Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C13×#494 ⋊ C2 |
| Sylow | C13 ⋊ #2248 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=dfg,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^12,h^b=h^12170 conjugacy classes — view the full character table.
| maximal subgroup of | #15776357, #15776358, #15776364, … |
| maximal normal subgroup of | #15776357, #15776358, #15776364, … |
| maximal quotient of | #15777584, #15777606, #15777608, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6767);