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 ⋊ #2347 |
504 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 233 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,b^2=ef,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^12,d^b=de290 conjugacy classes — view the full character table.
| maximal subgroup of | #15760085, #15760089, #15760113, … |
| maximal normal subgroup of | #15760085, #15760089, #15760113, … |
| maximal quotient of | #15784344, #15784378, #15784408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7403);