Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#364 ⋊ C2 |
| Sylow | C5 ⋊ #2166 |
122 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 55 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=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,c^b=cg,e^b=eg,h^b=h^4,e^c=eg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12010814, #12010816, #12010819, … |
| maximal normal subgroup of | #12010814, #12010816, #12010819, … |
| maximal quotient of | #12014317, #12014369, #12014640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2174);