Finite Group DatabasebetaFinite Group Databasebeta| order | 1584 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 9676800 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26×C3 |
| abelian | C24×C32×C11 |
| multiplicative | (ℤ/3752)ˣ, (ℤ/4824)ˣ, (ℤ/5628)ˣ, (ℤ/5796)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
804 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 1584 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(9,10,11)(15,16,17,18,19,20,21,22,23,24,25);(3,4)(12,13,14);(5,6);(7,8)1584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1584, 697);