Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4060 |
| Fitting | C2×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ C2×AGL(1,ℤ/8) |
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2)(3,4,6,7,5)(8,9,11,12)(10,15,14,13);(1,2)(9,13)(10,14)(12,15);(4,5)(6,7)(9,12)(13,15);(1,2)50 conjugacy classes — view the full character table.
| maximal subgroup of | #10604819, #10604827, C4×#4060, … |
| maximal normal subgroup of | #10604819, #10604827, C4×#4060, … |
| maximal quotient of | C2×#65074, C2×#65055, C2×#65053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1431);