Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #100×C293 ⋊ C2 |
| 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^292,d^b=de,g^b=g^292,d^c=df1619 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D293, C2×#34035917, #49160425, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D293, C2×#34035917, #49160425, … |
| maximal quotient of | #49156712, #49156734, #49156783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 337);