Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C11×#107 ⋊ C2 |
| Sylow | C11 ⋊ #357 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2^6,11|b^2=c,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^10,d^b=de,e^b=ef92 conjugacy classes — view the full character table.
| maximal subgroup of | D11×#357, C2×#10622129, #13070321, … |
| maximal normal subgroup of | D11×#357, C2×#10622129, #13070321, … |
| maximal quotient of | #13066576, #13066624, #13066661, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 48);