Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×#137 ⋊ C2 |
| Sylow | C5 ⋊ #3056 |
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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,b^2=e,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12136733, #12136736, #12136755, … |
| maximal normal subgroup of | #12136733, #12136736, #12136755, … |
| maximal quotient of | #12082073, #12082095, #12082117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17798);