Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | Q8×C4⋊AGL(1,𝔽5) |
| Fitting | C4×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ Q8×C4⋊C4 |
568 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 568 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) = 160 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | #13018974, #13018978, #13018982, … |
| maximal normal subgroup of | #13018974, #13018978, #13018982, … |
| maximal quotient of | C4⋊C4×C4⋊AGL(1,𝔽5), Q8×(C2×AGL(1,𝔽5))⋊C4, #13028032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19293);