Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #101 |
| Sylow | C5 ⋊ #836 |
| Sylow | C3 ⋊ #3968 |
76 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)(9,11,13,19)(10,14,16,17)(12,20,21,18)(15,23,24,22);(2,3)(4,5)(7,8)(9,10,12,15,13,16,21,24)(11,17,18,23,19,14,20,22)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,c^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^4,c^b=ce81 conjugacy classes — view the full character table.
| maximal subgroup of | #11746012, #11746013, #11746015, … |
| maximal normal subgroup of | #11746012, #11746013, #11746015, … |
| maximal quotient of | #11746349, #11746351, #11746364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 196);