Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | SD16×Dic5 |
| Sylow | C5 ⋊ C4×SD16 |
122 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(2,3)(4,5)(6,7,8,9);(1,2,4,5,3)(11,14)(12,17)(15,16);(10,11,13,16)(12,14,17,15)56 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#170, SD16⋊#170, #10604809, … |
| maximal normal subgroup of | SD16×#170, SD16⋊#170, #10604809, … |
| maximal quotient of | Dic5×#102, #10600949, #10600963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 788);