Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#686 |
| Fitting | C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C4×D8 |
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(1,2,4,5,3)(11,14)(12,17)(15,16);(2,3)(4,5)(10,11)(12,14)(13,16)(15,17);(6,7,8,9)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10598941, #10598944, #10598945, … |
| maximal normal subgroup of | #10598941, #10598944, #10598945, … |
| maximal quotient of | #10600251, #10600255, C4×#3941, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 640);