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 ⋊ #3967 |
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)(13,14,16,18)(15,19,20,17);(2,3)(4,5)(6,7,8)(9,10,11,12)(13,14,15,17,16,18,20,19)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,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 | #11746884, #11746907, #11746909, … |
| maximal normal subgroup of | #11746884, #11746907, #11746909, … |
| maximal quotient of | #11745843, #11745858, #11745862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 49);