Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×D4×D5 |
| Fitting | C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 169 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) = 80 |
A minimal faithful permutation representation — 4 generators on 13 points:
(2,3)(4,5);(1,2,4,5,3)(11,13);(10,11)(12,13);(6,7,8,9)80 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D4⋊C8, #10598960, #10598965, … |
| maximal normal subgroup of | D5×D4⋊C8, #10598960, #10598965, … |
| maximal quotient of | C4×#4027, C4×#4024, C4×#4031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1216);