Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×#127 ⋊ C2 |
| Sylow | C5 ⋊ #3038 |
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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|b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,f^c=fg,h^c=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #11995190, #11995196, #11995197, … |
| maximal normal subgroup of | #11995190, #11995196, #11995197, … |
| maximal quotient of | #12083182, #12083191, #12083198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16978);