Finite Group DatabasebetaFinite Group Databasebeta| order | 11072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D173⋊#100 |
| Sylow | C173 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,173|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^80,e^b=ef,g^c=g^172,g^e=g^172452 conjugacy classes — view the full character table.
| maximal subgroup of | #36368646, #100×#10621924, #36369409, … |
| maximal normal subgroup of | #36368646, #100×#10621924, #36369409, … |
| maximal quotient of | D173⋊#323, #36368803, #36368804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11072, 1532);