Finite Group Databasebeta

← Group #10698541

Character table — Group #10698541

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888888888888888242424242424242448484848
order12222222222236666666444466661212121212121212444488888888121212121212121224242424242424242424242424242424444444444444
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
χ5111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
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
χ11222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ12222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000000000000
χ13222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ14222222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1000000000000
χ15222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−3000000000000
χ16222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−33333000000000000
χ17222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−33333000000000000
χ18222222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3000000000000
χ1922222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000000020-20
χ2022222222-2-2-2-2222222222-22-2-2-2-2-222-2-222-2-200000000000000000000000000000000000000000000-2020
χ2122222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000020-2
χ2222222222-2-2-2-222222222-22-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000000-202
χ232222-2-2-2-222-2-2222-2-22-2-2000022-2-200000000002-222−2−222−2−2000022-2-222−2−222−2−222−2−222−2−2000000000000
χ242222-2-2-2-222-2-2222-2-22-2-2000022-2-200000000002-2−2−222−2−222000022-2-2−2−222−2−222−2−222−2−222000000000000
χ252222-2-2-2-222-2-2222-2-22-2-2000022-2-20000000000-2222−2−2−2−2220000-2-22222−2−222−2−2−2−222−2−222000000000000
χ262222-2-2-2-222-2-2222-2-22-2-2000022-2-20000000000-22−2−22222−2−20000-2-222−2−222−2−22222−2−222−2−2000000000000
χ272222-2-2-2-222-2-2-1-1-111-1110000-1-1113−33−33−33−3002-222−2−222−2−233−3−3-1-111ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ282222-2-2-2-222-2-2-1-1-111-1110000-1-1113−33−33−33−3002-2−2−222−2−22233−3−3-1-111−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ292222-2-2-2-222-2-2-1-1-111-1110000-1-1113−33−33−33−300-2222−2−2−2−222−3−33311-1-1ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000000
χ302222-2-2-2-222-2-2-1-1-111-1110000-1-1113−33−33−33−300-22−2−22222−2−2−3−33311-1-1−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000000
χ312222-2-2-2-222-2-2-1-1-111-1110000-1-111−33−33−33−33002-222−2−222−2−2−3−333-1-111ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ322222-2-2-2-222-2-2-1-1-111-1110000-1-111−33−33−33−33002-2−2−222−2−222−3−333-1-111−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ332222-2-2-2-222-2-2-1-1-111-1110000-1-111−33−33−33−3300-2222−2−2−2−22233−3−311-1-1ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000000
χ342222-2-2-2-222-2-2-1-1-111-1110000-1-111−33−33−33−3300-22−2−22222−2−233−3−311-1-1−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000000
χ3522-2-222-2-22-2-2222-22-2-22-200002-22-2000000002-200−i2i2−i2i2−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-2-222-2-22-2-2222-22-2-22-200002-22-2000000002-200i2−i2i2−i2i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3722-2-222-2-22-2-2222-22-2-22-200002-22-200000000-2200−i2i2−i2i2i2−i2i2−i2-22-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-222-2-22-2-2222-22-2-22-200002-22-200000000-2200i2−i2i2−i2−i2i2−i2i2-22-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-222-2-22-2-22-1-11-111-110000-11-113−3−33−333−32-200−i2i2−i2i2−i2i2−i2i2-11-113−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ4022-2-222-2-22-2-22-1-11-111-110000-11-113−3−33−333−32-200i2−i2i2−i2i2−i2i2−i2-11-113−33−3−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ4122-2-222-2-22-2-22-1-11-111-110000-11-113−3−33−333−3-2200−i2i2−i2i2i2−i2i2−i21-11-1−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7000000000000
χ4222-2-222-2-22-2-22-1-11-111-110000-11-113−3−33−333−3-2200i2−i2i2−i2−i2i2−i2i21-11-1−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7000000000000
χ4322-2-222-2-22-2-22-1-11-111-110000-11-11−333−33−3−332-200−i2i2−i2i2−i2i2−i2i2-11-11−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ4422-2-222-2-22-2-22-1-11-111-110000-11-11−333−33−3−332-200i2−i2i2−i2i2−i2i2−i2-11-11−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ4522-2-222-2-22-2-22-1-11-111-110000-11-11−333−33−3−33-2200−i2i2−i2i2i2−i2i2−i21-11-13−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23000000000000
