Finite Group Databasebeta

← Group #10691900

Character table — Group #10691900

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order122222344446666666444444441212121212121212121212124444444444121212121212121212121212121212121212121212121212888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ91111-1-1111-1-111-1-1-1-111-1ii−i−i-1111-1-1iiii−i−i−i−i11-1-1i−iii−i−i1-1ii−i−iiiii−i−i−i−i1-11111-1-1-1-111-1-1ii−i−i1-1i−i
χ101111-1-1111-1-111-1-1-1-111-1ii−i−i-1111-1-1iiii−i−i−i−i11-1-1i−iii−i−i1-1ii−i−iiiii−i−i−i−i1-11111-1-1-1-1-1-111−i−iii-11−ii
χ111111-1-1111-1-111-1-1-1-111-1ii−i−i-1111-1-1iiii−i−i−i−i-1-111i−i−i−iii1-1ii−i−i−i−i−i−iiiii1-1-1-1-1-1111111-1-1ii−i−i-11−ii
χ121111-1-1111-1-111-1-1-1-111-1ii−i−i-1111-1-1iiii−i−i−i−i-1-111i−i−i−iii1-1ii−i−i−i−i−i−iiiii1-1-1-1-1-11111-1-111−i−iii1-1i−i
χ131111-1-1111-1-111-1-1-1-111-1−i−iii-1111-1-1−i−i−i−iiiii11-1-1−ii−i−iii1-1−i−iii−i−i−i−iiiii1-11111-1-1-1-111-1-1−i−iii1-1−ii
χ141111-1-1111-1-111-1-1-1-111-1−i−iii-1111-1-1−i−i−i−iiiii11-1-1−ii−i−iii1-1−i−iii−i−i−i−iiiii1-11111-1-1-1-1-1-111ii−i−i-11i−i
χ151111-1-1111-1-111-1-1-1-111-1−i−iii-1111-1-1−i−i−i−iiiii-1-111−iiii−i−i1-1−i−iiiiiii−i−i−i−i1-1-1-1-1-1111111-1-1−i−iii-11i−i
χ161111-1-1111-1-111-1-1-1-111-1−i−iii-1111-1-1−i−i−i−iiiii-1-111−iiii−i−i1-1−i−iiiiiii−i−i−i−i1-1-1-1-1-11111-1-111ii−i−i1-1−ii
χ17222222222222222222-2-22222-2-22222222222220000-2-20000-2-2-2-2-2-200000000-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000220000-2-2222200000000-2-200000000000000000000
χ192222222-2-2-2-222222222-200002-2-2-2-2-2000000000000002-22-222000022-2-222-2-2-2-200000000000000000000
χ202222222-2-2-2-222222222-200002-2-2-2-2-200000000000000-22-22220000-2-222-2-222-2-200000000000000000000
χ212222222-2-2-2-22222222-220000-22-2-2-2-2000000002-22-2000000-2-20000000000002222-2-222-2-2000000000000
χ222222222-2-2-2-22222222-220000-22-2-2-2-200000000-22-22000000-2-200000000000022-2-222-2-222000000000000
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
χ24222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-111111111-1-111111111000000000000
χ25222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1111111112222-2-2-2-2-2-2-1-1111111111111-1-1-1-1-1-1-1-1-1-1000000000000
χ26222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-2-2-2-2-22222-1-11111-1-1-1-1-1-1-1-1-1-111111111000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000111111−i3i3−i3i3−i3i3−i3i311−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000111111i3−i3i3−i3i3−i3i3−i311i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000022000011-1-1-1-1−i3i3−i3i3−i3i3−i3i311i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111000022000011-1-1-1-1i3−i3i3−i3i3−i3i3−i311−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-12-200002-21111−i3−i3i3i3−i3−i3i3i30000002-22-2-1-1−i3i3−i3i3-1-111-1-11111−i3i3i3−i3−i3i3i3−i3000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-12-200002-21111−i3−i3i3i3−i3−i3i3i3000000-22-22-1-1−i3i3−i3i311-1-111-1-111i3−i3−i3i3i3−i3−i3i3000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-12-200002-21111i3i3−