Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊Dic5 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ #67⋊C4 |
| Sylow | C3 ⋊ D4×Dic5 |
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,4,5,3)(6,7,8)(13,14)(15,16);(7,8)(14,16);(2,3)(4,5)(9,10,11,12)(14,16)Polycyclic presentation:
2^5,3,5|a^2=d,c^a=ce,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11752788, #11752803, #11752808, … |
| maximal normal subgroup of | #11752788, #11752803, #11752808, … |
| maximal quotient of | #11748314, #67⋊#168, #11748496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 636);