Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ #449 |
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|e^2=f,b^a=bf,c^a=cd,g^a=g^10,c^b=ce,e^b=ef,e^c=ef89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#449, C2×#10622771, #13077829, … |
| maximal normal subgroup of | D11×#449, C2×#10622771, #13077829, … |
| maximal quotient of | #13067542, #13067559, #13067610, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 690);