Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×M16 ⋊ C2 |
| Sylow | C5 ⋊ #2920 |
484 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 197 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=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^b=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | #11988798, #11988802, #11988806, … |
| maximal normal subgroup of | #11988798, #11988802, #11988806, … |
| maximal quotient of | #12096775, C4×#65415, C4×#65407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12330);