Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×H(5,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #2901 |
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,h^f=h^461 conjugacy classes — view the full character table.
| maximal subgroup of | #13039538, #13039540, #13039541, … |
| maximal normal subgroup of | #13039538, #13039540, #13039541, … |
| maximal quotient of | #13029690, #13029691, #13029696, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19642);