Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1554 |
198 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,b^2=f,c^2=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,h^a=h^4,d^b=dg,e^b=efg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11991650, #11991651, #11991714, … |
| maximal normal subgroup of | #11991650, #11991651, #11991714, … |
| maximal quotient of | #11987328, #11987338, #11987451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3696);