Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #428 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=d,c^2=e,e^2=f,c^a=ce,e^a=ef,g^a=g^10,c^b=cf122 conjugacy classes — view the full character table.
| maximal subgroup of | #13068827, #13068828, #13068832, … |
| maximal normal subgroup of | #13068827, #13068828, #13068832, … |
| maximal quotient of | #13067368, #13067383, #13067401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 653);