Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C2×C4×Q8) |
| Fitting | C22×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ C22×C4×Q8 |
1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13021801, #13021878, AGL(1,𝔽5)×#391, … |
| maximal normal subgroup of | #13021801, #13021878, AGL(1,𝔽5)×#391, … |
| maximal quotient of | C22×C4⋊C4×AGL(1,𝔽5), C2×C4×Q8×AGL(1,𝔽5), C22×#65711, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 21487);