Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C11×SD16 ⋊ C2 |
| Sylow | C11 ⋊ #463 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=e,c^2=f,d^2=f,c^a=cef,g^a=g^10,c^b=cd,d^b=df,d^c=df89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#463, C2×#10622778, #13078067, … |
| maximal normal subgroup of | D11×#463, C2×#10622778, #13078067, … |
| maximal quotient of | #13068027, #13068041, #13068055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 697);