Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D293⋊#100 |
| Sylow | C293 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2344 |
Polycyclic presentation:
2^6,293|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^138,e^b=ef,g^c=g^292,g^e=g^292752 conjugacy classes — view the full character table.
| maximal subgroup of | #49173868, #100×#11924078, #49174631, … |
| maximal normal subgroup of | #49173868, #100×#11924078, #49174631, … |
| maximal quotient of | D293⋊#323, #49174025, #49174026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1532);