Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C13×D8 ⋊ C2 |
| Sylow | C13 ⋊ #3100 |
492 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^12,f^c=fg206 conjugacy classes — view the full character table.
| maximal subgroup of | #15832782, #15832784, #15832851, … |
| maximal normal subgroup of | #15832782, #15832784, #15832851, … |
| maximal quotient of | #15862915, #15865843, #15865845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14508);