Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #800 |
| Sylow | C3 ⋊ #3932 |
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)(9,10,15,21,20,24,11,14,13,17,18,23,12,16,19,22);(2,3)(4,5)(7,8)(10,14)(11,18)(12,20)(15,19)(16,23)(17,22)(21,24)Polycyclic presentation:
2^5,3,5|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^2,g^a=g^4123 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#800, #11746816, D3×#3932, … |
| maximal normal subgroup of | D5×#800, #11746816, D3×#3932, … |
| maximal quotient of | #11746324, #11746326, #11746330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 160);