Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D5×#104 |
| Fitting | C5×#104 ⋊ C2 |
| Sylow | C5 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 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:
(1,3)(2,5)(4,6)(7,8)(9,10,12,13,11);(1,2,4,7,5,3,8,6);(10,11)(12,13)56 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#104, #10604002, #10604003, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#104, #10604002, #10604003, … |
| maximal quotient of | D5×D4⋊C8, #10598958, #10598963, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 447);