Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C13×C4⋊C4 ⋊ C2 |
| Sylow | C13 ⋊ #3092 |
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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|c^2=e,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^12,f^c=fg272 conjugacy classes — view the full character table.
| maximal subgroup of | #15760949, #15760955, #15760956, … |
| maximal normal subgroup of | #15760949, #15760955, #15760956, … |
| maximal quotient of | #15862718, #15863652, #15864147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14433);