Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #124 |
| Sylow | C5 ⋊ #885 |
| Sylow | C3 ⋊ #4093 |
152 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 152 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)(10,12)(13,15,16,20)(14,18,17,19);(7,8)(13,14,16,17)(15,19,20,18);(2,3)(4,5)(9,10)(11,12)(14,17)(18,19)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=e,b^a=be,c^a=cd,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11752495, #11752564, #11752598, … |
| maximal normal subgroup of | #11752495, #11752564, #11752598, … |
| maximal quotient of | #11747374, #11747376, #11747379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 531);