Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C181 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^180,d^b=de,d^c=df1273 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽16)×D181, C2×#26041066, #37535359, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D181, C2×#26041066, #37535359, … |
| maximal quotient of | #37531649, #37531669, #37531718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 336);