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 ⋊ #918 |
| Sylow | C3 ⋊ #4061 |
120 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 38 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)(9,11,13,20)(10,14,16,24)(12,18,22,19)(15,23,21,17);(7,8)(11,18)(12,22)(14,23)(15,21)(17,24)(19,20);(2,3)(4,5)(9,10,13,16)(11,17,20,23)(12,21,22,15)(14,18,24,19)Polycyclic presentation:
2^5,3,5|a^2=e,c^2=e,d^2=e,c^a=cd,d^a=de,g^a=g^4,c^b=cde,d^b=de,f^b=f^2,d^c=de42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4061, #11754077, #11754090, … |
| maximal normal subgroup of | D3×#4061, #11754077, #11754090, … |
| maximal quotient of | #11747184, #11747212, #11747235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 600);