Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#427 ⋊ C2 |
| Sylow | C5 ⋊ #3342 |
340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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,b^2=g,c^2=eg,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^4,f^c=fg91 conjugacy classes — view the full character table.
| maximal subgroup of | #12256223, #12256225, #12256245, … |
| maximal normal subgroup of | #12256223, #12256225, #12256245, … |
| maximal quotient of | #12115573, #12116964, #12116968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13004);