Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#367 ⋊ C2 |
| Sylow | C5 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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=e,b^2=g,c^2=e,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^4,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D5×SD32, C2×#10600130, C4×#65205, … |
| maximal normal subgroup of | C4×D5×SD32, C2×#10600130, C4×#65205, … |
| maximal quotient of | #12011026, #12011201, #12011208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2212);