i3−i3i3i3−i3−i30000002-22-2-1-1i3−i3i3−i3-1-111-1-11111i3−i3−i3i3i3−i3−i3i3000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-12-200002-21111i3i3−i3−i3i3i3−i3−i3000000-22-22-1-1i3−i3i3−i311-1-111-1-111−i3i3i3−i3−i3i3i3−i3000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-220000-221111−i3−i3i3i3−i3−i3i3i32-22-200000011i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3-1-1-1-111-1-111000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-220000-221111−i3−i3i3i3−i3−i3i3i3-22-2200000011i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3-1-111-1-111-1-1000000000000
χ37222222-1-2-2-2-2-1-1-1-1-1-1-1-220000-221111i3i3−i3−i3i3i3−i3−i32-22-200000011−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3-1-1-1-111-1-111000000000000
χ38222222-1-2-2-2-2-1-1-1-1-1-1-1-220000-221111i3i3−i3−i3i3i3−i3−i3-22-2200000011−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3-1-111-1-111-1-1000000000000
χ392222-2-2222-2-222-2-2-2-22-222i2i−2i−2i2-222-2-22i2i2i2i−2i−2i−2i−2i0000−2i2i0000-22−2i−2i2i2i00000000-2200000000000000000000
χ402222-2-2222-2-222-2-2-2-22-22−2i−2i2i2i2-222-2-2−2i−2i−2i−2i2i2i2i2i00002i−2i0000-222i2i−2i−2i00000000-2200000000000000000000
χ412222-2-22-2-22222-2-2-2-22220000-2-2-2-222000000000000002i−2i−2i2i2-200002i2i−2i−2i−2i−2i2i2i-2200000000000000000000
χ422222-2-22-2-22222-2-2-2-22220000-2-2-2-22200000000000000−2i2i2i−2i2-20000−2i−2i2i2i2i2i−2i−2i-2200000000000000000000
χ432222-2-22-2-22222-2-2-2-22-2-2000022-2-222000000002-2-22000000-220000000000002-222-2-2-2-222000000000000
χ442222-2-22-2-22222-2-2-2-22-2-2000022-2-22200000000-222-2000000-220000000000002-2-2-22222-2-2000000000000
χ452222-2-2-122-2-2-1-11111-12-22i2i−2i−2i-22-1-111−i−i−i−iiiii22-2-22i−2i2i2i−2i−2i-11−i−iii−i−i−i−iiiii-11-1-1-1-11111000000000000
χ462222-2-2-122-2-2-1-11111-12-22i2i−2i−2i-22-1-111−i−i−i−iiiii-2-2222i−2i−2i−2i2i2i-11−i−iiiiiii−i−i−i−i-111111-1-1-1-1000000000000
χ472222-2-2-122-2-2-1-11111-12-2−2i−2i2i2i-22-1-111iiii−i−i−i−i22-2-2−2i2i−2i−2i2i2i-11ii−i−iiiii−i−i−i−i-11-1-1-1-11111000000000000
χ482222-2-2-122-2-2-1-11111-12-2−2i−2i2i2i-22-1-111iiii−i−i−i−i-2-222−2i2i2i2i−2i−2i-11ii−i−i−i−i−i−iiiii-111111-1-1-1-1000000000000
χ492222-2-2-122-2-2-1-11111-1-222i2i−2i−2i2-2-1-111−i−i−i−iiiii0000−2i2i00001-1ii−i−i3−33−3−33−331-1−i3i3−i3i3i3−i3i3−i3000000000000
χ502222-2-2-122-2-2-1-11111-1-222i2i−2i−2i2-2-1-111−i−i−i−iiiii0000−2i2i00001-1ii−i−i−33−333−33−31-1i3−i3i3−i3−i3i3−i3i3000000000000
χ512222-2-2-122-2-2-1-11111-1-22−2i−2i2i2i2-2-1-111iiii−i−i−i−i00002i−2i00001-1−i−iii3−33−3−33−331-1i3−i3i3−i3−i3i3−i3i3000000000000
χ522222-2-2-122-2-2-1-11111-1-22−2i−2i2i2i2-2-1-111iiii−i−i−i−i00002i−2i00001-1−i−iii−33−333−33−31-1−i3i3−i3i3i3−i3i3−i3000000000000
χ532222-2-2-1-2-222-1-11111-1220000-2-211-1-133−3−3−3−3330000002i−2i−2i2i-113−3−33−i−iiiii−i−i1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-1-2-222-1-11111-1220000-2-211-1-133−3−3−3−333000000−2i2i2i−2i-113−3−33ii−i−i−i−iii1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-1-2-222-1-11111-1220000-2-211-1-1−3−33333−3−30000002i−2i−2i2i-11−333−3−i−iiiii−i−i1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-1-2-222-1-11111-1220000-2-211-1-1−3−33333−3−3000000−2i2i2i−2i-11−333−3ii−i−i−i−iii1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-1-2-222-1-11111-1-2-200002211-1-133−3−3−3−3332-2-220000001-1−333−33−3−33−333−3-11-1-11111-1-1000000000000
