Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic30 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊#168) |
| Hall | C3×C5 ⋊ C4⋊C8 |
| Sylow | C5 ⋊ C4⋊(C3⋊C8) |
| Sylow | C3 ⋊ C4⋊#168 |
76 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);(2,3)(4,5)(7,8)(10,12)(13,14,15,17,16,18,19,20)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^2,g^a=g^4132 conjugacy classes — view the full character table.
| maximal subgroup of | #11745835, #11745837, #11745841, … |
| maximal normal subgroup of | #11745835, #11745837, #11745841, … |
| maximal quotient of | #11746278, #11746279, C4⋊(C3⋊#672), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 164);