Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C11 ⋊ #543 |
242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|a^2=e,d^2=e,c^a=cf,d^a=de,g^a=g^10,d^b=df122 conjugacy classes — view the full character table.
| maximal subgroup of | #13067538, #13067541, #13067572, … |
| maximal normal subgroup of | #13067538, #13067541, #13067572, … |
| maximal quotient of | #13071228, #13071230, #13071344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 933);