Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic30 |
| 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 ⋊ #4072 |
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)(14,18)(17,20);(13,15,16,19)(14,17,18,20);(2,3)(4,5)(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=e,c^a=ce,f^a=f^2,g^a=g^4132 conjugacy classes — view the full character table.
| maximal subgroup of | #11745970, #11745971, #11745976, … |
| maximal normal subgroup of | #11745970, #11745971, #11745976, … |
| maximal quotient of | #11751026, #11751027, #11751033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 891);