Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C13×Q32 ⋊ C2 |
| Sylow | C13 ⋊ #2222 |
140 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 45 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|a^2=g,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,e^c=eg,h^c=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | #15783614, #15783616, #15783621, … |
| maximal normal subgroup of | #15783614, #15783616, #15783621, … |
| maximal quotient of | #15777127, #15777144, #15777178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6632);