Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×#331 ⋊ C2 |
| Sylow | C13 ⋊ #1639 |
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 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=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^12,d^b=df,e^b=eg,d^c=dg,e^c=eg,h^c=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1639, C2×#13114016, #15838605, … |
| maximal normal subgroup of | D13×#1639, C2×#13114016, #15838605, … |
| maximal quotient of | #15751708, #15751720, #15751778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3690);