Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #328 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=d,b^2=cd,c^2=ef,b^a=bc,c^a=ce,g^a=g^10,c^b=cf,d^b=df119 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#328, C2×#10622105, #13067099, … |
| maximal normal subgroup of | D11×#328, C2×#10622105, #13067099, … |
| maximal quotient of | #13066440, #13066441, #13066496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 24);