Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #362 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=f,b^2=cd,c^2=ef,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^10,c^b=cf,d^b=df116 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#362, C2×#10622155, #13070362, … |
| maximal normal subgroup of | D11×#362, C2×#10622155, #13070362, … |
| maximal quotient of | #13066587, #13066635, #13066666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 74);