Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C11 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^6,11|a^2=c,b^2=d,c^2=f,b^a=be,g^a=g^10200 conjugacy classes — view the full character table.
| maximal subgroup of | #13066436, #13066437, #13066438, … |
| maximal normal subgroup of | #13066436, #13066437, #13066438, … |
| maximal quotient of | C11⋊#1273, #13066445, #13066447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 81);