Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C11 ⋊ C2 |
| Sylow | C11 ⋊ #466 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^10182 conjugacy classes — view the full character table.
| maximal subgroup of | #13066624, #13066626, #13066630, … |
| maximal normal subgroup of | #13066624, #13066626, #13066630, … |
| maximal quotient of | #13067971, #13067976, #13068005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 647);