Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊C8 |
| Fitting | C2×C5×C8 ⋊ C4 |
| Sylow | C5 ⋊ #336 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,5,4)(7,9)(10,11,12,14,13,15,16,17);(2,3,4,5)(6,7)(8,9)Polycyclic presentation:
2^6,5|a^2=c,b^2=d,d^2=f,b^a=be,g^a=g^2,g^c=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #10603839, #10603840, C8×C4⋊AGL(1,𝔽5), … |
| maximal normal subgroup of | #10603839, #10603840, C8×C4⋊AGL(1,𝔽5), … |
| maximal quotient of | #10598526, #10598529, #10598530, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 230);