Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C22⋊Q8 |
| Sylow | C5 ⋊ #896 |
| Sylow | C3 ⋊ #4042 |
148 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,10)(11,12)(13,15,16,19)(14,18,17,20);(7,8)(9,10,11,12)(14,17)(18,20);(2,3)(4,5)(9,10,11,12)(13,14)(15,18)(16,17)(19,20)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=e,c^2=d,b^a=bd,c^a=ce,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11752471, #11752504, #11752505, … |
| maximal normal subgroup of | #11752471, #11752504, #11752505, … |
| maximal quotient of | #11747180, #11747181, #11747182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 453);