Finite Group Databasebeta

← Group #10698831

Character table — Group #10698831

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212124444888888881212121212121212242424242424242424242424242424248888448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111
χ9222222222-2-222222-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000
χ10222222222-2-222222-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000
χ112222222-2-222-2-22222222-22-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i
χ122222222-2-222-2-22222222-22-22222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i
χ132222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-2-2-222220000000000000000000000000000000000000000002i−2i00
χ142222222-2-2-2-2-2-2222-2-2-2-22-2222-2-2-2-2-2-22222000000000000000000000000000000000000000000−2i2i00
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000
χ19222222-122-2-222-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−30000000000
χ20222222-122-2-222-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−333330000000000
χ21222222-122-2-222-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−333330000000000
χ22222222-122-2-222-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−30000000000
χ232222-2-222-2222-22222222-2-22-2-2-2-222-2-2-2-222000022-2-200000000000022-2-222-2-2000000000000000000
χ242222-2-222-2222-22222222-2-22-2-2-2-222-2-2-2-2220000-2-222000000000000-2-222-2-222000000000000000000
χ252222-2-222-2-2-22-2222-2-2-2-222-2-2-22222-2-222-2-2000000002i2i−2i−2i00000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ262222-2-222-2-2-22-2222-2-2-2-222-2-2-22222-2-222-2-200000000−2i−2i2i2i0000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ272222-2-22-2222-2222222222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000022-2-2000000
χ282222-2-22-2222-2222222222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000-2-222000000
χ292222-2-22-22-2-2-22222-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000000000002-20000
χ302222-2-22-22-2-2-22222-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000-220000
χ312222-2-2-12-2222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-1000022-2-20000−i3−i3i3i3−i3−i3i3i3-1-111-1-111−i3−i3i3i3i3i3−i3−i30000000000
χ322222-2-2-12-2222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-1000022-2-20000i3i3−i3−i3i3i3−i3−i3-1-111-1-111i3i3−i3−i3−i3−i3i3i30000000000
χ332222-2-2-12-2222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000-2-2220000−i3−i3i3i3−i3−i3i3i311-1-111-1-1i3i3−i3−i3−i3−i3i3i30000000000
χ342222-2-2-12-2222-2-1-1-1-1-1-1-1-2-221111-1-11111-1-10000-2-2220000i3i3−i3−i3i3i3−i3−i311-1-111-1-1−i3−i3i3i3i3i3−i3−i30000000000
χ352222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-1-111000000002i2i−2i−2i−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−iii−i−iii0000000000
χ362222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-1-111000000002i2i−2i−2ii3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−iii−i−iii0000000000
χ372222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-1-11100000000−2i−2i2i2i−i3−i3i3i3i3i3−i3−i3−3−33333−3−3ii−i−iii−i−i0000000000
χ382222-2-2-12-2-2-22-2-1-1-1111122-211-1-1-1-111-1-11100000000−2i−2i2i2ii3i3−i3−i3−i3−i3i3i333−3−3−3−333ii−i−iii−i−i0000000000
χ3922-2-22-222200-2-2-22-200000002-2002-22-20000002-22−22−22−22−200002-22-22−22−22−22−22−22−22−22−20000000000
χ4022-2-22-222200-2-2-22-200000002-2002-22-20000002-2−22−22−22−2200002-22-2−22−22−22−22−22−22−22−220000000000
χ4122-2-22-222200-2-2-22-200000002-2002-22-2000000-222−22−2−22−220000-22-222−22−22−22−2−22−22−22−220000000000
χ4222-2-22-222200-2-2-22-200000002-2002-22-2000000-22−22−222−22−20000-22-22−22−22−22−222−22−22−22−20000000000
χ4322-2-22-2-12200-2-21-1133−3−3000-113−3-11-113−33−3002-22−22−22−22−23−33−3-11-11ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ4422-2-22-2-12200-2-21-1133−3−3000-113−3-11-113−33−3002-2−22−22−22−223−33−3-11-11−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ4522-2-22-2-12200-2-21-1133−3−3000-113−3-11-113−33−300-222−22−2−22−22−33−331-11-1ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000
χ4622-2-22-2-12200-2-21-1133−3−3000-113−3-11-113−33−300-22−22−222−22−2−33−331-11-1−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000
