Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C13×#357 ⋊ C2 |
| Sylow | C13 ⋊ #2240 |
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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|b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^c=h^12170 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2240, C2×#13117058, #16018217, … |
| maximal normal subgroup of | D13×#2240, C2×#13117058, #16018217, … |
| maximal quotient of | #15779297, #15780832, #15780833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6732);