Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C5×SD32 ⋊ C2 |
| Sylow | C5 ⋊ #2248 |
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^482 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2248, C2×#10602272, #12254702, … |
| maximal normal subgroup of | D5×#2248, C2×#10602272, #12254702, … |
| maximal quotient of | #12013960, #12013962, #12013964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4354);