Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #1519 |
340 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 97 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=e,c^2=g,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^12,c^b=cf,d^b=dg,e^b=efg200 conjugacy classes — view the full character table.
| maximal subgroup of | #15754450, #15754451, #15754461, … |
| maximal normal subgroup of | #15754450, #15754451, #15754461, … |
| maximal quotient of | #15750904, #15750908, #15750971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3078);