Finite Group Databasebeta

← Group #10714311

Character table — Group #10714311

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order12222344446881212242424246668881212122424242424244488121212121616161616161616242424244848484848484848484848484848484824444444
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
χ11222222-2-2-2-2200-2-20000222000-2-2-20000002-20022-2-222−2−222−2−200002222−2−2−2−22222−2−2−2−200000000
χ12222222-2-2-2-2200-2-20000222000-2-2-20000002-20022-2-2−2−222−2−2220000−2−2−2−22222−2−2−2−2222200000000
χ13222222-2-2-2-2200-2-20000222000-2-2-2000000-2200-2-22222−2−2−2−22200002222−2−2−2−2−2−2−2−2222200000000
χ14222222-2-2-2-2200-2-20000222000-2-2-2000000-2200-2-222−2−22222−2−20000−2−2−2−222222222−2−2−2−200000000
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
χ2322222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−32-200-1-11122−2−222−2−233−3−3ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ2300000000
χ2422222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−32-200-1-111−2−222−2−22233−3−3−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ2300000000
χ2522222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−3-220011-1-122−2−2−2−222−3−333ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ2300000000
χ2622222-1-2-2-2-2-1001133−3−3-1-1-100011133−3−33−3-220011-1-1−2−22222−2−2−3−333−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ2300000000
χ2722222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−332-200-1-11122−2−222−2−2−3−333ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ700000000
χ2822222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−332-200-1-111−2−222−2−222−3−333−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ700000000
χ2922222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−33-220011-1-122−2−2−2−22233−3−3ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ700000000
χ3022222-1-2-2-2-2-10011−3−333-1-1-1000111−3−333−33-220011-1-1−2−22222−2−233−3−3−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7ζ13−ζ23ζ13−ζ23ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23−ζ5+ζ7−ζ5+ζ700000000
χ31222-2-222-22-22222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000000000000000002i−2i0000
χ32222-2-222-22-22222222222-2-2-2-222-2-2-2-2-2-22200000000000000000000000000000000000000−2i2i0000
χ33222-2-222-22-22-2-222-2-2-2-22-2-222-22-2-22222-2-20000000000000000000000000000000000002-2000000
χ34222-2-222-22-22-2-222-2-2-2-22-2-222-22-2-22222-2-2000000000000000000000000000000000000-22000000
χ3522-22-222-2-22200-2-20000-22-20002-22000000002-20000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3622-22-222-2-22200-2-20000-22-20002-22000000002-20000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3722-22-222-2-22200-2-20000-22-20002-2200000000-220000−i2i2−i2i2i2−i2i2−i2-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3822-22-222-2-22200-2-20000-22-20002-2200000000-220000i2−i2i2−i2−i2i2−i2i2-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ3922-22-22-222-2222222222-22-22-2-2-22-22-22-2-2-20000000000002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i00000000
χ4022-22-22-222-2222222222-22-22-2-2-22-22-22-2-2-2000000000000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i00000000
χ4122-22-22-222-22-2-222-2-2-2-2-22-2-222-22-2-22-2222000000002i−2i−2i2i000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ4222-22-22-222-22-2-222-2-2-2-2-22-2-222-22-2-22-222200000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ4322-22-2-12-2-22-1001133−3−31-11000-11-13−3−33−33002-23−33−3−i2i2−i2i2−i2i2−i2i2-11-11ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ4422-22-2-12-2-22-1001133−3−31-11000-11-13−3−33−33002-23−33−3i2−i2i2−i2i2−i2i2−i2-11-11−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ4522-22-2-12-2-22-1001133−3−31-11000-11-13−3−33−3300-22−33−33−i2i2−i2i2i2−i2i2−i21-11-1ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ4622-22-2-12-2-22-1001133−