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 ⋊ #824 |
| Sylow | C3 ⋊ #3956 |
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)(7,8)(9,11,17,18,13,19,12,20)(10,14,15,23,16,22,24,21);(2,3)(4,5)(6,7,8)(9,10,12,15,13,16,17,24)(11,14,18,21,19,22,20,23)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=cde,c^2=e,b^a=bd,d^a=de,g^a=g^4,c^b=ce,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747124, #11747125, #11748085, … |
| maximal normal subgroup of | #11747124, #11747125, #11748085, … |
| maximal quotient of | #11745851, #11745859, #11745860, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 39);