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 ⋊ #909 |
| 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)(9,12,14,13)(10,16,17,21)(11,19,20,22)(15,23,24,18);(7,8)(9,11,14,20)(10,15,17,24)(12,19,13,22)(16,23,21,18);(2,3)(4,5)(9,10,13,16,14,17,12,21)(11,18,19,24,20,23,22,15)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=e,c^2=e,d^2=e,b^a=bd,c^a=ce,g^a=g^4,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747119, #11747124, #11748085, … |
| maximal normal subgroup of | #11747119, #11747124, #11748085, … |
| maximal quotient of | #11746884, #11746909, #11746932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 398);