Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Fitting | C82×C13 ⋊ C2 |
| Sylow | C13 ⋊ #1708 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=d,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12422 conjugacy classes — view the full character table.
| maximal subgroup of | #15776685, D13×#1708, C2×#13114437, … |
| maximal normal subgroup of | #15776685, D13×#1708, C2×#13114437, … |
| maximal quotient of | #15756693, #15762653, #15762659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4111);