Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #418 |
190 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(11,16)(12,13)(15,17);(10,12,14,13)(11,15,17,16);(2,3)(4,5)(6,7,8,9)(10,11)(12,15)(13,16)(14,17)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^4,c^b=cf,e^c=ef62 conjugacy classes — view the full character table.
| maximal subgroup of | #10600436, #10600456, #10600865, … |
| maximal normal subgroup of | #10600436, #10600456, #10600865, … |
| maximal quotient of | #10602347, #10602351, #10602390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 842);