Finite Group Databasebeta

← Group #10696059

Character table — Group #10696059

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888888888888888242424242424242448484848
order12224444223446661212121244446612121212121212121212444488888888121212121212121224242424242424242424242424242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ922222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-20000000000000000000000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-222220000000000000000000000000000
χ112222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ122222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ132222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ142222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ152222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3000000000000
χ162222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333000000000000
χ172222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333000000000000
χ182222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3000000000000
χ1922222222-2-22-2-222222222-22-2-2-2-2-222-2-222-2-20000000022-2-2000000000000000022-2-222-2-2000000000000
χ2022222222-2-22-2-222222222-22-2-2-2-2-222-2-222-2-200000000-2-2220000000000000000-2-222-2-222000000000000
χ2122222222-2-22-2-22222222-22-22-2-2-2-2-2-222-2-222000022-2-200000000000022-2-222-2-200000000000000000000
χ2222222222-2-22-2-22222222-22-22-2-2-2-2-2-222-2-2220000-2-222000000000000-2-222-2-22200000000000000000000
χ2322222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-111-1-1110000000022-2-233−3−333−3−333−3−3−3−333-1-111-1-111000000000000
χ2422222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-111-1-1110000000022-2-2−3−333−3−333−3−33333−3−3-1-111-1-111000000000000
χ2522222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-111-1-11100000000-2-22233−3−333−3−3−3−33333−3−311-1-111-1-1000000000000
χ2622222222-2-2-1-2-2-1-1-1-1-1-1-12-22-21111-1-111-1-11100000000-2-222−3−333−3−33333−3−3−3−33311-1-111-1-1000000000000
χ2722222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111-1-111-1-1000022-2-2000033−3−3−3−333-1-111-1-111−3−33333−3−3000000000000
χ2822222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111-1-111-1-1000022-2-20000−3−33333−3−3-1-111-1-11133−3−3−3−333000000000000
χ2922222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111-1-111-1-10000-2-222000033−3−3−3−33311-1-111-1-133−3−3−3−333000000000000
χ3022222222-2-2-1-2-2-1-1-1-1-1-1-1-22-22111111-1-111-1-10000-2-2220000−3−33333−3−311-1-111-1-1−3−33333−3−3000000000000
χ312222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-2-2-22200000000000000000000000000000000000022-2-200000000
χ322222-2-2-2-2222-2-2222-2-2-2-22-2-2222-2-222-2-2-2-222000000000000000000000000000000000000-2-22200000000
χ332222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22222-2-2000000000000000000000000000000000000000022-2-20000
χ342222-2-2-2-2222-2-2222-2-2-2-2-222-222-2-2-2-22222-2-20000000000000000000000000000000000000000-2-2220000
χ352222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222222-2-2-2-200000000000000000000000000000000000000000000002i−2i
χ362222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2222222-2-2-2-20000000000000000000000000000000000000000000000−2i2i
χ372222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000000002-200
χ382222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-222-2-2-2-2222200000000000000000000000000000000000000000000-2200
χ3922-2-222-2-22-222-22-2-222-2-200002-22-200000000002-22−22−22−22−200002-22-22−22−22−22−22−22−22−22−2000000000000
χ4022-2-222-2-22-222-22-2-222-2-200002-22-200000000002-2−22−22−22−2200002-22-2−22−22−22−22−22−22−22−22000000000000
χ4122-2-222-2-22-222-22-2-222-2-200002-22-20000000000-222−22−2−22−220000-22-222−22−22−22−2−22−22−22−22000000000000
χ4222-2-222-2-22-222-22-2-222-2-200002-22-20000000000-22−22−222−22−20000-22-22−22−22−22−222−22−22−22−2000000000000
