Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C13×M16 ⋊ C4 |
| Sylow | C13 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^5,e^b=eg,h^b=h^8,h^c=h^12,h^e=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#344, #16785245, #16785365, … |
| maximal normal subgroup of | #261×#344, #16785245, #16785365, … |
| maximal quotient of | #16779181, #16779184, #16779189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20222);