Finite Group Databasebeta

← Group #10697476

Character table — Group #10697476

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888888888888888884848484848484848
order12222234444666121212124444661212121212121212121288888888888824242424242424242424242424242424242424242424242424444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1
χ61111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-111-1-1
χ9222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000
χ112222222-2-2-2-2222-2-2-2-22-22-222-2-222-2-222-2-20000000022-2-200000000000000002222-2-2-2-200000000
χ122222222-2-2-2-2222-2-2-2-22-22-222-2-222-2-222-2-200000000-2-2220000000000000000-2-2-2-2222200000000
χ132222222-2-2-2-2222-2-2-2-2-22-2222-2-2-2-222-2-222000022-2-20000000000002222-2-2-2-20000000000000000
χ142222222-2-2-2-2222-2-2-2-2-22-2222-2-2-2-222-2-2220000-2-222000000000000-2-2-2-222220000000000000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000
χ19222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-1111133−3−333−3−333−3−333−3−300000000
χ20222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-2-200000000-1-1-1-11111−3−333−3−333−3−333−3−33300000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-133−3−333−3−3−3−333−3−33300000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-222000000001111-1-1-1-1−3−333−3−33333−3−333−3−300000000
χ23222222-1-2-2-2-2-1-1-111112-22-2-1-111-1-111-1-1110000000022-2-233−3−333−3−333−3−3−3−333-1-1-1-1111100000000
χ24222222-1-2-2-2-2-1-1-111112-22-2-1-111-1-111-1-1110000000022-2-2−3−333−3−333−3−33333−3−3-1-1-1-1111100000000
χ25222222-1-2-2-2-2-1-1-111112-22-2-1-111-1-111-1-11100000000-2-22233−3−333−3−3−3−33333−3−31111-1-1-1-100000000
χ26222222-1-2-2-2-2-1-1-111112-22-2-1-111-1-111-1-11100000000-2-222−3−333−3−33333−3−3−3−3331111-1-1-1-100000000
χ27222222-1-2-2-2-2-1-1-11111-22-22-1-11111-1-111-1-1000022-2-2000033−3−3−3−333-1-1-1-11111−3−33333−3−300000000
χ28222222-1-2-2-2-2-1-1-11111-22-22-1-11111-1-111-1-1000022-2-20000−3−33333−3−3-1-1-1-1111133−3−3−3−33300000000
χ29222222-1-2-2-2-2-1-1-11111-22-22-1-11111-1-111-1-10000-2-222000033−3−3−3−3331111-1-1-1-133−3−3−3−33300000000
χ30222222-1-2-2-2-2-1-1-11111-22-22-1-11111-1-111-1-10000-2-2220000−3−33333−3−31111-1-1-1-1−3−33333−3−300000000
χ312222-2-2222-2-2222-2-2-2-222-2-2-2-2222222-2-2-2-20000000000000000000000000000000000000000002i−2i
χ322222-2-2222-2-2222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000000000000000000000000000−2i2i
χ332222-2-2222-2-2222-2-2-2-2-2-222-2-222-2-2-2-2222200000000000000000000000000000000000000002-200
χ342222-2-2222-2-2222-2-2-2-2-2-222-2-222-2-2-2-222220000000000000000000000000000000000000000-2200
χ352222-2-22-2-22222222222-2-22-2-2-2-222-2-2-2-222000000000000000000000000000000000000200-20000
χ362222-2-22-2-22222222222-2-22-2-2-2-222-2-2-2-222000000000000000000000000000000000000-20020000
χ372222-2-22-2-2222222222-222-2-2-2-2-2-2-22222-2-200000000000000000000000000000000000002-200000
χ382222-2-22-2-2222222222-222-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000000-2200000
χ392-2-222-222-22-22-2-222-2-200002-22-200000000002i−2i2−22−2−i2i2−i2i200002i−2i2i−2i2−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ402-2-222-222-22-22-2-222-2-200002-22-200000000002i−2i−22−22i2−i2i2−i200002i−2i2i−2i−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ412-2-222-222-22-22-2-222-2-200002-22-20000000000−2i2i2−22−2i2−i2i2−i20000−2i2i−2i2i2−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ422-2-222-222-22-22-2-222-2-200002-22-20000000000−2i2i−22−22−i2i2−i2i20000−2i2i−2i2i−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ432-2-222-22-22-222-2-2-2-22200002-2-22000000002i−2i002−2−22−i2i2i2−i22i−2i2i−2i00002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ442-2-222-22-22-222-2-2-2-22200002-2-22000000002i−2i00−222−2i2−i2−i2i22i−2i2i−2i0000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ452-2-222