χ4722-2-22-2-12200-2-21-11−3−333000-11−33-11-11−33−33002-22−22−22−22−2−33−33-11-11ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ4822-2-22-2-12200-2-21-11−3−333000-11−33-11-11−33−33002-2−22−22−22−22−33−33-11-11−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ4922-2-22-2-12200-2-21-11−3−333000-11−33-11-11−33−3300-222−22−2−22−223−33−31-11-1ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000
χ5022-2-22-2-12200-2-21-11−3−333000-11−33-11-11−33−3300-22−22−222−22−23−33−31-11-1−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000
χ5122-2-2-2222-200-22-22-20000000-22002-2-2200002i−2i002−2−22−i2i2i2−i22i−2i−2i2i00002−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000
χ5222-2-2-2222-200-22-22-20000000-22002-2-2200002i−2i00−222−2i2−i2−i2i22i−2i−2i2i0000−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000
χ5322-2-2-2222-200-22-22-20000000-22002-2-220000−2i2i002−2−22i2−i2−i2i2−2i2i2i−2i00002−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000
χ5422-2-2-2222-200-22-22-20000000-22002-2-220000−2i2i00−222−2−i2i2i2−i2−2i2i2i−2i0000−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000
χ5522-2-2-22-12-200-221-1133−3−30001-1−33-111-1−333−32i−2i002−2−22−i2i2i2−i2−iii−i−i3i3i3−i3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ5622-2-2-22-12-200-221-1133−3−30001-1−33-111-1−333−32i−2i00−222−2i2−i2−i2i2−iii−i−i3i3i3−i3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ5722-2-2-22-12-200-221-1133−3−30001-1−33-111-1−333−3−2i2i002−2−22i2−i2−i2i2i−i−iii3−i3−i3i3ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ70000000000
χ5822-2-2-22-12-200-221-1133−3−30001-1−33-111-1−333−3−2i2i00−222−2−i2i2i2−i2i−i−iii3−i3−i3i3−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ70000000000
χ5922-2-2-22-12-200-221-11−3−3330001-13−3-111-13−3−332i−2i002−2−22−i2i2i2−i2−iii−ii3−i3−i3i3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ6022-2-2-22-12-200-221-11−3−3330001-13−3-111-13−3−332i−2i00−222−2i2−i2−i2i2−iii−ii3−i3−i3i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ6122-2-2-22-12-200-221-11−3−3330001-13−3-111-13−3−33−2i2i002−2−22i2−i2−i2i2i−i−ii−i3i3i3−i3ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ230000000000
χ6222-2-2-22-12-200-221-11−3−3330001-13−3-111-13−3−33−2i2i00−222−2−i2i2i2−i2i−i−ii−i3i3i3−i3−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ230000000000
χ63444444-2-4-444-4-4-2-2-2-2-2-2-2-44-4-2-2-2-2222222220000000000000000000000000000000000000000000000
χ64444444-2-4-4-4-4-4-4-2-2-222224-44-2-2222222-2-2-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4444-44-2-2-2-2-2-2-24-4-4222222-2-2-2-2220000000000000000000000000000000000000000000000
χ664444-4-4-2-44-4-4-44-2-2-22222-44422-2-222-2-222-2-20000000000000000000000000000000000000000000000
χ6744-4-44-44-4-40044-44-400000004-400-44-4400000000000000000000000000000000000000000000000000
χ6844-4-44-4-2-4-400442-222323−23−23000-2223−232-22-2−2323−23230000000000000000000000000000000000000000000000
χ6944-4-44-4-2-4-400442-22−23−232323000-22−23232-22-223−2323−230000000000000000000000000000000000000000000000
χ7044-4-4-444-44004-4-44-40000000-4400-444-400000000000000000000000000000000000000000000000000
χ7144-4-4-44-2-44004-42-222323−23−230002-2−23232-2-2223−23−23230000000000000000000000000000000000000000000000
χ7244-4-4-44-2-44004-42-22−23−2323230002-223−232-2-22−232323−230000000000000000000000000000000000000000000000
χ734-4-44004004-4004-4-44-44-400000000000000000000000000000000000000000000000000000−2i22i2000000
χ744-4-44004004-4004-4-44-44-4000000000000000000000000000000000000000000000000000002i2−2i2000000
χ754-4-4400400-44004-4-4-44-44000000000000000000000000000000000000000000000000000−2i22i200000000
χ764-4-4400400-44004-4-4-44-440000000000000000000000000000000000000000000000000002i2−2i200000000
χ778-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ788-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000
χ798-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-4008-800-444-44-440000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-400-8800-4444-44-40000000000000000000000000000000000000000000000000000000000000

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