Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#407 ⋊ C2 |
| Sylow | C13 ⋊ #2973 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,f^2=g,b^a=be,c^a=cg,d^a=de,c^b=ce,h^b=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15756927, #15756930, #15757885, … |
| maximal normal subgroup of | #15756927, #15756930, #15757885, … |
| maximal quotient of | #15861595, #15861607, #15861654, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13537);