Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #3363 |
336 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 139 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=g,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,d^b=de,f^c=fg,h^c=h^4115 conjugacy classes — view the full character table.
| maximal subgroup of | #12089497, #12089504, #12089557, … |
| maximal normal subgroup of | #12089497, #12089504, #12089557, … |
| maximal quotient of | Q8×#3948, #12116108, #12118252, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13746);