Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#100 |
| Sylow | C5 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,3,5,4)(7,12)(8,9);(6,8,10,9)(7,11,12,13);(2,3,4,5)(6,7,9,13,10,12,8,11)Polycyclic presentation:
2^6,5|a^2=d,b^2=f,d^2=f,c^a=ce,e^a=ef,g^a=g^2,c^b=cf,d^c=df,g^d=g^432 conjugacy classes — view the full character table.
| maximal subgroup of | #10598567, AGL(1,𝔽5)×#100, D5⋊AΣL(1,𝔽16), … |
| maximal normal subgroup of | #10598567, AGL(1,𝔽5)×#100, D5⋊AΣL(1,𝔽16), … |
| maximal quotient of | D5⋊#323, #10604202, #10604207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1116);