Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D5×#99 |
| Fitting | C5×#99 ⋊ C2 |
| Sylow | C5 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 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)(6,8)(7,10)(9,13)(11,12);(6,7)(8,12,13,10)(9,11);(2,3)(4,5)44 conjugacy classes — view the full character table.
| maximal subgroup of | #10598567, #10598568, D5×AΣL(1,𝔽16), … |
| maximal normal subgroup of | #10598567, #10598568, D5×AΣL(1,𝔽16), … |
| maximal quotient of | D5×#323, #10598912, #10598913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 370);