Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C13×#332 ⋊ C2 |
| Sylow | C13 ⋊ #1702 |
162 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 49 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=dfg,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12,c^b=cf,h^b=h^12,e^c=eg,h^c=h^12137 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1702, C2×#13114407, #15845601, … |
| maximal normal subgroup of | D13×#1702, C2×#13114407, #15845601, … |
| maximal quotient of | #15756037, #15759132, #15759164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4081);