Finite Group Databasebeta

← Group #10691914

Character table — Group #10691914

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466666664444444412121212121212121212121222224444446666666612121212121212121212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-1111-1-1111-1-1-1-11-1ii−i−i1-111-1-1iiii−i−i−i−i11-1-1i−iii−i−i1111-1-1-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111-1-1111-1-1111-1-1-1-11-1ii−i−i1-111-1-1iiii−i−i−i−i11-1-1i−iii−i−i1111-1-1-1-111-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111-1-1111-1-1111-1-1-1-11-1ii−i−i1-111-1-1iiii−i−i−i−i-1-111i−i−i−iii-1-1-1-1111111-1-1ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ121111-1-1111-1-1111-1-1-1-11-1ii−i−i1-111-1-1iiii−i−i−i−i-1-111i−i−i−iii-1-1-1-1111111-1-1ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ131111-1-1111-1-1111-1-1-1-11-1−i−iii1-111-1-1−i−i−i−iiiii11-1-1−ii−i−iii1111-1-1-1-111-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ141111-1-1111-1-1111-1-1-1-11-1−i−iii1-111-1-1−i−i−i−iiiii11-1-1−ii−i−iii1111-1-1-1-111-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ151111-1-1111-1-1111-1-1-1-11-1−i−iii1-111-1-1−i−i−i−iiiii-1-111−iiii−i−i-1-1-1-1111111-1-1−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111-1-1111-1-1111-1-1-1-11-1−i−iii1-111-1-1−i−i−i−iiiii-1-111−iiii−i−i-1-1-1-1111111-1-1−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ17222222222222222222-2-22222-2-22222222222220000-2-2000000000000-2-2-2-2-2-2-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000022000000000000-2-2-2-2222200000000000000000000
χ192222222-2-2-2-222222222-20000-22-2-2-2-2000000000000002-22-2000000002-22-2000022-2-222-2-2000000000000
χ202222222-2-2-2-222222222-20000-22-2-2-2-200000000000000-22-22000000002-22-20000-2-222-2-222000000000000
χ212222222-2-2-2-22222222-2200002-2-2-2-2-2000000002-22-200000022-2-222-2-2-22-22000000000000000000000000
χ222222222-2-2-2-22222222-2200002-2-2-2-2-200000000-22-22000000-2-222-2-222-22-22000000000000000000000000
χ23222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-111111111000000000000
χ25222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1111111112222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000
χ26222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-2-2-2-2-2222211111111-1-1-1-11111-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000−i3i3−i3i3−i3i3−i3i311111111−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000i3−i3i3−i3i3−i3i3−i311111111i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000220000−i3i3−i3i3−i3i3−i3i31111-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111110000220000i3−i3i3−i3i3−i3i3−i31111-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-12-20000-221111−i3−i3i3i3−i3−i3i3i30000002-22-2−i3i3i3−i3−i3i3i3−i3-11-11−i3i3−i3i3-1-111-1-111000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-12-20000-221111−i3−i3i3i3−i3−i3i3i3000000-22-22i3−i3−i3i3i3−i3−i3i3-11-11−i3i3−i3i311-1-111-1-1000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-12-20000-221111i3i3−i3−i3i3i3−i3−i30000002-22-2i3−i3−i3i3i3−i3−i3i3-11-11i3−i3i3−i3-1-111-1-111000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-12-20000-221111i3i3−i3−i3i3i3−i3−i3000000-22-22−i3i3i3−i3−i3i3i3−i3-11-11i3−i3i3−i311-1-111-1-1000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-2200002-21111−i3−i3i3i3−i3−i3i3i32-22-2000000-1-111-1-1111-11-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-2200002-21111−i3−i3i3i3−i3−i3i3i3-22-2200000011-1-111-1-11-11-1i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000
χ37222222-1-2-2-2-2-1-1-1-1-1-1-1-2200002-21111i3i3−i3−i3i3i3−i3−i32-22-2000000-1-111-1-1111-11-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000
χ38222222-1-2-2-2-2-1-1-1-1-1-1-1-2200002-21111i3i3−i3−i3i3i3−i3−i3-22-2200000011-1-111-1-11-11-1−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3000000000000
χ392222-2-2222-2-2222-2-2-2-2-222i2i−2i−2i-2222-2-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000000000-2-222−2i−2i2i2i00000000000000000000
χ402222-2-2222-2-2222-2-2-2-2-22−2i−2i2i2i-2222-2-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000000000-2-2222i2i−2i−2i00000000000000000000
χ412222-2-22-2-222222-2-2-2-2220000-2-2-2-222000000000000002i−2i−2i2i000000002-2-2200002i2i−2i−2i−2i−2i2i2i000000000000
χ422222-2-22-2-222222-2-2-2-2220000-2-2-2-22200000000000000−2i2i2i−2i000000002-2-220000−2i−2i2i2i2i2i−2i−2i000000000000
χ432222-2-22-2-222222-2-2-2-2-2-2000022-2-222000000002-2-2200000022-2-2-2-222-222-2000000000000000000000000
