Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#368 ⋊ C2 |
| Sylow | C5 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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,c^2=e,d^2=fg,e^2=g,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 | #12019905, #12019907, #12019910, … |
| maximal normal subgroup of | #12019905, #12019907, #12019910, … |
| maximal quotient of | #12011021, #12011026, #12011033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2232);