Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C13 ⋊ #2956 |
458 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^5,e^b=eg,d^c=dg,h^c=h^8,h^f=h^1277 conjugacy classes — view the full character table.
| maximal subgroup of | #16804709, #16804710, #16804713, … |
| maximal normal subgroup of | #16804709, #16804710, #16804713, … |
| maximal quotient of | #16795221, #16795222, #16795224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21284);