Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C11 ⋊ #366 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=de,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^10182 conjugacy classes — view the full character table.
| maximal subgroup of | #13066794, #13066795, #13066797, … |
| maximal normal subgroup of | #13066794, #13066795, #13066797, … |
| maximal quotient of | #13066688, #13066708, #13066816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 61);