Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #91110 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #827 |
| 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)(6,7,8)(10,14)(11,18)(12,19)(15,16)(17,23)(20,24)(21,22);(2,3)(4,5)(7,8)(9,10,13,17)(11,14,20,23)(12,21,19,16)(15,24,22,18)Polycyclic presentation:
2^5,3,5|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^4,c^b=cd,d^b=de60 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#827, #11748271, D3×#3959, … |
| maximal normal subgroup of | D5×#827, #11748271, D3×#3959, … |
| maximal quotient of | #11746311, #11746313, #11746383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 187);