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=c,c^2=f,d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^10,d^b=def,e^b=ef86 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#362, C2×#10622134, #13070362, … |
| maximal normal subgroup of | D11×#362, C2×#10622134, #13070362, … |
| maximal quotient of | #13066585, #13066633, #13066664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 53);