Finite Group Databasebeta

← Group #10714592

Character table — Group #10714592

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order12222344446881212242424246668881212122424242424244488121212121616161616161616242424244848484848484848484848484848484822248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ922222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-222-2-2222200000000-2-2-2-2000000000000000000000000
χ1022222222222-2-222-2-2-2-2222-2-2-2222-2-2-2-2-2-2-2-222-2-2-2-2000000002222000000000000000000000000
χ11222222-2-2-2-2200-2-20000222000-2-2-20000002-20022-2-2−i2−i2i2i2−i2−i2i2i20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000
χ12222222-2-2-2-2200-2-20000222000-2-2-20000002-20022-2-2i2i2−i2−i2i2i2−i2−i20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000
χ13222222-2-2-2-2200-2-20000222000-2-2-2000000-2200-2-222−i2−i2i2i2i2i2−i2−i20000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200000000
χ14222222-2-2-2-2200-2-20000222000-2-2-2000000-2200-2-222i2i2−i2−i2−i2−i2i2i20000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200000000
χ1522222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1622222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000
χ1722222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000
χ1822222-12222-122-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000
χ1922222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-2-2-1-1-1-100000000111133−3−333−3−333−3−333−3−300000000
χ2022222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-111111122-2-2-1-1-1-1000000001111−3−333−3−333−3−333−3−33300000000
χ2122222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-222111100000000-1-1-1-133−3−333−3−3−3−333−3−33300000000
χ2222222-12222-1-2-2-1-11111-1-1-1-2-2-2-1-1-1111111-2-222111100000000-1-1-1-1−3−333−3−33333−3−333−3−300000000
χ2322222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−32-200-1-111−i2−i2i2i2−i2−i2i2i233−3−3ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ2422222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−32-200-1-111i2i2−i2−i2i2i2−i2−i233−3−3−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ2522222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−3-220011-1-1−i2−i2i2i2i2i2−i2−i2−3−333ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ2300000000
χ2622222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−3-220011-1-1i2i2−i2−i2−i2−i2i2i2−3−333−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ2300000000
χ2722222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−332-200-1-111−i2−i2i2i2−i2−i2i2i2−3−333ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ2822222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−332-200-1-111i2i2−i2−i2i2i2−i2−i2−3−333−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ2922222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−33-220011-1-1−i2−i2i2i2i2i2−i2−i233−3−3ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ700000000
χ3022222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−33-220011-1-1i2i2−i2−i2−i2−i2i2i233−3−3−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7ζ13+ζ23ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23−ζ5−ζ7−ζ5−ζ700000000
χ31222-2-2222-2-22222222222-2-22-2-22-2-22-22-2-2-20000000000002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i00000000
χ32222-2-2222-2-22222222222-2-22-2-22-2-22-22-2-2-2000000000000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i00000000
χ33222-2-2222-2-22-2-222-2-2-2-22-2-2-2222-2-2-22-2222000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ34222-2-2222-2-22-2-222-2-2-2-22-2-2-2222-2-2-22-222200000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ35222-2-22-2-222200-2-200002-2-2000-222000000002-200002−2−222−2−222-22-22−22−2−22−222−22−2−22−2200000000
χ36222-2-22-2-222200-2-200002-2-2000-222000000002-20000−222−2−222−22-22-2−22−222−22−2−22−222−22−200000000
χ37222-2-22-2-222200-2-200002-2-2000-22200000000-2200002−2−22−222−2-22-222−22−2−22−22−22−222−22−200000000
χ38222-2-22-2-222200-2-200002-2-2000-22200000000-220000−222−22−2−22-22-22−22−222−22−22−22−2−22−2200000000
χ39222-2-2-122-2-2-122-1-1-1-1-1-1-1112-2-2-111-11-111100003−33−300002i−2i2i−2i3−3−33−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii00000000
χ40222-2-2-122-2-2-122-1-1-1-1-1-1-1112-2-2-111-11-111100003−33−30000−2i2i−2i2i3−3−33i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i00000000
