Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#341 ⋊ C2 |
| Sylow | C5 ⋊ #2020 |
342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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=g,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,d^b=dg,f^b=fg,h^b=h^4,d^c=dg,e^c=eg,f^c=fg,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | #12011449, #12011454, #12011460, … |
| maximal normal subgroup of | #12011449, #12011454, #12011460, … |
| maximal quotient of | #11999913, #11999930, #11999988, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1819);