Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #126 |
| Sylow | C5 ⋊ #898 |
| Sylow | C3 ⋊ #4025 |
120 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 44 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)(10,14)(11,15)(17,19,20,23)(18,21,22,24);(7,8)(9,11,12,15)(10,13,14,16)(19,23)(21,24);(2,3)(4,5)(9,10)(11,13)(12,14)(15,16)(17,18,20,22)(19,21,23,24)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=de,c^2=d,c^a=cde,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11752491, #11752492, #11752568, … |
| maximal normal subgroup of | #11752491, #11752492, #11752568, … |
| maximal quotient of | #11748604, #11748614, #11748617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 418);