Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #2991 |
394 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 221 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,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^4,c^b=ceg130 conjugacy classes — view the full character table.
| maximal subgroup of | #11993577, #11993581, #11993591, … |
| maximal normal subgroup of | #11993577, #11993581, #11993591, … |
| maximal quotient of | #12098142, #12098327, #12098364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16336);