Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#100 ⋊ C2 |
| Sylow | C11 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 88 |
Polycyclic presentation:
2^6,11|b^2=c,c^2=f,b^a=bd,c^a=ce,g^a=g^10,d^b=de,e^b=ef,d^c=df68 conjugacy classes — view the full character table.
| maximal subgroup of | D11×AΣL(1,𝔽16), C2×#10622113, #13070256, … |
| maximal normal subgroup of | D11×AΣL(1,𝔽16), C2×#10622113, #13070256, … |
| maximal quotient of | #13066543, #13066565, #13066614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 32);