Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #329 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=c,c^2=ef,d^2=f,b^a=bd,d^a=def,g^a=g^10,c^b=ce,d^b=df89 conjugacy classes — view the full character table.
| maximal subgroup of | #13066763, #13066764, #13066766, … |
| maximal normal subgroup of | #13066763, #13066764, #13066766, … |
| maximal quotient of | #13066437, #13066442, #13066497, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 97);