Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C5×#354 ⋊ C2 |
| Sylow | C5 ⋊ #2126 |
258 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 258 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) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=g,d^2=g,b^a=bd,d^a=df,f^a=fg,d^b=dg,e^b=efg,h^b=h^4,h^c=h^4,e^d=eg52 conjugacy classes — view the full character table.
| maximal subgroup of | #12019549, #12019557, #12019585, … |
| maximal normal subgroup of | #12019549, #12019557, #12019585, … |
| maximal quotient of | #12008405, #12008455, #12008573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2033);