Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #443 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=d,d^2=f,e^2=f,g^a=g^10,c^b=ce,e^b=ef,e^c=ef98 conjugacy classes — view the full character table.
| maximal subgroup of | #13070494, #13070497, #13070499, … |
| maximal normal subgroup of | #13070494, #13070497, #13070499, … |
| maximal quotient of | D8×C11⋊C8, SD16×C11⋊C8, Q16×C11⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 728);