Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #135 |
| Sylow | C5 ⋊ #916 |
| Sylow | C3 ⋊ #4050 |
124 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 124 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)(9,12,13,20,14,21,11,18)(10,16,15,19,17,23,22,24);(7,8)(9,11,14,13)(10,15,17,22)(12,18,21,20)(16,19,23,24);(2,3)(4,5)(9,10)(11,15)(12,19)(13,22)(14,17)(16,20)(18,23)(21,24)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=d,d^2=e,c^a=cd,d^a=de,g^a=g^4,f^b=f^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4050, #11753970, #11753972, … |
| maximal normal subgroup of | D3×#4050, #11753970, #11753972, … |
| maximal quotient of | #11747643, #11747677, #11747679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 348);