Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×M16 |
| Fitting | C2×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ C22×M16 |
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 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 — 4 generators on 15 points:
(1,2)(3,4,6,7,5)(9,12)(13,15);(8,9,10,13,11,12,14,15);(4,5)(6,7);(1,2)80 conjugacy classes — view the full character table.
| maximal subgroup of | D5×H(3,ℤ/4), D5×#338, D5×#339, … |
| maximal normal subgroup of | D5×H(3,ℤ/4), D5×#338, D5×#339, … |
| maximal quotient of | C2×#64990, #10610213, C2×D5×#97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1415);