Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | Q8×D5⋊C8 |
| unambiguous semidirect product | D5⋊(C8×Q8) |
| Sylow | C5 ⋊ C2×C8×Q8 |
440 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 228 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #13016961, #13016969, #13016977, … |
| maximal normal subgroup of | #13016961, #13016969, #13016977, … |
| maximal quotient of | C4⋊C4×D5⋊C8, C4×Q8×#170, C4×#65703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19273);