Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #1954 |
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,b^2=df,c^2=e,f^2=g,b^a=bd,c^a=ce,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1954, C2×#10600709, #12102886, … |
| maximal normal subgroup of | D5×#1954, C2×#10600709, #12102886, … |
| maximal quotient of | #11998070, #11998074, #11998078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2791);