Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #2320 |
444 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 229 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=g,b^2=e,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^12,c^b=ce284 conjugacy classes — view the full character table.
| maximal subgroup of | #15759847, #15759851, #15759861, … |
| maximal normal subgroup of | #15759847, #15759851, #15759861, … |
| maximal quotient of | #15784195, #15784212, #15784235, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7161);