Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C13×#322 ⋊ C2 |
| Sylow | C13 ⋊ #1714 |
198 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 69 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=d,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12,c^b=cf266 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1714, C2×#13114458, #15850648, … |
| maximal normal subgroup of | D13×#1714, C2×#13114458, #15850648, … |
| maximal quotient of | #15756704, #15762691, #15762698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4132);