Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C13×C4⋊C16 ⋊ C2 |
| Sylow | C13 ⋊ D4×C16 |
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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,c^2=e,e^2=f,f^2=g,b^a=bd,h^b=h^12,h^c=h^12320 conjugacy classes — view the full character table.
| maximal subgroup of | #15774621, #15774623, #15774628, … |
| maximal normal subgroup of | #15774621, #15774623, #15774628, … |
| maximal quotient of | #15774623, #15774684, #15774712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6329);