Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C11×C4⋊Q8 ⋊ C2 |
| Sylow | C11 ⋊ #486 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=e,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^10,c^b=ce,d^c=df92 conjugacy classes — view the full character table.
| maximal subgroup of | #13067705, #13067706, #13067712, … |
| maximal normal subgroup of | #13067705, #13067706, #13067712, … |
| maximal quotient of | #13068743, #13069298, #13069421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 620);