Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C13×SD16 ⋊ C2 |
| Sylow | C13 ⋊ #3357 |
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^12,c^b=cg,d^b=de,h^b=h^12,f^c=fg,h^d=h^12197 conjugacy classes — view the full character table.
| maximal subgroup of | #15853856, #15853858, #15853901, … |
| maximal normal subgroup of | #15853856, #15853858, #15853901, … |
| maximal quotient of | #15879370, #15879381, #15880645, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17138);