Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #104 |
| Sylow | C5 ⋊ #805 |
| Sylow | C3 ⋊ #3957 |
88 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)(9,10,11,15,12,14,16,13);(2,3)(4,5)(6,7,8)(10,13,14,15)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=cd,d^2=e,b^a=bd,g^a=g^4,c^b=ce,d^b=de,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#805, #11747109, #11748064, … |
| maximal normal subgroup of | D5×#805, #11747109, #11748064, … |
| maximal quotient of | #11745839, #11745845, #11745848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 57);