Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #470 |
110 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 110 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=f,c^2=f,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^10,c^b=cef,d^c=df86 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#470, C2×#10622665, #13078220, … |
| maximal normal subgroup of | D11×#470, C2×#10622665, #13078220, … |
| maximal quotient of | #13068103, #13068108, #13068137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 584);