Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C13×Q32 ⋊ C2 |
| Sylow | C13 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,d^c=dg,h^d=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | #15783609, #15783613, #15783623, … |
| maximal normal subgroup of | #15783609, #15783613, #15783623, … |
| maximal quotient of | #16015833, #16015959, #16016266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17659);