Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C13×M16 ⋊ C4 |
| Sylow | C13 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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=f,b^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^8,h^b=h^12,f^c=fg,h^f=h^1292 conjugacy classes — view the full character table.
| maximal subgroup of | #16777389, #16777390, #16788268, … |
| maximal normal subgroup of | #16777389, #16777390, #16788268, … |
| maximal quotient of | #16781871, #16781872, #16781875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20393);