Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #3069 |
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^4,d^b=dg,h^b=h^4,f^c=fg73 conjugacy classes — view the full character table.
| maximal subgroup of | #12136827, #12136828, #12136849, … |
| maximal normal subgroup of | #12136827, #12136828, #12136849, … |
| maximal quotient of | #12082081, #12082092, #12082125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17816);