Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×#100 |
| Fitting | C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 40 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,4,5,3)(7,10)(8,12);(6,7,8,11,9,10,12,13);(2,3)(4,5)44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598573, D5×AΣL(1,𝔽16), #10599928, … |
| maximal normal subgroup of | #10598573, D5×AΣL(1,𝔽16), #10599928, … |
| maximal quotient of | #10598894, #10598896, #10598897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 371);