Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C11×M16 ⋊ C2 |
| Sylow | C11 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^10,c^b=cf122 conjugacy classes — view the full character table.
| maximal subgroup of | #13068585, #13068587, #13068990, … |
| maximal normal subgroup of | #13068585, #13068587, #13068990, … |
| maximal quotient of | #13067008, #13067034, #13067060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 663);