Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×AGL(1,ℤ/8) |
| Fitting | C5×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C5 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 4 generators on 13 points:
(2,6)(5,7)(9,10,12,13,11);(2,5)(3,8)(6,7);(1,2)(3,5)(4,6)(7,8);(10,11)(12,13)44 conjugacy classes — view the full character table.
| maximal subgroup of | #10604863, #10604866, D5×#453, … |
| maximal normal subgroup of | #10604863, #10604866, D5×#453, … |
| maximal quotient of | #10610597, #10610601, #10610609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1444);