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 ⋊ #100 |
| Sylow | C5 ⋊ #823 |
| Sylow | C3 ⋊ #3955 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,4,5,3)(7,8)(9,11,12,15,13,14,16,10);(2,3)(4,5)(6,7,8)(9,10,12,14,13,15,16,11)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=cd,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 | #11747118, #11747119, #11748082, … |
| maximal normal subgroup of | #11747118, #11747119, #11748082, … |
| maximal quotient of | #11745848, #11745854, #11745863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 36);