Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2043 |
298 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 93 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=g,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^4,c^b=cf,e^b=eg,f^b=fg,h^b=h^4,e^c=eg,f^c=fg88 conjugacy classes — view the full character table.
| maximal subgroup of | #11988156, #11988157, #11988163, … |
| maximal normal subgroup of | #11988156, #11988157, #11988163, … |
| maximal quotient of | #12002648, #12002653, #12002702, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2508);