Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ #108 |
| Sylow | C5 ⋊ #819 |
| Sylow | C3 ⋊ #3951 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,5,3)(6,7,8)(9,11,13,20,14,21,12,19)(10,15,16,18,17,23,22,24);(2,3)(4,5)(7,8)(9,10,12,16,14,17,13,22)(11,18,19,23,21,24,20,15)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #11745904, #11745906, #11745916, … |
| maximal normal subgroup of | #11745904, #11745906, #11745916, … |
| maximal quotient of | #11746278, #11746279, #11746373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 179);