Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90939 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #800 |
| Sylow | C3 ⋊ #3959 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,5,3)(7,8)(10,14)(11,18)(12,19)(15,22)(16,23)(17,21)(20,24);(2,3)(4,5)(6,7,8)(9,10,11,15,19,22,24,14,13,17,20,23,12,16,18,21)Polycyclic presentation:
2^5,3,5|a^2=c,c^2=de,d^2=e,b^a=bce,g^a=g^4,c^b=cd,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#800, #11746816, #11746828, … |
| maximal normal subgroup of | D5×#800, #11746816, #11746828, … |
| maximal quotient of | #11745894, #11745902, #11745942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 20);