Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊M32 |
| Sylow | C5 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,5,4)(6,8,10,17,11,9,16,18)(7,13,15,20,12,14,19,21);(7,12)(13,14)(15,19)(20,21);(2,3,4,5)(6,7,9,14,10,15,18,21,11,12,8,13,16,19,17,20)Polycyclic presentation:
2^6,5|a^2=d,c^2=e,d^2=e,e^2=f,b^a=bf,g^a=g^2,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10598603, #10598604, #10598605, … |
| maximal normal subgroup of | #10598603, #10598604, #10598605, … |
| maximal quotient of | #10603823, #10603825, D5⋊(C4⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1053);