Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#497 ⋊ C2 |
| Sylow | C13 ⋊ #3289 |
448 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 448 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) = 416 |
Polycyclic presentation:
2^7,13|a^2=g,b^2=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=de,e^b=eg,h^b=h^12,f^c=fg,h^c=h^12,e^d=eg,h^d=h^12122 conjugacy classes — view the full character table.
| maximal subgroup of | #15783657, #15783661, #15783671, … |
| maximal normal subgroup of | #15783657, #15783661, #15783671, … |
| maximal quotient of | #15852295, #15852310, #15852340, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16285);