Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#339 ⋊ C2 |
| Sylow | C5 ⋊ #1733 |
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1733, C2×#10599546, #12096689, … |
| maximal normal subgroup of | D5×#1733, C2×#10599546, #12096689, … |
| maximal quotient of | #11988737, #11988743, #11988746, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1628);