Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×D5⋊C8 |
| derived, Sylow | C5 ⋊ C22×C4×C8 |
760 conjugacy classes of subgroups; only the 434 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#1273, #13015272, #13015276, … |
| maximal normal subgroup of | D5⋊#1273, #13015272, #13015276, … |
| maximal quotient of | C2×C8×D5⋊C8, C2×#10603807, M16×D5⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19105);