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 ⋊ #4061 |
120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 120 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)(9,11,13,18)(10,15,14,21)(12,20,19,17)(16,23,22,24);(7,8)(10,14)(11,17)(12,19)(15,23)(18,20)(21,24);(2,3)(4,5)(9,10)(11,15)(12,16)(13,14)(17,24)(18,21)(19,22)(20,23)Polycyclic presentation:
2^5,3,5|c^2=e,d^2=e,b^a=be,g^a=g^4,c^b=cd,d^b=de,f^b=f^2,d^c=de45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4061, #11754074, #11754080, … |
| maximal normal subgroup of | D3×#4061, #11754074, #11754080, … |
| maximal quotient of | #11747158, #11747168, #11747205, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 589);