Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #339 |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(10,12,14,11)(13,17,15,16);(2,3)(4,5)(10,11,13,16,14,12,15,17)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,c^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^4,e^b=ef68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599489, #10599494, #10599504, … |
| maximal normal subgroup of | #10599489, #10599494, #10599504, … |
| maximal quotient of | #10598106, #10598109, #10598110, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 90);