Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1995 |
244 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=deg,c^2=ef,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cef,d^a=dg,c^b=cg,h^b=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11986694, #11991672, #11991677, … |
| maximal normal subgroup of | #11986694, #11991672, #11991677, … |
| maximal quotient of | #11999314, #11999318, #11999322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3390);