Finite Group Databasebeta

← Group #73022

Character table — Group #73022

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37
size1111222222668888888888888888121212242424244848
order1222448888443666121212122424242424242424488888822
χ11111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1
χ3111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-111-1-11-1
χ4111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-111-11
χ5222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222000000
χ6222222-2-2-2-222-1-1-1-1-1-1-1-1111111112-2-2000000
χ72222-2-20000222222-2-2-2-200000000-200000000
χ82222-2-2000022-1-1-1-111113333−3−3−3−3-200000000
χ92222-2-2000022-1-1-1-11111−3−3−3−33333-200000000
χ1022-2-22-222-2-200-111-111-1-111-1-111-1-1000−i2i2−i2i200
χ1122-2-22-222-2-200-111-111-1-111-1-111-1-1000i2−i2i2−i200
χ1222-2-22-2-2-22200-111-111-1-1-1-111-1-111000−i2i2i2−i200
χ1322-2-22-2-2-22200-111-111-1-1-1-111-1-111000i2−i2−i2i200
χ142-22-2002−22−2-2222-2-200002−22−22−22−202−2000000
χ152-22-2002−22−2-22-1-1113−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2302−2000000
χ162-22-2002−22−2-22-1-111−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ702−2000000
χ172-22-200−22−22-2222-2-20000−22−22−22−220−22000000
χ182-22-200−22−22-22-1-1113−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230−22000000
χ192-22-200−22−22-22-1-111−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70−22000000
χ203333333333-1-10000000000000000-1-1-11111-1-1
χ213333333333-1-10000000000000000-1-1-1-1-1-1-111
χ22333333-3-3-3-3-1-10000000000000000-11111-1-1-11
χ23333333-3-3-3-3-1-10000000000000000-111-1-1111-1
χ2444-4-44-444-4-4001-1-11-1-111-1-111-1-111000000000
χ2544-4-44-4-4-444001-1-11-1-11111-1-111-1-1000000000
χ2644-4-4-440000001-1-1111-1-133−3−3−3−333000000000
χ2744-4-4-440000001-1-1111-1-1−3−33333−3−3000000000
χ2844-4-4-44000000-222-2-2-22200000000000000000
χ294-4-440022−22−2222001-11-13−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000
χ304-4-440022−22−2222001-11-1−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000
χ314-4-440022−22−222200-22-2200002−2−222−2−22000000000
χ324-4-4400−222222−22001-11-13−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000
χ334-4-4400−222222−22001-11-1−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000
χ344-4-4400−222222−2200-22-220000−222−2−222−2000000000
χ356666-6-60000-2-20000000000000000200000000
χ366-66-60032−3232−322-200000000000000000−22000000
χ376-66-600−3232−32322-2000000000000000002−2000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.