Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#436 ⋊ C2 |
| Sylow | C13 ⋊ #2969 |
370 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,h^a=h^12,c^b=cg,h^b=h^12,d^c=dg,h^c=h^12,h^d=h^12218 conjugacy classes — view the full character table.
| maximal subgroup of | #15833832, #15833836, #15833869, … |
| maximal normal subgroup of | #15833832, #15833836, #15833869, … |
| maximal quotient of | #15861190, #15861221, #15861314, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13517);