Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×C22⋊C8 ⋊ C4 |
| Sylow | C13 ⋊ #1305 |
200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 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=d,b^2=e,d^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^5,c^b=cg,d^b=df,h^b=h^8,h^d=h^12,h^e=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129738, #16780153, #16780158, … |
| maximal normal subgroup of | C2×#13129738, #16780153, #16780158, … |
| maximal quotient of | #16776869, #16776872, #16776874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19412);