Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #501 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,4,5,3)(6,8,9,13)(7,10,11,12)(15,19)(16,21)(18,20);(6,7,9,11)(8,12,13,10)(15,18)(19,20);(2,3)(4,5)(14,15,16,20,17,18,21,19)Polycyclic presentation:
2^6,5|a^2=e,b^2=d,c^2=d,e^2=f,b^a=bf,c^a=ce,g^a=g^4,c^b=cd,e^c=ef44 conjugacy classes — view the full character table.
| maximal subgroup of | #10602038, #10602040, #10602045, … |
| maximal normal subgroup of | #10602038, #10602040, #10602045, … |
| maximal quotient of | #10600362, #10600363, #10600371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 707);