Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6758 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ M32 |
| Sylow | C5 ⋊ #812 |
| Sylow | C3 ⋊ #3990 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,5,3,4)(6,7,8)(9,11,13,20,14,12,19,21)(10,15,16,22,17,18,23,24);(2,3,4,5)(7,8)(9,10,12,15,13,16,21,22,14,17,11,18,19,23,20,24)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=d,d^2=e,b^a=be,f^a=f^2,g^a=g^3,g^c=g^460 conjugacy classes — view the full character table.
| maximal subgroup of | #11746452, #11746453, #11746464, … |
| maximal normal subgroup of | #11746452, #11746453, #11746464, … |
| maximal quotient of | #11746757, #11746758, #11746759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 295);