Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #6715 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #106 |
| Sylow | C5 ⋊ #808 |
| Sylow | C3 ⋊ #3940 |
72 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)(6,7,8)(9,10,11,12)(14,17)(15,19)(18,20);(2,3)(4,5)(7,8)(13,14,15,17,16,18,19,20)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=c,d^2=e,b^a=bde,f^a=f^2,g^a=g^4,d^b=de84 conjugacy classes — view the full character table.
| maximal subgroup of | #11747141, #11747143, #11747147, … |
| maximal normal subgroup of | #11747141, #11747143, #11747147, … |
| maximal quotient of | #11746301, #11746308, #11746315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 168);