Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C11×M32 ⋊ C2 |
| Sylow | C11 ⋊ #350 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^10,d^b=df128 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#350, C2×#10622153, #13070242, … |
| maximal normal subgroup of | D11×#350, C2×#10622153, #13070242, … |
| maximal quotient of | #13066541, #13066557, #13066570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 72);