Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C13×#498 ⋊ C2 |
| Sylow | C13 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=df,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,e^c=efg,f^c=fg,h^c=h^12155 conjugacy classes — view the full character table.
| maximal subgroup of | #15776676, #15776677, #15776681, … |
| maximal normal subgroup of | #15776676, #15776677, #15776681, … |
| maximal quotient of | #15779017, #15779615, #15780615, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6678);