Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1277 |
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=ef,h^a=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11986067, #11986068, #11986070, … |
| maximal normal subgroup of | #11986067, #11986068, #11986070, … |
| maximal quotient of | #11985828, #11985834, #11985838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 227);