χ442222-2-22-2-222222-2-2-2-2-2-2000022-2-22200000000-222-2000000-2-22222-2-2-222-2000000000000000000000000
χ452222-2-2-122-2-2-1-1-111112-22i2i−2i−2i2-2-1-111−i−i−i−iiiii22-2-22i−2i2i2i−2i−2i-1-1-1-11111-1-111−i−iii−i−i−i−iiiii000000000000
χ462222-2-2-122-2-2-1-1-111112-22i2i−2i−2i2-2-1-111−i−i−i−iiiii-2-2222i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−iiiiiii−i−i−i−i000000000000
χ472222-2-2-122-2-2-1-1-111112-2−2i−2i2i2i2-2-1-111iiii−i−i−i−i22-2-2−2i2i−2i−2i2i2i-1-1-1-11111-1-111ii−i−iiiii−i−i−i−i000000000000
χ482222-2-2-122-2-2-1-1-111112-2−2i−2i2i2i2-2-1-111iiii−i−i−i−i-2-222−2i2i2i2i−2i−2i1111-1-1-1-1-1-111ii−i−i−i−i−i−iiiii000000000000
χ492222-2-2-122-2-2-1-1-11111-222i2i−2i−2i-22-1-111−i−i−i−iiiii0000−2i2i0000−i3i3−i3i3i3−i3i3−i311-1-1ii−i−i3−33−3−33−33000000000000
χ502222-2-2-122-2-2-1-1-11111-222i2i−2i−2i-22-1-111−i−i−i−iiiii0000−2i2i0000i3−i3i3−i3−i3i3−i3i311-1-1ii−i−i−33−333−33−3000000000000
χ512222-2-2-122-2-2-1-1-11111-22−2i−2i2i2i-22-1-111iiii−i−i−i−i00002i−2i0000−i3i3−i3i3i3−i3i3−i311-1-1−i−iii−33−333−33−3000000000000
χ522222-2-2-122-2-2-1-1-11111-22−2i−2i2i2i-22-1-111iiii−i−i−i−i00002i−2i0000i3−i3i3−i3−i3i3−i3i311-1-1−i−iii3−33−3−33−33000000000000
χ532222-2-2-1-2-222-1-1-11111220000-2-211-1-133−3−3−3−3330000002i−2i−2i2i−i3i3i3−i3i3−i3−i3i3-111-13−3−33−i−iiiii−i−i000000000000
χ542222-2-2-1-2-222-1-1-11111220000-2-211-1-133−3−3−3−333000000−2i2i2i−2ii3−i3−i3i3−i3i3i3−i3-111-13−3−33ii−i−i−i−iii000000000000
χ552222-2-2-1-2-222-1-1-11111220000-2-211-1-1−3−33333−3−30000002i−2i−2i2ii3−i3−i3i3−i3i3i3−i3-111-1−333−3−i−iiiii−i−i000000000000
χ562222-2-2-1-2-222-1-1-11111220000-2-211-1-1−3−33333−3−3000000−2i2i2i−2i−i3i3i3−i3i3−i3−i3i3-111-1−333−3ii−i−i−i−iii000000000000
χ572222-2-2-1-2-222-1-1-11111-2-200002211-1-133−3−3−3−3332-2-22000000-1-11111-1-11-1-11−333−33−3−33−333−3000000000000
χ582222-2-2-1-2-222-1-1-11111-2-200002211-1-133−3−3−3−333-222-200000011-1-1-1-1111-1-11−333−3−333−33−3−33000000000000
χ592222-2-2-1-2-222-1-1-11111-2-200002211-1-1−3−33333−3−32-2-22000000-1-11111-1-11-1-113−3−33−333−33−3−33000000000000
χ602222-2-2-1-2-222-1-1-11111-2-200002211-1-1−3−33333−3−3-222-200000011-1-1-1-1111-1-113−3−333−3−33−333−3000000000000
χ612-2-222-222-22-22-2-222-2-2002i−2i2i−2i002-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000002−22−2−i2i2−i2i20000
χ622-2-222-222-22-22-2-222-2-2002i−2i2i−2i002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−22−22i2−i2i2−i20000
χ632-2-222-222-22-22-2-222-2-200−2i2i−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000002−22−2i2−i2i2−i20000
χ642-2-222-222-22-22-2-222-2-200−2i2i−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−22−22−i2i2−i2i20000
χ652-2-22-2222-2-222-2-2-2-222002-2-22002-2-222-22-2-22-2200000000000000000000000000000000002−2−22−222−20000
χ662-2-22-2222-2-222-2-2-2-222002-2-22002-2-222-22-2-22-220000000000000000000000000000000000−222−22−2−220000
χ672-2-22-2222-2-222-2-2-2-22200-222-2002-2-22-22-222-22-200000000000000000000000000000000002−2−222−2−220000
χ682-2-22-2222-2-222-2-2-2-22200-222-2002-2-22-22-222-22-20000000000000000000000000000000000−222−2−222−20000
χ694-4-444-44-44-444-4-444-4-400000000-44-44000000000000000000000000000000000000000000000000000000
χ704-4-444-4-24-44-4-222-2-222004i−4i4i−4i00-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ714-4-444-4-24-44-4-222-2-22200−4i4i−4i4i00-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-4-444-4-2-44-44-222-2-222000000002-22-223−23−232323−23−23230000000000000000000000000000000000000000000000
χ734-4-444-4-2-44-44-222-2-222000000002-22-2−232323−23−232323−230000000000000000000000000000000000000000000000
χ744-4-44-444-444-44-4-4-4-44400000000-444-4000000000000000000000000000000000000000000000000000000
χ754-4-44-44-24-4-44-22222-2-2004-4-4400-222-2-22-222-22-20000000000000000000000000000000000000000000000
χ764-4-44-44-24-4-44-22222-2-200-444-400-222-22-22-2-22-220000000000000000000000000000000000000000000000
χ774-4-44-44-2-444-4-22222-2-2000000002-2-22−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ784-4-44-44-2-444-4-22222-2-2000000002-2-222i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-44−4i34i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-444i3−4i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ828-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-88-800-4000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-4000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).