Finite Group Databasebeta

← Group #10692386

Character table — Group #10692386

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12222234444666224466666612121212444444441212121212121212121244444444246612121212121244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ91111-1-1111-1-11111-11-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i1-1i−ii−i1-1
χ101111-1-1111-1-11111-11-111-1-1-1-111-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i-11−ii−ii-11
χ111111-1-1111-1-11111-11-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i1-1i−i−ii-11
χ121111-1-1111-1-11111-11-111-1-1-1-111-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i-11−iii−i1-1
χ131111-1-1111-1-11111-11-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii1-1−iii−i-11
χ141111-1-1111-1-11111-11-111-1-1-1-111-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii-11i−i−ii1-1
χ151111-1-1111-1-11111-11-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii1-1−ii−ii1-1
χ161111-1-1111-1-11111-11-111-1-1-1-111-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii-11i−ii−i-11
χ17222222222-2-2222-2-2-22-2-22-2-2222-2-200000000-2200000000222200000000000000-2-2000000
χ18222222222-2-2222-2-2-22-2-22-2-2222-2-200000000-2200000000-2-2-2-20000000000000022000000
χ192222222-2-222222-2-22-2-2-22-2-22-2-222000000002-20000000000002222000000000000-2-20000
χ202222222-2-222222-2-22-2-2-22-2-22-2-222000000002-2000000000000-2-2-2-2000000000000220000
χ212222222-2-2-2-222222-2-2222222-2-2-2-22-22-20000-2-200000000000000000000002-22-200000000
χ222222222-2-2-2-222222-2-2222222-2-2-2-2-22-220000-2-20000000000000000000000-22-2200000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-100000000
χ25222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ26222222-12222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-1111100000000
χ27222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-111112-22-2000011−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i3-11-1100000000
χ28222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-111112-22-2000011i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i3-11-1100000000
χ29222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111-22-22000011−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i31-11-100000000
χ30222222-1-2-2-2-2-1-1-122-2-2-1-1-1-1-1-11111-22-22000011i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i31-11-100000000
χ312222-2-222222222-22-2-2-2-2-222-2222200000000-2-20000000022-2-200000000000000-22000000
χ322222-2-222222222-22-2-2-2-2-222-2222200000000-2-200000000-2-222000000000000002-2000000
χ332222-2-22-2-2222222-2-2222-2-2-2-2-2-2222i−2i−2i2i0000-2200000000000000000000002i−2i−2i2i00000000
χ342222-2-22-2-2222222-2-2222-2-2-2-2-2-222−2i2i2i−2i0000-220000000000000000000000−2i2i2i−2i00000000
χ352222-2-22-2-2-2-2222-2222-2-2-222-2-2-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i0000
χ362222-2-22-2-2-2-2222-2222-2-2-222-2-2-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i0000
χ372222-2-2-122-2-2-1-1-12-22-2-1-11111-1-1112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii000000002-2-1-111−i−iii00000000
χ382222-2-2-122-2-2-1-1-12-22-2-1-11111-1-1112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i00000000-2211-1-1−i−iii00000000
χ392222-2-2-122-2-2-1-1-12-22-2-1-11111-1-111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii00000000-2211-1-1ii−i−i00000000
χ402222-2-2-122-2-2-1-1-12-22-2-1-11111-1-111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i000000002-2-1-111ii−i−i00000000
χ412222-2-2-1-2-222-1-1-12-2-22-1-1111111-1-12i−2i−2i2i00001-133−3−3−3−3330000000000−i3i3i3−i3−iii−i00000000
χ422222-2-2-1-2-222-1-1-12-2-22-1-1111111-1-12i−2i−2i2i00001-1−3−33333−3−30000000000i3−i3−i3i3−iii−i00000000
χ432222-2-2-1-2-222-1-1-12-2-22-1-1111111-1-1−2i2i2i−2i00001-133−3−3−3−3330000000000i3−i3−i3i3i−i−ii00000000
χ442222-2-2-1-2-222-1-1-12-2-22-1-1111111-1-1−2i2i2i−2i00001-1−3−33333−3−30000000000−i3i3i3−i3i−i−ii00000000
χ45444444-244-4-4-2-2-2-4-4-4422-222-2-2-222000000002-20000000000000000000000000000000000
χ46444444-2-4-444-2-2-2-4-44-422-222-222-2-200000000-220000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-44-4-4222-2-22-2-2-2-200000000220000000000000000000000000000000000
χ484444-4-4-2-4-4-4-4-2-2-2-4444222-2-22222200000000-2-20000000000000000000000000000000000
χ4944-4-40044-400-44-400000000004-400000000000000000000004i−4i0000000000000000000000
χ5044-4-40044-400-44-400000000004-40000000000000000000000−4i4i0000000000000000000000
χ5144-4-4004-4400-44-40000000000-44000000000000000000004i−4i000000000000000000000000
χ5244-4-4004-4400-44-40000000000-4400000000000000000000−4i4i000000000000000000000000
χ534-44-4004004i−4i4-4-40000000000004i−4i00000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ544-44-4004004i−4i4-4-40000000000004i−4i0000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ554-44-400400−4i4i4-4-4000000000000−4i4i00000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ564-44-400400−4i4i4-4-4000000000000−4i4i0000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ574-4-444-440000-4-44000000400-4000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ584-4-444-440000-4-44000000400-400000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ594-4-444-4-2000022-20000−2i32i3-2−2i32i32000000002i−2i2i−2i002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ1100000000000000000000000000
χ604-4-444-4-2000022-20000−2i32i3-2−2i32i3200000000−2i2i−2i2i00−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ1100000000000000000000000000
χ614-4-444-4-2000022-200002i3−2i3-22i3−2i32000000002i−2i2i−2i002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ700000000000000000000000000
χ624-4-444-4-2000022-200002i3−2i3-22i3−2i3200000000−2i2i−2i2i00−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ700000000000000000000000000
χ634-4-44-4440000-4-44000000-4004000000002-2-22002-22-2-22-2200000000000000000000000000
χ644-4-44-4440000-4-44000000-400400000000-222-200-22-222-22-200000000000000000000000000
χ654-4-44-44-2000022-20000−2i32i322i3−2i3-2000000002-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ664-4-44-44-2000022-20000−2i32i322i3−2i3-200000000-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ674-4-44-44-2000022-200002i3−2i32−2i32i3-2000000002-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ684-4-44-44-2000022-200002i3−2i32−2i32i3-200000000-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ6988-8-800-48-8004-440000000000-440000000000000000000000000000000000000000000000
χ7088-8-800-4-88004-4400000000004-40000000000000000000000000000000000000000000000
χ718-88-800-4008i−8i-444000000000000−4i4i00000000000000000000000000000000000000000000
χ728-88-800-400−8i8i-4440000000000004i−4i00000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.