Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C293 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^138,c^b=cf,d^b=df,g^d=g^292758 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037027, D293⋊#350, #49175027, … |
| maximal normal subgroup of | C2×#34037027, D293⋊#350, #49175027, … |
| maximal quotient of | #49173707, #49173723, D4⋊#17989805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1447);