Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#358 ⋊ C2 |
| Sylow | C13 ⋊ #2139 |
232 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 69 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=e,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=df,f^b=fg,h^b=h^12,h^c=h^12164 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#2139, C2×#13116547, #16015820, … |
| maximal normal subgroup of | D13×#2139, C2×#13116547, #16015820, … |
| maximal quotient of | #15772663, #15772907, #15772959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6221);