Finite Group Databasebeta

← Group #72266433

Character table — Group #72266433

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size111133334444121212121212121224242424242424244848484896969696969696969696969696969696256256256256256256256256256256256256256256256256
order1222222222222222222222222222444444444444444444443366666666666666
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ422222222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000-1-11111-1-1-11111-1-1-1
χ522222222-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000001+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32
χ622222222-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000001−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32
χ733333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ833333333333333333333-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ933333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000
χ1033333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-10000000000000000
χ1133333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000
χ1244-4-44-4-4444-4-444-4-4-444-400000000000000000000000000001111-1-11-1-111-1-11-1-1
χ1344-4-44-4-4444-4-444-4-4-444-40000000000000000000000000000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32
χ1444-4-44-4-4444-4-444-4-4-444-40000000000000000000000000000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32
χ1544-4-44-4-44-4-44444-4-44-4-44000000000000000000000000000011-1-1111-1-1-1-1111-1-1
χ1644-4-44-4-44-4-44444-4-44-4-440000000000000000000000000000−1−i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32
χ1744-4-44-4-44-4-44444-4-44-4-440000000000000000000000000000−1+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32
χ184-44-4-44-444-44-44-44-4-44-440000000000000000000000000000111-11-1-11-11-11-1-11-1
χ194-44-4-44-444-44-44-44-4-44-440000000000000000000000000000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32
χ204-44-4-44-444-44-44-44-4-44-440000000000000000000000000000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32
χ214-44-4-44-44-44-444-44-44-44-4000000000000000000000000000011-11-11-11-1-11-11-11-1
χ224-44-4-44-44-44-444-44-44-44-40000000000000000000000000000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ234-44-4-44-44-44-444-44-44-44-40000000000000000000000000000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ244-4-44-4-4444-4-444-4-4444-4-40000000000000000000000000000111-1-11-1-111-1-11-1-11
χ254-4-44-4-4444-4-444-4-4444-4-40000000000000000000000000000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
χ264-4-44-4-4444-4-444-4-4444-4-40000000000000000000000000000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ274-4-44-4-444-444-44-4-44-4-444000000000000000000000000000011-111-1-1-11-111-1-1-11
χ284-4-44-4-444-444-44-4-44-4-4440000000000000000000000000000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
χ294-4-44-4-444-444-44-4-44-4-4440000000000000000000000000000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32
χ3066666666-6-6-6-66666-6-6-6-6-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ3166-6-66-6-6666-6-6-2-2222-2-222222-2-2-2-222-2-200002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ3266-6-66-6-6666-6-6-2-2222-2-222222-2-2-2-222-2-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ3366-6-66-6-6666-6-6-2-2222-2-22-2-2-2-22222-2-22200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ3466-6-66-6-6666-6-6-2-2222-2-22-2-2-2-22222-2-2220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ3566-6-66-6-66-6-666-2-222-222-22222-2-2-2-2-2-22222-2-20000000022-2-20000000000000000
χ3666-6-66-6-66-6-666-2-222-222-22222-2-2-2-2-2-222-2-22200000000-2-2220000000000000000
χ3766-6-66-6-66-6-666-2-222-222-2-2-2-2-2222222-2-222-2-200000000-2-2220000000000000000
χ3866-6-66-6-66-6-666-2-222-222-2-2-2-2-2222222-2-2-2-2220000000022-2-20000000000000000
χ396-66-6-66-666-66-6-22-222-22-222-2-222-2-22-22-200002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ406-66-6-66-666-66-6-22-222-22-222-2-222-2-22-22-20000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ416-66-6-66-666-66-6-22-222-22-2-2-222-2-222-22-2200002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ426-66-6-66-666-66-6-22-222-22-2-2-222-2-222-22-220000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ436-66-6-66-66-66-66-22-22-22-2222-2-222-2-2-22-222-22-200002-22-200000000000000000000
χ446-66-6-66-66-66-66-22-22-22-2222-2-222-2-2-22-22-22-220000-22-2200000000000000000000
χ456-66-6-66-66-66-66-22-22-22-22-2-222-2-2222-22-22-22-20000-22-2200000000000000000000
χ466-66-6-66-66-66-66-22-22-22-22-2-222-2-2222-22-2-22-2200002-22-200000000000000000000
χ476-6-66-6-6666-6-66-222-2-2-22222-2-2-2-2222-2-222-2-222-2-22000000000000000000000000
χ486-6-66-6-6666-6-66-222-2-2-22222-2-2-2-2222-2-22-222-2-222-2000000000000000000000000
χ496-6-66-6-6666-6-66-222-2-2-222-2-22222-2-2-222-22-2-22-222-2000000000000000000000000
χ506-6-66-6-6666-6-66-222-2-2-222-2-22222-2-2-222-2-222-22-2-22000000000000000000000000
χ516-6-66-6-666-666-6-222-222-2-222-2-2-2-222-222-2000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ526-6-66-6-666-666-6-222-222-2-222-2-2-2-222-222-200000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ536-6-66-6-666-666-6-222-222-2-2-2-22222-2-22-2-22000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ546-6-66-6-666-666-6-222-222-2-2-2-22222-2-22-2-2200000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ55121212121212121212121212-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000
χ561212121212121212-12-12-12-12-4-4-4-4444400000000000000000000000000000000000000000000
χ5724242424-8-8-8-80000000000004-44-44-44-4000000000000000000000000000000000000
χ5824242424-8-8-8-8000000000000-44-44-44-44000000000000000000000000000000000000
χ592424-24-24-888-80000000000004-44-4-44-44000000000000000000000000000000000000
χ602424-24-24-888-8000000000000-44-444-44-4000000000000000000000000000000000000
χ6124-2424-248-88-80000000000004-4-444-4-44000000000000000000000000000000000000
χ6224-2424-248-88-8000000000000-444-4-444-4000000000000000000000000000000000000
χ6324-24-242488-8-80000000000004-4-44-444-4000000000000000000000000000000000000
χ6424-24-242488-8-8000000000000-444-44-4-44000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).