Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #91110 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×D8 ⋊ C2 |
| Hall | C3×C5 ⋊ D16 |
| Sylow | C5 ⋊ #826 |
| Sylow | C3 ⋊ #3958 |
56 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)(11,14)(12,21)(13,17)(15,18)(16,19)(20,23)(22,24)Polycyclic presentation:
2^5,3,5|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×#826, #11748265, D3×#3958, … |
| maximal normal subgroup of | D5×#826, #11748265, D3×#3958, … |
| maximal quotient of | #11746310, #11746312, #11746340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 186);