Finite Group DatabasebetaFinite Group Databasebeta| order | 704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C11×D8 ⋊ C2 |
| Sylow | C11 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 176 |
Polycyclic presentation:
2^6,11|b^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^10,c^b=cf,d^c=de,e^c=ef86 conjugacy classes — view the full character table.
| maximal subgroup of | #13070512, #13070517, #13070560, … |
| maximal normal subgroup of | #13070512, #13070517, #13070560, … |
| maximal quotient of | #13070326, #13070332, #13070402, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(704, 679);