Finite Group DatabasebetaFinite Group Databasebeta| order | 9536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C149 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,149|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^148,d^b=de,d^c=df1049 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D149, C2×#23749412, #34046329, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D149, C2×#23749412, #34046329, … |
| maximal quotient of | #34042619, #34042639, #34042688, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9536, 336);