Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C5×D8 ⋊ C2 |
| Sylow | C5 ⋊ #3280 |
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^4,d^b=de,e^b=eg,e^d=eg91 conjugacy classes — view the full character table.
| maximal subgroup of | #12255751, #12255758, #12255788, … |
| maximal normal subgroup of | #12255751, #12255758, #12255788, … |
| maximal quotient of | #12088883, #12088898, #12088913, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17652);