Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C11 ⋊ #519 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|a^2=e,b^2=f,c^2=f,d^a=df,g^a=g^10,c^b=cf134 conjugacy classes — view the full character table.
| maximal subgroup of | #13068728, #13068830, #13068833, … |
| maximal normal subgroup of | #13068728, #13068830, #13068833, … |
| maximal quotient of | #13070973, #13070981, #13071202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 1262);