Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C11 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=e,c^2=d,d^2=f,g^a=g^10,c^b=ce140 conjugacy classes — view the full character table.
| maximal subgroup of | #13066927, #13066929, #13066935, … |
| maximal normal subgroup of | #13066927, #13066929, #13066935, … |
| maximal quotient of | #13068360, C22⋊C8×Dic11, #13068464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 250);