Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #64671 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #328 |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,4,5,3)(6,8)(7,10,11,12)(9,13)(15,18,19,20);(2,3)(4,5)(6,7,9,11)(8,12,13,10)(14,15)(16,18)(17,19)(20,21)Polycyclic presentation:
2^6,5|a^2=f,b^2=c,d^2=ef,b^a=bd,c^a=ce,d^a=def,g^a=g^4,d^b=df59 conjugacy classes — view the full character table.
| maximal subgroup of | #10599069, #10599072, #10599073, … |
| maximal normal subgroup of | #10599069, #10599072, #10599073, … |
| maximal quotient of | #10597968, #10597971, #10597981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 10);