Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2245 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^12,c^b=cg,h^b=h^12,h^c=h^12158 conjugacy classes — view the full character table.
| maximal subgroup of | #15776581, #15776582, #15776588, … |
| maximal normal subgroup of | #15776581, #15776582, #15776588, … |
| maximal quotient of | #15779304, #15780855, #15781154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6757);