Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#338 ⋊ C2 |
| Sylow | C13 ⋊ #2069 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=de,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^12,c^b=cf,f^b=fg,h^b=h^12,d^c=dg,h^c=h^12155 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2069, C2×#13116235, #15891644, … |
| maximal normal subgroup of | D13×#2069, C2×#13116235, #15891644, … |
| maximal quotient of | #15767549, #15767563, #15767577, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5909);