Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #1661 |
208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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=f,c^2=g,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^12,d^b=df,e^b=eg,d^c=dg,e^c=efg134 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1661, C2×#13114153, #15844072, … |
| maximal normal subgroup of | D13×#1661, C2×#13114153, #15844072, … |
| maximal quotient of | #15751717, #15751724, #15751741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3827);