Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 516096 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C4×C5×C9 |
| multiplicative | (ℤ/3135)ˣ, (ℤ/3256)ˣ, (ℤ/3344)ˣ, (ℤ/3800)ˣ, (ℤ/4180)ˣ, (ℤ/4344)ˣ, (ℤ/4752)ˣ, (ℤ/4884)ˣ, (ℤ/5400)ˣ, (ℤ/5700)ˣ, (ℤ/5940)ˣ, (ℤ/6270)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2×C3 | C24×C3×C5 |
| socle, prime radical | C24×C3×C5 | C2×C3 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
708 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4)(11,12,13,14,15,16,17,18,19)(20,21,22,23,24);(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, 1676);