Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C11⋊C16) |
| Sylow | C11 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=g^10200 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊(C11⋊C16), #13066572, #13066574, … |
| maximal normal subgroup of | D4⋊(C11⋊C16), #13066572, #13066574, … |
| maximal quotient of | #13066680, #13066686, #13066694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 19);