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 ⋊ #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)(9,11,12,18,13,19,21,24)(10,14,15,22,16,17,20,23);(2,3)(4,5)(6,7,8)(9,10,13,16)(11,17,19,14)(12,20,21,15)(18,22,24,23)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,g^a=g^4,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747120, #11747121, #11748083, … |
| maximal normal subgroup of | #11747120, #11747121, #11748083, … |
| maximal quotient of | #11745849, #11745855, #11745856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 37);