χ41222-2-2-122-2-2-122-1-1-1-1-1-1-1112-2-2-111-11-11110000−33−3300002i−2i2i−2i−333−3i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii00000000
χ42222-2-2-122-2-2-122-1-1-1-1-1-1-1112-2-2-111-11-11110000−33−330000−2i2i−2i2i−333−3−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i00000000
χ43222-2-2-122-2-2-1-2-2-1-11111-111-222-1111-11-1-1-100003−33−32i−2i2i−2i0000−333−3−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i300000000
χ44222-2-2-122-2-2-1-2-2-1-11111-111-222-1111-11-1-1-100003−33−3−2i2i−2i2i0000−333−3i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i300000000
χ45222-2-2-122-2-2-1-2-2-1-11111-111-222-1111-11-1-1-10000−33−332i−2i2i−2i00003−3−33−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i300000000
χ46222-2-2-122-2-2-1-2-2-1-11111-111-222-1111-11-1-1-10000−33−33−2i2i−2i2i00003−3−33i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i300000000
χ47222-2-2-1-2-222-1001133−3−3-1110001-1-13−3−33−33002-2−333−32−2−222−2−22-11-11ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ48222-2-2-1-2-222-1001133−3−3-1110001-1-13−3−33−33002-2−333−3−222−2−222−2-11-11−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ49222-2-2-1-2-222-1001133−3−3-1110001-1-13−3−33−3300-223−3−332−2−22−222−21-11-1ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ50222-2-2-1-2-222-1001133−3−3-1110001-1-13−3−33−3300-223−3−33−222−22−2−221-11-1−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ51222-2-2-1-2-222-10011−3−333-1110001-1-1−333−33−3002-23−3−332−2−222−2−22-11-11ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ52222-2-2-1-2-222-10011−3−333-1110001-1-1−333−33−3002-23−3−33−222−2−222−2-11-11−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ53222-2-2-1-2-222-10011−3−333-1110001-1-1−333−33−300-22−333−32−2−22−222−21-11-1ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ54222-2-2-1-2-222-10011−3−333-1110001-1-1−333−33−300-22−333−3−222−22−2−221-11-1−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ5522-22-22-222-2222222222-22-2-2-22-22-2-2-2-2-22200000000000000000000000000000000000000002-200
χ5622-22-22-222-2222222222-22-2-2-22-22-2-2-2-2-2220000000000000000000000000000000000000000-2200
χ5722-22-22-222-22-2-222-2-2-2-2-22-222-2-22-22222-2-20000000000000000000000000000000000000000002i−2i
χ5822-22-22-222-22-2-222-2-2-2-2-22-222-2-22-22222-2-2000000000000000000000000000000000000000000−2i2i
χ5922-2-222-22-22222222222-2-22-22-2-2-22-22-22-2-2000000000000000000000000000000000000002-20000
χ6022-2-222-22-22222222222-2-22-22-2-2-22-22-22-2-200000000000000000000000000000000000000-220000
χ6122-2-222-22-222-2-222-2-2-2-2-2-222-22-2-222-22-2220000000000000000000000000000000000002-2000000
χ6222-2-222-22-222-2-222-2-2-2-2-2-222-22-2-222-22-222000000000000000000000000000000000000-22000000
χ6344-44-444-4-44400-4-40000-44-40004-4400000000000000000000000000000000000000000000000000
χ6444-44-4-24-4-44-200222323−23−232-22000-22-2−23−23232323−2300000000000000000000000000000000000000000000
χ6544-44-4-24-4-44-20022−23−2323232-22000-22-22323−23−23−232300000000000000000000000000000000000000000000
χ6644-44-4-2-444-4-244-2-2-2-2-2-22-22-4-442-222222-2-200000000000000000000000000000000000000000000
χ6744-44-4-2-444-4-2-4-4-2-222222-2244-42-22-2-2-2-22200000000000000000000000000000000000000000000
χ6844-4-4444-44-4400-4-40000-4-4400044-400000000000000000000000000000000000000000000000000
χ6944-4-44-24-44-4-200222323−23−2322-2000-2-22−232323−23−232300000000000000000000000000000000000000000000
χ7044-4-44-24-44-4-20022−23−23232322-2000-2-2223−23−232323−2300000000000000000000000000000000000000000000
χ7144-4-44-2-44-44-244-2-2-2-2-2-222-2-44-422-22-22-22200000000000000000000000000000000000000000000
χ7244-4-44-2-44-44-2-4-4-2-2222222-24-4422-2-22-22-2-200000000000000000000000000000000000000000000
χ738-800080000-842−420042−4242−4200000000000000000000000000000000000000000000000000000000000
χ748-800080000-8−424200−4242−424200000000000000000000000000000000000000000000000000000000000
χ758-8000-40000442−4243−434ζ5−4ζ7−4ζ5+4ζ74ζ13−4ζ23−4ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000
χ768-8000-40000442−42−43434ζ13−4ζ23−4ζ13+4ζ234ζ5−4ζ7−4ζ5+4ζ700000000000000000000000000000000000000000000000000000000000
χ778-8000-400004−424243−43−4ζ5+4ζ74ζ5−4ζ7−4ζ13+4ζ234ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000
χ788-8000-400004−4242−4343−4ζ13+4ζ234ζ13−4ζ23−4ζ5+4ζ74ζ5−4ζ700000000000000000000000000000000000000000000000000000000000

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