Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1919877120 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210×C3 |
| abelian | C25×C32×C5 |
| multiplicative | (ℤ/5208)ˣ, (ℤ/5544)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
4488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 5 generators on 21 points:
(1,2)(11,12,13)(17,18,19,20,21);(3,4)(14,15,16);(5,6);(7,8);(9,10)1440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5958);