Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #904 |
| Sylow | C3 ⋊ #4062 |
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,4,5,3)(6,7,8)(9,11,12,17,13,18,19,24)(10,15,16,23,14,20,21,22);(7,8)(10,14)(11,17)(12,19)(15,22)(18,24)(20,23);(2,3)(4,5)(9,10)(11,15)(12,16)(13,14)(17,23)(18,20)(19,21)(22,24)Polycyclic presentation:
2^5,3,5|c^2=d,d^2=e,b^a=be,g^a=g^4,c^b=cd,d^b=de,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11751679, #11751681, #11751685, … |
| maximal normal subgroup of | #11751679, #11751681, #11751685, … |
| maximal quotient of | #11747642, #11747669, #11747671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 345);