Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×#344 ⋊ C2 |
| Sylow | C13 ⋊ #2080 |
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 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=d,d^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^12,c^b=cf,d^b=dg,e^b=eg,h^b=h^12,f^c=fg158 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2080, C2×#13116291, #15891844, … |
| maximal normal subgroup of | D13×#2080, C2×#13116291, #15891844, … |
| maximal quotient of | #15767691, #15767696, #15767701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 5965);