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)(10,11,12,14,13,15,16,17);(11,15)(14,17);(2,3)(4,5)(6,7,8,9)(11,14)(12,16)(15,17)Polycyclic presentation:
2^6,5|a^2=d,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf62 conjugacy classes — view the full character table.
| maximal subgroup of | #10599528, #10599529, #10599551, … |
| maximal normal subgroup of | #10599528, #10599529, #10599551, … |
| maximal quotient of | #10600607, #10600608, #10600609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 748);