Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C13×C4⋊C4 ⋊ C4 |
| Sylow | C13 ⋊ #1344 |
146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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=d,b^2=g,c^2=f,b^a=bc,c^a=ce,e^a=eg,h^a=h^8,c^b=cf,d^b=def,d^c=dg,h^d=h^1283 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129816, D13⋊#1344, #16787638, … |
| maximal normal subgroup of | C2×#13129816, D13⋊#1344, #16787638, … |
| maximal quotient of | #16776965, #16776969, #16776981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19490);