Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#3957 |
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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 — 3 generators on 15 points:
(3,4,6,7,5)(8,10,11,14,12,13,15,9);(4,5)(6,7)(8,9)(10,11)(12,14)(13,15);(1,2)68 conjugacy classes — view the full character table.
| maximal subgroup of | #10599507, #10599512, #10599521, … |
| maximal normal subgroup of | #10599507, #10599512, #10599521, … |
| maximal quotient of | C2×#64684, #10600590, C2×#64685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 765);