Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C13×C22⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ #3538 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=f,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,c^b=cg,d^b=df,h^b=h^12206 conjugacy classes — view the full character table.
| maximal subgroup of | #15755208, #15755209, #15755212, … |
| maximal normal subgroup of | #15755208, #15755209, #15755212, … |
| maximal quotient of | #16025689, #16025898, #16025900, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18755);