Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#3952 |
| Fitting | C22×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 19 points:
(4,6)(7,8,10,11,9)(12,13,14,16,15,17,18,19);(3,4)(5,6)(8,9)(10,11);(1,2)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10598013, #10598760, #10598764, … |
| maximal normal subgroup of | #10598013, #10598760, #10598764, … |
| maximal quotient of | C2×#64679, #10600527, C2×#64676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 735);