Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1307 |
130 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 42 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|a^2=d,b^2=e,d^2=g,e^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^8,c^b=cg,d^b=df,h^d=h^1286 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129741, #16780225, #16780228, … |
| maximal normal subgroup of | C2×#13129741, #16780225, #16780228, … |
| maximal quotient of | #16776871, #16776872, #16776874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19415);