Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2000 |
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^12,c^b=cf,d^b=dg200 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2000, C2×#13115839, #15889719, … |
| maximal normal subgroup of | D13×#2000, C2×#13115839, #15889719, … |
| maximal quotient of | #15763127, #15763134, #15763155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5513);