χ4322-2-222-2-22-2-12-2-111-1-1110000-11-113−33−33−33−3002-22−22−22−22−23−33−3-11-11ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ4422-2-222-2-22-2-12-2-111-1-1110000-11-113−33−33−33−3002-2−22−22−22−223−33−3-11-11−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ4522-2-222-2-22-2-12-2-111-1-1110000-11-113−33−33−33−300-222−22−2−22−22−33−331-11-1ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ4622-2-222-2-22-2-12-2-111-1-1110000-11-113−33−33−33−300-22−22−222−22−2−33−331-11-1−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ4722-2-222-2-22-2-12-2-111-1-1110000-11-11−33−33−33−33002-22−22−22−22−2−33−33-11-11ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ4822-2-222-2-22-2-12-2-111-1-1110000-11-11−33−33−33−33002-2−22−22−22−22−33−33-11-11−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ4922-2-222-2-22-2-12-2-111-1-1110000-11-11−33−33−33−3300-222−22−2−22−223−33−31-11-1ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ5022-2-222-2-22-2-12-2-111-1-1110000-11-11−33−33−33−3300-22−22−222−22−23−33−31-11-1−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ5122-2-222-2-2-222-222-2-222-2-20000-22-22000000002-2002−2−222−2−222-2-2200002−2−222−2−222−2−222−2−22000000000000
χ5222-2-222-2-2-222-222-2-222-2-20000-22-22000000002-200−222−2−222−22-2-220000−222−2−222−2−222−2−222−2000000000000
χ5322-2-222-2-2-222-222-2-222-2-20000-22-2200000000-22002−2−22−222−2-222-200002−2−222−2−22−222−2−222−2000000000000
χ5422-2-222-2-2-222-222-2-222-2-20000-22-2200000000-2200−222−22−2−22-222-20000−222−2−222−22−2−222−2−22000000000000
χ5522-2-222-2-2-22-1-22-111-1-11100001-11-13−3−333−3−332-2002−2−222−2−22-111-1−333−3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ5622-2-222-2-2-22-1-22-111-1-11100001-11-13−3−333−3−332-200−222−2−222−2-111-1−333−3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ5722-2-222-2-2-22-1-22-111-1-11100001-11-13−3−333−3−33-22002−2−22−222−21-1-113−3−33ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7000000000000
χ5822-2-222-2-2-22-1-22-111-1-11100001-11-13−3−333−3−33-2200−222−22−2−221-1-113−3−33−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7000000000000
χ5922-2-222-2-2-22-1-22-111-1-11100001-11-1−333−3−333−32-2002−2−222−2−22-111-13−3−33ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ6022-2-222-2-2-22-1-22-111-1-11100001-11-1−333−3−333−32-200−222−2−222−2-111-13−3−33−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ6122-2-222-2-2-22-1-22-111-1-11100001-11-1−333−3−333−3-22002−2−22−222−21-1-11−333−3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23000000000000
χ6222-2-222-2-2-22-1-22-111-1-11100001-11-1−333−3−333−3-2200−222−22−2−221-1-11−333−3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23000000000000
χ634444-4-4-4-444-2-4-4-2-2-222224-4-44-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ644444-4-4-4-444-2-4-4-2-2-22222-444-4-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-4-4-244-2-2-2222244-4-422-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-4-4-244-2-2-22222-4-44422-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ6744-4-4-4-4444-44-444-4-4-4-44400004-4-4400000000000000000000000000000000000000000000000000000000
χ6844-4-4-4-4444-4-2-44-22222-2-20000-222-223−23−2323−232323−23000000000000000000000000000000000000000000000000
χ6944-4-4-4-4444-4-2-44-22222-2-20000-222-2−232323−2323−23−2323000000000000000000000000000000000000000000000000
χ7044-4-4-4-444-4444-44-4-4-4-4440000-444-400000000000000000000000000000000000000000000000000000000
χ7144-4-4-4-444-44-24-4-22222-2-200002-2-2223−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ7244-4-4-4-444-44-24-4-22222-2-200002-2-22−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ734-44-44i−4i4i−4i00400-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000002-22i−2i00000000
χ744-44-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000-22−2i2i00000000
χ754-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000002-2−2i2i00000000
χ764-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000-222i−2i00000000
χ774-4-444i−4i−4i4i00400-4-444i−4i−4i4i000000000000000000000000000000000000000000000000000000002i−2i2-20000
χ784-4-444i−4i−4i4i00400-4-444i−4i−4i4i00000000000000000000000000000000000000000000000000000000−2i2i-220000
χ794-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000002i−2i-220000
χ804-4-44−4i4i4i−4i00400-4-44−4i4i4i−4i00000000000000000000000000000000000000000000000000000000−2i2i2-20000
χ818-88-88i−8i8i−8i00-4004-44−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ828-88-8−8i8i−8i8i00-4004-444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ838-8-888i−8i−8i8i00-40044-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ848-8-88−8i8i8i−8i00-40044-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000

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