Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ #926 |
| Sylow | C3 ⋊ #4018 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(13,15,16,19)(14,18,17,20);(7,8)(9,10,11,12)(14,17)(18,20);(2,3)(4,5)(13,14)(15,18)(16,17)(19,20)Polycyclic presentation:
2^5,3,5|b^2=d,c^2=e,b^a=be,g^a=g^4,f^b=f^284 conjugacy classes — view the full character table.
| maximal subgroup of | #11746518, #11746520, #11747645, … |
| maximal normal subgroup of | #11746518, #11746520, #11747645, … |
| maximal quotient of | #11746868, #11746870, #11746872, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 433);