-22-22-222-2-2-2-22200002-2-2200000000−2i2i002−2−22i2−i2−i2i2−2i2i−2i2i00002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ462-2-222-22-22-222-2-2-2-22200002-2-2200000000−2i2i00−222−2−i2i2i2−i2−2i2i−2i2i0000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ472-2-222-2-12-22-2-111-1-1110000-11-113−33−33−33−3002i−2i2−22−2−i2i2−i2i2−i3i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ482-2-222-2-12-22-2-111-1-1110000-11-113−33−33−33−3002i−2i−22−22i2−i2i2−i2−i3i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ492-2-222-2-12-22-2-111-1-1110000-11-113−33−33−33−300−2i2i2−22−2i2−i2i2−i2i3−i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ502-2-222-2-12-22-2-111-1-1110000-11-113−33−33−33−300−2i2i−22−22−i2i2−i2i2i3−i3−i3i3i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ512-2-222-2-12-22-2-111-1-1110000-11-11−33−33−33−33002i−2i2−22−2−i2i2−i2i2i3−i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ522-2-222-2-12-22-2-111-1-1110000-11-11−33−33−33−33002i−2i−22−22i2−i2i2−i2i3−i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ532-2-222-2-12-22-2-111-1-1110000-11-11−33−33−33−3300−2i2i2−22−2i2−i2i2−i2−i3i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ542-2-222-2-12-22-2-111-1-1110000-11-11−33−33−33−3300−2i2i−22−22−i2i2−i2i2−i3i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ552-2-222-2-1-22-22-11111-1-10000-111-13−3−333−3−332i−2i002−2−22−i2i2i2−i2−ii−iii3−i3−i3i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ562-2-222-2-1-22-22-11111-1-10000-111-13−3−333−3−332i−2i00−222−2i2−i2−i2i2−ii−iii3−i3−i3i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ572-2-222-2-1-22-22-11111-1-10000-111-13−3−333−3−33−2i2i002−2−22i2−i2−i2i2i−ii−i−i3i3i3−i3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ582-2-222-2-1-22-22-11111-1-10000-111-13−3−333−3−33−2i2i00−222−2−i2i2i2−i2i−ii−i−i3i3i3−i3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ592-2-222-2-1-22-22-11111-1-10000-111-1−333−3−333−32i−2i002−2−22−i2i2i2−i2−ii−ii−i3i3i3−i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ602-2-222-2-1-22-22-11111-1-10000-111-1−333−3−333−32i−2i00−222−2i2−i2−i2i2−ii−ii−i3i3i3−i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ612-2-222-2-1-22-22-11111-1-10000-111-1−333−3−333−3−2i2i002−2−22i2−i2−i2i2i−ii−ii3−i3−i3i3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ622-2-222-2-1-22-22-11111-1-10000-111-1−333−3−333−3−2i2i00−222−2−i2i2i2−i2i−ii−ii3−i3−i3i3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ634444-4-4-244-4-4-2-2-2222244-4-422-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-2-2-22222-4-44422-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ654444-4-4-2-4-444-2-2-2-2-2-2-24-4-442222-2-22222-2-200000000000000000000000000000000000000000000
χ664444-4-4-2-4-444-2-2-2-2-2-2-2-444-4222222-2-2-2-22200000000000000000000000000000000000000000000
χ674-4-44-4444-4-444-4-4-4-4440000-444-40000000000000000000000000000000000000000000000000000
χ684-4-44-444-444-44-4-444-4-40000-44-440000000000000000000000000000000000000000000000000000
χ694-4-44-44-24-4-44-22222-2-200002-2-2223−2323−23−2323−232300000000000000000000000000000000000000000000
χ704-4-44-44-24-4-44-22222-2-200002-2-22−2323−232323−2323−2300000000000000000000000000000000000000000000
χ714-4-44-44-2-444-4-222-2-22200002-22-223−23−2323−232323−2300000000000000000000000000000000000000000000
χ724-4-44-44-2-444-4-222-2-22200002-22-2−232323−2323−23−232300000000000000000000000000000000000000000000
χ7388-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000
χ7488-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000
χ7588-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000
χ768-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000000
χ778-88-800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000
χ788-88-800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000

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