Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ #1393 |
232 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 44 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=d,b^2=e,c^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dfg,d^c=dg,h^d=h^458 conjugacy classes — view the full character table.
| maximal subgroup of | #13014231, #13014232, #13014233, … |
| maximal normal subgroup of | #13014231, #13014232, #13014233, … |
| maximal quotient of | #13013632, #13013684, #13013718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 775);