Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #2028 |
246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 246 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) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=d,c^2=g,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^12,c^b=cf,e^b=eg,e^c=eg194 conjugacy classes — view the full character table.
| maximal subgroup of | #15750512, #15750514, #15775681, … |
| maximal normal subgroup of | #15750512, #15750514, #15775681, … |
| maximal quotient of | #15765894, #15765899, #15765914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5671);