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 ⋊ #833 |
| 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)(9,10,11,14,12,13,15,16);(2,3)(4,5)(6,7,8)(10,13)(11,15)Polycyclic presentation:
2^5,3,5|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 | #11747114, #11747115, #11748083, … |
| maximal normal subgroup of | #11747114, #11747115, #11748083, … |
| maximal quotient of | #11745846, #11745852, #11745861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 34);