Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #3387 |
326 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^d=h^12143 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3387, C2×#13127763, #16743475, … |
| maximal normal subgroup of | D13×#3387, C2×#13127763, #16743475, … |
| maximal quotient of | #15879561, #15879580, #15881233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17437);