Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×C22⋊C8 ⋊ C4 |
| Sylow | C5 ⋊ #1280 |
264 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 64 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=d,b^2=e,d^2=g,b^a=bc,c^a=cf,d^b=df,h^b=h^2,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598551, #13015524, #13015527, … |
| maximal normal subgroup of | C2×#10598551, #13015524, #13015527, … |
| maximal quotient of | #13013209, #13013211, #13013217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 633);