Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ #469 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|d^2=f,b^a=be,c^a=cef,g^a=g^10,c^b=cd,d^b=df,d^c=df86 conjugacy classes — view the full character table.
| maximal subgroup of | #13070560, #13070829, D11×#469, … |
| maximal normal subgroup of | #13070560, #13070829, D11×#469, … |
| maximal quotient of | #13068092, #13068097, #13068126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 691);