Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2113 |
228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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=e,e^2=f,f^2=g,b^a=bd,h^a=h^8,c^b=cg,h^e=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #16777312, #16777314, #16777317, … |
| maximal normal subgroup of | #16777312, #16777314, #16777317, … |
| maximal quotient of | #16786704, #16786774, #16786838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20740);