Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1481 |
216 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 89 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,b^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cg,d^b=df,h^b=h^12278 conjugacy classes — view the full character table.
| maximal subgroup of | #15754760, #15754762, #15754767, … |
| maximal normal subgroup of | #15754760, #15754762, #15754767, … |
| maximal quotient of | #15751254, #15751278, #15751287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2912);