Finite Group Databasebeta

← Group #10714073

Character table — Group #10714073

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222222222222222224444444444444448888888888888888888888888888888888884848484848484848
order12222344446881212242424246668881212122424242424244488121212121616161616161616242424244848484848484848484848484848484822224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-11-1-1
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-11-111
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
χ31222-2-222-22-22222222222-2-2-2-222-2-2-2-2-2-22200000000000000000000000000000000000000020-200
χ32222-2-222-22-22222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000000000000000000-20200
χ33222-2-222-22-22-2-222-2-2-2-22-2-222-22-2-22222-2-20000000000000000000000000000000000000000002i−2i
χ34222-2-222-22-22-2-222-2-2-2-22-2-222-22-2-22222-2-2000000000000000000000000000000000000000000−2i2i
χ3522-22-22-2-222222222222-2-222-2-2-2-222-22-2-2-20000000000000000000000000000000000000020-2000
χ3622-22-22-2-222222222222-2-222-2-2-2-222-22-2-2-200000000000000000000000000000000000000-202000
χ3722-22-22-2-2222-2-222-2-2-2-2-2-22-222-2-22-22-22220000000000000000000000000000000000002-2000000
χ3822-22-22-2-2222-2-222-2-2-2-2-2-22-222-2-22-22-2222000000000000000000000000000000000000-22000000
χ3922-2-2222-2-22200-2-20000-22-20002-22000000002-200002−22−22−22−22-22-22−22−22−22−22−22−22−22−200000000
χ4022-2-2222-2-22200-2-20000-22-20002-22000000002-20000−22−22−22−222-22-2−22−22−22−22−22−22−22−2200000000
χ4122-2-2222-2-22200-2-20000-22-20002-2200000000-2200002−22−2−22−22-22-222−22−22−22−2−22−22−22−2200000000
χ4222-2-2222-2-22200-2-20000-22-20002-2200000000-220000−22−222−22−2-22-22−22−22−22−222−22−22−22−200000000
χ4322-2-222-222-2222222222-22-2-22-2-22-2-22-22-2-2000000002-2-22000000002-22-2-22-220000000000000000
χ4422-2-222-222-2222222222-22-2-22-2-22-2-22-22-2-200000000-222-200000000-22-222-22-20000000000000000
χ4522-2-222-222-22-2-222-2-2-2-2-22-22-22-22-22-22-2220000000000002-2-220000000000002-22-2-22-2200000000
χ4622-2-222-222-22-2-222-2-2-2-2-22-22-22-22-22-22-222000000000000-222-2000000000000-22-222-22-200000000
χ4722-2-22-12-2-22-1001133−3−31-11000-11-1−333−3−33002-23−33−32−22−22−22−2-11-11ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ4822-2-22-12-2-22-1001133−3−31-11000-11-1−333−3−33002-23−33−3−22−22−22−22-11-11−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ4922-2-22-12-2-22-1001133−3−31-11000-11-1−333−3−3300-22−33−332−22−2−22−221-11-1ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ5022-2-22-12-2-22-1001133−3−31-11000-11-1−333−3−3300-22−33−33−22−222−22−21-11-1−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ5122-2-22-12-2-22-10011−3−3331-11000-11-13−3−333−3002-2−33−332−22−22−22−2-11-11ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ5222-2-22-12-2-22-10011−3−3331-11000-11-13−3−333−3002-2−33−33−22−22−22−22-11-11−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ5322-2-22-12-2-22-10011−3−3331-11000-11-13−3−333−300-223−33−32−22−2−22−221-11-1ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ5422-2-22-12-2-22-10011−3−3331-11000-11-13−3−333−300-223−33−3−22−222−22−21-11-1−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ5522-2-22-1-222-2-122-1-1-1-1-1-11-11-22-21-111-11-11100003−3−332-2-220000−333−3-11-111-11-1−333−33−3−3300000000
χ5622-2-22-1-222-2-122-1-1-1-1-1-11-11-22-21-111-11-11100003−3−33-222-20000−333−31-11-1-11-113−3−33−333−300000000
χ5722-2-22-1-222-2-122-1-1-1-1-1-11-11-22-21-111-11-1110000−333−32-2-2200003−3−33-11-111-11-13−3−33−333−300000000
χ5822-2-22-1-222-2-122-1-1-1-1-1-11-11-22-21-111-11-1110000−333−3-222-200003−3−331-11-1-11-11−333−33−3−3300000000
χ5922-2-22-1-222-2-1-2-2-1-111111-112-221-11-11-11-1-100003−3−3300002-2-223−3−333−3−33−333−3-11-111-11-100000000
χ6022-2-22-1-222-2-1-2-2-1-111111-112-221-11-11-11-1-100003−3−330000-222-23−3−33−333−33−3−331-11-1-11-1100000000
χ6122-2-22-1-222-2-1-2-2-1-111111-112-221-11-11-11-1-10000−333−300002-2-22−333−3−333−33−3−33-11-111-11-100000000
χ6222-2-22-1-222-2-1-2-2-1-111111-112-221-11-11-11-1-10000−333−30000-222-2−333−33−3−33−333−31-11-1-11-1100000000
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
χ6844-44-4444-4-4400-4-40000-4-4400044-400000000000000000000000000000000000000000000000000
χ6944-44-4-244-4-4-200222323−23−2322-2000-2-2223−23−2323−232300000000000000000000000000000000000000000000
χ7044-44-4-244-4-4-20022−23−23232322-2000-2-22−232323−2323−2300000000000000000000000000000000000000000000
χ7144-44-4-2-4-444-244-2-2-2-2-2-222-24-4-422-2-22-222200000000000000000000000000000000000000000000
χ7244-44-4-2-4-444-2-4-4-2-2222222-2-44422-22-22-2-2-200000000000000000000000000000000000000000000
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.