Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C13 ⋊ #3028 |
716 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 161 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=g,d^2=g,b^a=be,c^a=cf,d^a=dg,h^a=h^12,f^b=fg,e^c=eg233 conjugacy classes — view the full character table.
| maximal subgroup of | #15781909, #15781910, #15781913, … |
| maximal normal subgroup of | #15781909, #15781910, #15781913, … |
| maximal quotient of | #15836958, #15836965, #15836972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13916);