Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | Aut(G) = C23×D3×AGL(1,𝔽5) (order 960) · Inn(G) = C2×D3×AGL(1,𝔽5) · Out(G) = C22 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #131 |
| Sylow | C5 ⋊ #907 |
| Sylow | C3 ⋊ #4131 |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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:
(1,2,3,5,4)(6,7,8)(10,15)(11,17)(16,22)(18,23);(7,8)(9,11)(10,14)(12,18)(13,17)(15,21)(16,20)(19,23)(22,24);(2,3,4,5)(9,10,12,16,13,15,19,22)(11,14,18,20,17,21,23,24)Polycyclic presentation:
2^5,3,5|a^2=d,d^2=e,c^a=ce,g^a=g^2,c^b=ce,f^b=f^2,g^d=g^439 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#907, #11756823, D3×#4131, … |
| maximal normal subgroup of | D5⋊#907, #11756823, D3×#4131, … |
| maximal quotient of | #11751761, #11751772, #11751778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1005);