Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #3186 |
520 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 520 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|f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^4,c^b=ce,f^c=fg,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #11995872, #11995874, #11999721, … |
| maximal normal subgroup of | #11995872, #11995874, #11999721, … |
| maximal quotient of | #12108306, #12109570, #12110433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12424);