3−31-11000-11-13−3−33−3300-22−33−33i2−i2i2−i2−i2i2−i2i21-11-1−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ4722-22-2-12-2-22-10011−3−3331-11000-11-1−333−33−3002-2−33−33−i2i2−i2i2−i2i2−i2i2-11-11ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ4822-22-2-12-2-22-10011−3−3331-11000-11-1−333−33−3002-2−33−33i2−i2i2−i2i2−i2i2−i2-11-11−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ4922-22-2-12-2-22-10011−3−3331-11000-11-1−333−33−300-223−33−3−i2i2−i2i2i2−i2i2−i21-11-1ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ5022-22-2-12-2-22-10011−3−3331-11000-11-1−333−33−300-223−33−3i2−i2i2−i2−i2i2−i2i21-11-1−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ5122-22-2-1-222-2-122-1-1-1-1-1-11-112-2-21-11-11-111100003−3−3300002i−2i−2i2i−333−3−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i00000000
χ5222-22-2-1-222-2-122-1-1-1-1-1-11-112-2-21-11-11-111100003−3−330000−2i2i2i−2i−333−3i3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii00000000
χ5322-22-2-1-222-2-122-1-1-1-1-1-11-112-2-21-11-11-11110000−333−300002i−2i−2i2i3−3−33i3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i00000000
χ5422-22-2-1-222-2-122-1-1-1-1-1-11-112-2-21-11-11-11110000−333−30000−2i2i2i−2i3−3−33−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii00000000
χ5522-22-2-1-222-2-1-2-2-1-111111-11-2221-111-11-1-1-100003−3−332i−2i−2i2i00003−3−33−ii−iii−ii−ii3−i3−i3i3−i3i3i3−i300000000
χ5622-22-2-1-222-2-1-2-2-1-111111-11-2221-111-11-1-1-100003−3−33−2i2i2i−2i00003−3−33i−ii−i−ii−ii−i3i3i3−i3i3−i3−i3i300000000
χ5722-22-2-1-222-2-1-2-2-1-111111-11-2221-111-11-1-1-10000−333−32i−2i−2i2i0000−333−3−ii−iii−ii−i−i3i3i3−i3i3−i3−i3i300000000
χ5822-22-2-1-222-2-1-2-2-1-111111-11-2221-111-11-1-1-10000−333−3−2i2i2i−2i0000−333−3i−ii−i−ii−iii3−i3−i3i3−i3i3i3−i300000000
χ5922-2-222-2-222222222222-2-22-22-2-2-22-22-22-2-200000000000000000000000000000000000000002-200
χ6022-2-222-2-222222222222-2-22-22-2-2-22-22-22-2-20000000000000000000000000000000000000000-2200
χ6122-2-222-2-2222-2-222-2-2-2-2-2-222-22-2-222-22-2220000000000000000000000000000000000000000002-2
χ6222-2-222-2-2222-2-222-2-2-2-2-2-222-22-2-222-22-222000000000000000000000000000000000000000000-22
χ63444-4-44-44-44400-4-400004-4-4000-44400000000000000000000000000000000000000000000000000
χ64444-4-4-24-44-4-244-2-2-2-2-2-2-222-4-44-2222222-2-200000000000000000000000000000000000000000000
χ65444-4-4-24-44-4-2-4-4-2-22222-22244-4-222-2-2-2-22200000000000000000000000000000000000000000000
χ66444-4-4-2-44-44-200222323−23−23-2220002-2-2−23−23232323−2300000000000000000000000000000000000000000000
χ67444-4-4-2-44-44-20022−23−232323-2220002-2-22323−23−23−232300000000000000000000000000000000000000000000
χ6844-4-44444-4-4400-4-40000-4-4400044-400000000000000000000000000000000000000000000000000
χ6944-4-44-244-4-4-200222323−23−2322-2000-2-22−232323−23−232300000000000000000000000000000000000000000000
χ7044-4-44-244-4-4-20022−23−23232322-2000-2-2223−23−232323−2300000000000000000000000000000000000000000000
χ7144-4-44-2-4-444-244-2-2-2-2-2-222-2-44-422-22-22-22200000000000000000000000000000000000000000000
χ7244-4-44-2-4-444-2-4-4-2-2222222-24-4422-2-22-22-2-200000000000000000000000000000000000000000000
χ738-800080000-8−4i24i200−4i24i2−4i24i200000000000000000000000000000000000000000000000000000000000
χ748-800080000-84i2−4i2004i2−4i24i2−4i200000000000000000000000000000000000000000000000000000000000
χ758-8000-400004−4i24i243−434ζ5+4ζ7−4ζ5−4ζ74ζ13+4ζ23−4ζ13−4ζ2300000000000000000000000000000000000000000000000000000000000
χ768-8000-400004−4i24i2−43434ζ13+4ζ23−4ζ13−4ζ234ζ5+4ζ7−4ζ5−4ζ700000000000000000000000000000000000000000000000000000000000
χ778-8000-4000044i2−4i243−43−4ζ5−4ζ74ζ5+4ζ7−4ζ13−4ζ234ζ13+4ζ2300000000000000000000000000000000000000000000000000000000000
χ788-8000-4000044i2−4i2−4343−4ζ13−4ζ234ζ13+4ζ23−4ζ5−4ζ74ζ5+4ζ700000000000000000000000000000000000000000000000000000000000

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