Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #2060 |
246 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 246 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) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=d,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,e^b=eg,e^c=eg82 conjugacy classes — view the full character table.
| maximal subgroup of | #11986929, #11986931, #12012210, … |
| maximal normal subgroup of | #11986929, #11986931, #12012210, … |
| maximal quotient of | #12003703, #12003718, #12003730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2448);