Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #467 |
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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=ce,d^c=df92 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#467, C2×#10622664, #13078192, … |
| maximal normal subgroup of | D11×#467, C2×#10622664, #13078192, … |
| maximal quotient of | #13067979, #13067984, #13068013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 583);