Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2344 |
Polycyclic presentation:
2^6,293|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^138,d^b=de,g^b=g^292,d^c=df,g^d=g^292743 conjugacy classes — view the full character table.
| maximal subgroup of | D293⋊AΣL(1,𝔽16), C2×#34037030, #49175038, … |
| maximal normal subgroup of | D293⋊AΣL(1,𝔽16), C2×#34037030, #49175038, … |
| maximal quotient of | #49173710, #49173729, #49173764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1450);