Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C11×#97 ⋊ C2 |
| Sylow | C11 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=e,c^2=d,d^2=f,c^a=cf,g^a=g^10,c^b=cf140 conjugacy classes — view the full character table.
| maximal subgroup of | #13067201, #13067203, #13067206, … |
| maximal normal subgroup of | #13067201, #13067203, #13067206, … |
| maximal quotient of | #13066895, #13066904, #13066912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 239);