Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6706 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C42×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ #104 |
| Sylow | C5 ⋊ #805 |
| 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)(6,7,8)(10,13,14,15);(2,3)(4,5)(7,8)(9,10)(11,13)(12,14)(15,16)Polycyclic presentation:
2^5,3,5|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^2,g^a=g^4126 conjugacy classes — view the full character table.
| maximal subgroup of | #11747016, #11747017, #11747018, … |
| maximal normal subgroup of | #11747016, #11747017, #11747018, … |
| maximal quotient of | #11746272, #11746273, #11746277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 165);