χ582222-2-2-1-2-222-1-11111-1-2-200002211-1-133−3−3−3−333-222-20000001-1−333−3−333−33−3−33-1111-1-1-1-111000000000000
χ592222-2-2-1-2-222-1-11111-1-2-200002211-1-1−3−33333−3−32-2-220000001-13−3−33−333−33−3−33-11-1-11111-1-1000000000000
χ602222-2-2-1-2-222-1-11111-1-2-200002211-1-1−3−33333−3−3-222-20000001-13−3−333−3−33−333−3-1111-1-1-1-111000000000000
χ6122-2-22-222-22-22-222-2-2-2002-22-2002-22-22-22-22-22-200000000000000000000000000000000002−22−22−22−20000
χ6222-2-22-222-22-22-222-2-2-2002-22-2002-22-22-22-22-22-20000000000000000000000000000000000−22−22−22−220000
χ6322-2-22-222-22-22-222-2-2-200-22-22002-22-2-22-22-22-2200000000000000000000000000000000002−22−2−22−220000
χ6422-2-22-222-22-22-222-2-2-200-22-22002-22-2-22-22-22-220000000000000000000000000000000000−22−222−22−20000
χ6522-2-2-2222-2-222-2-2-222-2002i−2i−2i2i002-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000002−2−22i2−i2−i2i20000
χ6622-2-2-2222-2-222-2-2-222-2002i−2i−2i2i002-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−222−2−i2i2i2−i20000
χ6722-2-2-2222-2-222-2-2-222-200−2i2i2i−2i002-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000002−2−22−i2i2i2−i20000
χ6822-2-2-2222-2-222-2-2-222-200−2i2i2i−2i002-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−222−2i2−i2−i2i20000
χ6944-4-44-44-44-444-444-4-4-400000000-44-44000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-24-44-4-22-2-2222004-44-400-22-22-22-22-22-220000000000000000000000000000000000000000000000
χ7144-4-44-4-24-44-4-22-2-222200-44-4400-22-222-22-22-22-20000000000000000000000000000000000000000000000
χ7244-4-44-4-2-44-44-22-2-2222000000002-22-2−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7344-4-44-4-2-44-44-22-2-2222000000002-22-22i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7444-4-4-444-444-44-4-4-444-400000000-444-4000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-24-4-44-2222-2-22004i−4i−4i4i00-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7644-4-4-44-24-4-44-2222-2-2200−4i4i4i−4i00-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7744-4-4-44-2-444-4-2222-2-22000000002-2-2223−23−2323−232323−230000000000000000000000000000000000000000000000
χ7844-4-4-44-2-444-4-2222-2-22000000002-2-22−232323−2323−23−23230000000000000000000000000000000000000000000000
χ798-88-80080000-880000-8000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4−4i34i3−4i34i34000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44i3−4i34i3−4i34000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-800008000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044−4i34i34i3−4i3-4000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-40000444i3−4i3−4i34i3-4000000000000000000000000000000000000000000000000000000000000000000

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