Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(6,7,8,9)(11,15)(12,17)(14,16);(11,14)(15,16);(2,3)(4,5)(10,11,12,16,13,14,17,15)Polycyclic presentation:
2^6,5|a^2=e,c^2=d,e^2=f,b^a=bf,c^a=ce,g^a=g^4,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599773, #10599774, #10599775, … |
| maximal normal subgroup of | #10599773, #10599774, #10599775, … |
| maximal quotient of | #10600261, #10600274, #10600299, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 591);