Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#379 ⋊ C2 |
| Sylow | C5 ⋊ #1781 |
880 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,b^a=bd,c^a=ce,d^a=dg,f^b=fg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11986646, #11991869, #11991902, … |
| maximal normal subgroup of | #11986646, #11991869, #11991902, … |
| maximal quotient of | #11990626, #11990629, #11990636, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2373);