Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #3131 |
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^b=h^4,h^c=h^4100 conjugacy classes — view the full character table.
| maximal subgroup of | #11994609, #11994611, #11994623, … |
| maximal normal subgroup of | #11994609, #11994611, #11994623, … |
| maximal quotient of | #12099492, #12101917, #12102939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17094);