Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C11×C16 ⋊ C2 |
| Sylow | C11 ⋊ #359 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=cd,c^2=ef,e^2=f,b^a=bc,c^a=ce,d^a=df,e^a=ef,g^a=g^10182 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#359, C2×#10622148, #13070342, … |
| maximal normal subgroup of | D11×#359, C2×#10622148, #13070342, … |
| maximal quotient of | #13066578, #13066581, #13066632, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 67);