Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #340 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(10,11,12,13)(15,18)(16,21)(19,20);(2,3)(4,5)(6,7,8,9)(14,15,16,19,17,20,21,18)Polycyclic presentation:
2^6,5|a^2=d,b^2=c,d^2=f,b^a=bde,g^a=g^4,d^b=df68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599573, #10599574, #10599575, … |
| maximal normal subgroup of | #10599573, #10599574, #10599575, … |
| maximal quotient of | #10598103, #10598110, #10598111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 87);