Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1454 |
178 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,e^2=g,c^a=cfg,h^a=h^2,c^b=cf,h^c=h^4,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#1454, C2×#10604014, #13029023, … |
| maximal normal subgroup of | D5⋊#1454, C2×#10604014, #13029023, … |
| maximal quotient of | #13015264, #13015286, #13016672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6096);