Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#332 ⋊ C2 |
| Sylow | C5 ⋊ #1540 |
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,c^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^b=h^4,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1540, C2×#10599210, #12067612, … |
| maximal normal subgroup of | D5×#1540, C2×#10599210, #12067612, … |
| maximal quotient of | #11987238, #11987258, #11987584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1292);