Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C13×#533 ⋊ C2 |
| Sylow | C13 ⋊ #3131 |
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=f,c^2=e,d^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^12,h^b=h^12,h^c=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15758227, #15758243, #15758245, … |
| maximal normal subgroup of | #15758227, #15758243, #15758245, … |
| maximal quotient of | #15863111, #15865532, #15866555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14835);