Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C11 ⋊ #365 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=d,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^10,c^b=cf116 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#365, C2×#10622151, #13070387, … |
| maximal normal subgroup of | D11×#365, C2×#10622151, #13070387, … |
| maximal quotient of | #13066682, #13066715, C2×#10622151 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 70);