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 ⋊ #942 |
| Sylow | C3 ⋊ #4097 |
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)(11,18)(14,23)(17,24)(19,21);(7,8)(9,11)(10,14)(12,21)(13,18)(15,24)(16,23)(17,20)(19,22);(2,3)(4,5)(9,10,13,16)(11,17,18,24)(12,20,22,15)(14,21,23,19)Polycyclic presentation:
2^5,3,5|a^2=e,d^2=e,b^a=bd,d^a=de,g^a=g^4,c^b=ce,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747115, #11747120, #11748083, … |
| maximal normal subgroup of | #11747115, #11747120, #11748083, … |
| maximal quotient of | #11746900, #11746904, #11746919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 385);