Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ D3×M16 |
| Sylow | C3 ⋊ D5×M16 |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,4,5,3)(6,7,8)(10,11)(15,16);(7,8)(9,11,12,16,13,10,14,15);(2,3)(4,5)(9,10,12,15,13,11,14,16)Polycyclic presentation:
2^5,3,5|a^2=d,b^2=d,d^2=e,c^a=ce,g^a=g^4,c^b=ce,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | #11747112, #11747113, #11748060, … |
| maximal normal subgroup of | #11747112, #11747113, #11748060, … |
| maximal quotient of | #11746844, #11746852, #11746856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 368);