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 ⋊ #103 |
| Sylow | C5 ⋊ #816 |
| Sylow | C3 ⋊ #3942 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,5,3)(7,8)(9,11,12,10)(14,17)(15,19)(18,20);(2,3)(4,5)(6,7,8)(9,10,12,11)(13,14,15,17,16,18,19,20)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=de,c^2=e,b^a=bcd,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11746913, #11746914, #11746930, … |
| maximal normal subgroup of | #11746913, #11746914, #11746930, … |
| maximal quotient of | #11745845, #11745860, #11745863, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 51);