Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #137 |
| Sylow | C5 ⋊ #951 |
| Sylow | C3 ⋊ #4055 |
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)(9,12,14,13)(10,16,17,22)(11,19,20,21)(15,23,24,18);(7,8)(9,11,13,19,14,20,12,21)(10,15,16,18,17,24,22,23);(2,3)(4,5)(9,10)(11,18)(12,16)(13,22)(14,17)(15,19)(20,23)(21,24)Polycyclic presentation:
2^5,3,5|b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^4,c^b=ce,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747119, #11747124, #11748092, … |
| maximal normal subgroup of | #11747119, #11747124, #11748092, … |
| maximal quotient of | #11746889, #11746893, #11746934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 389);