Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C11×#107 ⋊ C2 |
| Sylow | C11 ⋊ #478 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=d,c^2=e,e^2=f,c^a=cde,e^a=ef,g^a=g^10,c^b=cef,e^b=ef89 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#478, C2×#10622504, #13078402, … |
| maximal normal subgroup of | D11×#478, C2×#10622504, #13078402, … |
| maximal quotient of | #13068625, #13068860, #13068878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 423);