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 ⋊ #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)(9,12,13,11,14,19,22,20)(10,16,17,23,18,21,24,15);(7,8)(9,11,14,20)(10,15,18,23)(12,22,19,13)(16,17,21,24);(2,3)(4,5)(9,10)(11,15)(12,21)(13,17)(14,18)(16,19)(20,23)(22,24)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=d,d^2=e,c^a=ce,g^a=g^4,c^b=cd,d^b=de,f^b=f^251 conjugacy classes — view the full character table.
| maximal subgroup of | #11753959, #11753960, C2×#91260, … |
| maximal normal subgroup of | #11753959, #11753960, C2×#91260, … |
| maximal quotient of | #11747605, #11747611, #11747617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 336);