | |
456 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(7,8,9,10,11)(17,19)(20,21,23,22);(4,5,6)(12,13,14,15)(16,17,18,19)(20,22,23,21)900 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1438);