Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C293 ⋊ #359 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^138,c^b=ce,e^b=ef,g^b=g^292,g^d=g^292533 conjugacy classes — view the full character table.
| maximal subgroup of | D293⋊#359, C2×#34037044, #49175099, … |
| maximal normal subgroup of | D293⋊#359, C2×#34037044, #49175099, … |
| maximal quotient of | #49173740, #49173741, #49173776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1464);