Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1768 |
260 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,c^a=cg,h^a=h^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1768, C2×#10601235, C4×#65128, … |
| maximal normal subgroup of | D5×#1768, C2×#10601235, C4×#65128, … |
| maximal quotient of | #11990447, #11990449, #11990454, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3317);