Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D5 |
| Fitting | C22×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 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) = 17 |
| transitive degree | μt(G) = 160 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,4,5,3)(7,9);(2,3)(4,5)(6,7)(8,9);(10,11,12,14,13,15,16,17)104 conjugacy classes — view the full character table.
| maximal subgroup of | #10599894, #10599895, #10599896, … |
| maximal normal subgroup of | #10599894, #10599895, #10599896, … |
| maximal quotient of | C8×#685, C8×#683, #10600577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 736);