Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #3140 |
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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|b^2=fg,c^2=e,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,d^b=dg,h^b=h^12,d^c=dg,h^c=h^12200 conjugacy classes — view the full character table.
| maximal subgroup of | #15760536, #15760538, #15763823, … |
| maximal normal subgroup of | #15760536, #15760538, #15763823, … |
| maximal quotient of | #15863139, #15865639, #15865648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14896);