Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#405 ⋊ C2 |
| Sylow | C13 ⋊ #2929 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^12,h^b=h^12296 conjugacy classes — view the full character table.
| maximal subgroup of | #15772417, #15779783, #15779802, … |
| maximal normal subgroup of | #15772417, #15779783, #15779802, … |
| maximal quotient of | #15832789, #15832798, #15832807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13206);