Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6653 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #104 |
| Sylow | C5 ⋊ #825 |
| Sylow | C3 ⋊ #3937 |
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)(10,14,16,15);(2,3)(4,5)(6,7,8)(9,10,11,15,13,16,12,14)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=cd,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^4,f^b=f^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3937, #11747111, #11748068, … |
| maximal normal subgroup of | D3×#3937, #11747111, #11748068, … |
| maximal quotient of | #11745838, #11745844, #11745848, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 56);