Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#413 ⋊ C2 |
| Sylow | C5 ⋊ #3022 |
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^4,e^b=eg,f^b=fg,h^b=h^4,e^c=eg73 conjugacy classes — view the full character table.
| maximal subgroup of | #12018318, #12018319, #12018325, … |
| maximal normal subgroup of | #12018318, #12018319, #12018325, … |
| maximal quotient of | #12071705, #12071736, #12071783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12531);