Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C13×M16 ⋊ C4 |
| Sylow | C13 ⋊ #2873 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=f,e^2=g,d^a=dg,c^b=cg,h^b=h^8,h^f=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16785558, #16785560, #16785561, … |
| maximal normal subgroup of | #16785558, #16785560, #16785561, … |
| maximal quotient of | #16792582, #16792583, #16792584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21073);