Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1351 |
162 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 162 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=e,c^2=fg,b^a=bc,c^a=ce,e^a=eg,h^a=h^8,c^b=cf,d^b=defg,h^b=h^12,d^c=dg,h^d=h^1283 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊#1351, C2×#13129831, #16787720, … |
| maximal normal subgroup of | D13⋊#1351, C2×#13129831, #16787720, … |
| maximal quotient of | #16777053, #16777071, #16777450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19505);