χ4622-2-222-2-22-2-22-1-11-111-110000-11-11−333−33−3−33-2200i2−i2i2−i2−i2i2−i2i21-11-13−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23000000000000
χ4722-2-2-2-2222-22-222-2-22-2-222-2-222-2-2222-2-2-2-22200002i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ4822-2-2-2-2222-22-222-2-22-2-222-2-222-2-2222-2-2-2-2220000−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ4922-2-2-2-2222-22-222-2-22-2-22-222-22-2-22-2-22222-2-2000000002i−2i−2i2i00000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ5022-2-2-2-2222-22-222-2-22-2-22-222-22-2-22-2-22222-2-200000000−2i2i2i−2i0000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ5122-2-2-2-2222-22-2-1-111-111-12-2-22-111-1-1-11111-1-100002i−2i−2i2i00003−3−33−333−3−iii−i−iii−i−i3i3i3−i3i3−i3−i3i3000000000000
χ5222-2-2-2-2222-22-2-1-111-111-12-2-22-111-1-1-11111-1-100002i−2i−2i2i0000−333−33−3−33−iii−i−iii−ii3−i3−i3i3−i3i3i3−i3000000000000
χ5322-2-2-2-2222-22-2-1-111-111-12-2-22-111-1-1-11111-1-10000−2i2i2i−2i00003−3−33−333−3i−i−iii−i−iii3−i3−i3i3−i3i3i3−i3000000000000
χ5422-2-2-2-2222-22-2-1-111-111-12-2-22-111-1-1-11111-1-10000−2i2i2i−2i0000−333−33−3−33i−i−iii−i−ii−i3i3i3−i3i3−i3−i3i3000000000000
χ5522-2-2-2-2222-22-2-1-111-111-1-222-2-111-111-1-1-1-111000000002i−2i−2i2i3−3−333−3−33i3−i3−i3i3−i3i3i3−i3−iii−i−iii−i000000000000
χ5622-2-2-2-2222-22-2-1-111-111-1-222-2-111-111-1-1-1-111000000002i−2i−2i2i−333−3−333−3−i3i3i3−i3i3−i3−i3i3−iii−i−iii−i000000000000
χ5722-2-2-2-2222-22-2-1-111-111-1-222-2-111-111-1-1-1-11100000000−2i2i2i−2i3−3−333−3−33−i3i3i3−i3i3−i3−i3i3i−i−iii−i−ii000000000000
χ5822-2-2-2-2222-22-2-1-111-111-1-222-2-111-111-1-1-1-11100000000−2i2i2i−2i−333−3−333−3i3−i3−i3i3−i3i3i3−i3i−i−iii−i−ii000000000000
χ5922-2-2-2-222-22-2222-2-22-2-2222-2-2-222-22222-2-2-2-20000000000000000000000000000000000002i2i−2i−2i00000000
χ6022-2-2-2-222-22-2222-2-22-2-2222-2-2-222-22222-2-2-2-2000000000000000000000000000000000000−2i−2i2i2i00000000
χ6122-2-2-2-222-22-2222-2-22-2-22-2-222-222-2-2-2-2-22222000000000000000000000000000000000000000022-2-20000
χ6222-2-2-2-222-22-2222-2-22-2-22-2-222-222-2-2-2-2-222220000000000000000000000000000000000000000-2-2220000
χ6344444444-4-4-4-4-2-2-2-2-2-2-2-24-44-42222-2-222-2-222000000000000000000000000000000000000000000000000
χ6444444444-4-4-4-4-2-2-2-2-2-2-2-2-44-44222222-2-222-2-2000000000000000000000000000000000000000000000000
χ654444-4-4-4-4-4-444444-4-44-4-40000-4-44400000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-4-444-2-2-222-222000022-2-223−23−232323−23−2323000000000000000000000000000000000000000000000000
χ674444-4-4-4-4-4-444-2-2-222-222000022-2-2−232323−23−232323−23000000000000000000000000000000000000000000000000
χ6844-4-444-4-4-444-444-44-4-44-40000-44-4400000000000000000000000000000000000000000000000000000000
χ6944-4-444-4-4-444-4-2-22-222-2200002-22-223−2323−23−2323−2323000000000000000000000000000000000000000000000000
χ7044-4-444-4-4-444-4-2-22-222-2200002-22-2−2323−232323−2323−23000000000000000000000000000000000000000000000000
χ7144-4-4-4-444-44-44-2-222-222-244-4-42-2-22-2-2-2-22222000000000000000000000000000000000000000000000000
χ7244-4-4-4-444-44-44-2-222-222-2-4-4442-2-222222-2-2-2-2000000000000000000000000000000000000000000000000
χ734-44-44-4-4400004-44-4-4-44400000000000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ744-44-44-4-4400004-44-4-4-4440000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ754-44-4-444-400004-4444-4-4-4000000000000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ764-44-4-444-400004-4444-4-4-400000000000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ774-4-444-44-400004-4-4-4444-4000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ784-4-444-44-400004-4-4-4444-400000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ794-4-44-44-4400004-4-44-44-4400000000000000000000000000000000000000000000000000002-2-2200000000
χ804-4-44-44-4400004-4-44-44-440000000000000000000000000000000000000000000000000000-222-200000000
χ818-88-88-8-880000-44-4444-4-40000000000000000000000000000000000000000000000000000000000000000
χ828-88-8-888-80000-44-4-4-44440000000000000000000000000000000000000000000000000000000000000000
χ838-8-888-88-80000-4444-4-4-440000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-88-880000-444-44-44-40000000000000000000000000000000000000000000000000000000000000000

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