Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #2084 |
230 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 230 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) = 1664 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=d,c^2=dg,f^2=g,b^a=bd,c^a=ce,h^a=h^12,c^b=cf,f^b=fg,f^c=fg200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2084, C2×#13116315, #15891902, … |
| maximal normal subgroup of | D13×#2084, C2×#13116315, #15891902, … |
| maximal quotient of | #15767838, #15767843, #15767855, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5989);