Finite Group Databasebeta

← Group #10695096

Character table — Group #10695096

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212668888888812121212121212121212242424242424242424242424242424244444444488888888448812121212242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-111
χ91111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−i1-1i−i
χ101111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iii-11−ii
χ111111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1i−i11-1-1ii−i−i-11−ii
χ121111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−i111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−ii-1-111−i−iii1-1i−i
χ131111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-111111-1−ii11-1-1−i−iii-11i−i
χ141111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-11i−i-1-111ii−i−i1-1−ii
χ151111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii1-1−ii
χ161111-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−i-11i−i
χ172222222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2322222222-2-22-2-222-2-222-2-22222222-2-222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-22-2-222-2-222-2-22222222-2-2-2-222-2-222-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-22-2-2-2-222-2-2222222222-2-200000000-2-2-2-22222-2-200000000000000000000000022-2-222-2-20000000000000000
χ2622222222-2-22-2-2-2-222-2-2222222222-2-200000000-2-2-2-22222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-11122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-11122-2-222-2-211-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-111-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-111-2-222-2-22211-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ322222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-222−2i−2i2i2i2i2i−2i−2i-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-22200000000-2-2-2-222-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ342222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-22200000000-2-2-2-222-2-222000000000000000000000000-2-22222-2-20000000000000000
χ352222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−330000
χ362222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-12i2i−2i−2i−2i−2i2i2i11-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−30000
χ372222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−30000
χ382222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-1−2i−2i2i2i2i2i−2i−2i11-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−330000
χ392222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-20000000022-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-20000000022-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii0000
χ422222-2-2-2-2-2-2-12222-2-2-2-222-1-1-11111112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ432222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ442222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ452-22-22i−2i2i−2i00200002i−2i002-2-22-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-22i−2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002-2002i−2i0000000000000000
χ462-22-22i−2i2i−2i00200002i−2i002-2-22-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-22i−2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00-2200−2i2i0000000000000000
χ472-22-22i−2i2i−2i00200002i−2i002-2-22-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-22i−2i00−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00-2200−2i2i0000000000000000
χ482-22-22i−2i2i−2i00200002i−2i002-2-22-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-22i−2i00−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-2002i−2i0000000000000000
χ492-22-22i−2i2i−2i0020000−2i2i00-22-22-22i−2i2i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000-22−2i2i001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i2-2002i−2i000000000000000000
χ502-22-22i−2i2i−2i0020000−2i2i00-22-22-22i−2i2i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000-22−2i2i001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200−2i2i000000000000000000
χ512-22-22i−2i2i−2i0020000−2i2i00-22-22-22i−2i2i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000-22−2i2i00−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200−2i2i000000000000000000
χ522-22-22i−2i2i−2i0020000−2i2i00-22-22-22i−2i2i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000-22−2i2i00−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-2002i−2i000000000000000000
χ532-22-2−2i2i−2i2i00200002i−2i00-22-22-2−2i2i−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000-222i−2i001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i2-200−2i2i000000000000000000
χ542-22-2−2i2i−2i2i00200002i−2i00-22-22-2−2i2i−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000-222i−2i001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i1−i1−i−1+i−1−i1+i1+i−1−i-22002i−2i000000000000000000
χ552-22-2−2i2i−2i2i00200002i−2i00-22-22-2−2i2i−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000-222i−2i00−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i-22002i−2i000000000000000000
χ562-22-2−2i2i−2i2i00200002i−2i00-22-22-2−2i2i−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000-222i−2i00−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-200−2i2i000000000000000000
χ572-22-2−2i2i−2i2i0020000−2i2i002-2-22-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-2−2i2i001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002-200−2i2i0000000000000000
χ582-22-2−2i2i−2i2i0020000−2i2i002-2-22-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-2−2i2i001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00-22002i−2i0000000000000000
χ592-22-2−2i2i−2i2i0020000−2i2i002-2-22-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-2−2i2i00−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00-22002i−2i0000000000000000
χ602-22-2−2i2i−2i2i0020000−2i2i002-2-22-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-2−2i2i00−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-200−2i2i0000000000000000
χ614444444444-244-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-200000000-2-222222222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-4-4-444-4-444-2-2-2-2-2-2-222000000002222-2-2-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-4-4-4-4-44444-2-2-22222-2-2000000002222-2-222-2-2000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-244-4-44444-4-4-2-2-222222200000000-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ6544-4-444-4-44-444-4000000004-4-4-4-4444-4000000004-400000000000000000000000000000000000000000000000000000000
χ6644-4-444-4-44-4-24-400000000-22222-2-2-2200000000-22000000006−66−66−66−66−66−66−66−600000000000000000000000000000000
χ6744-4-444-4-44-4-24-400000000-22222-2-2-2200000000-2200000000−66−66−66−66−66−66−66−6600000000000000000000000000000000
χ6844-4-444-4-4-444-44000000004-4-4-4-444-4400000000-4400000000000000000000000000000000000000000000000000000000
χ6944-4-444-4-4-44-2-4400000000-22222-2-22-2000000002-2000000006−66−6−66−666−66−6−66−6600000000000000000000000000000000
χ7044-4-444-4-4-44-2-4400000000-22222-2-22-2000000002-200000000−66−666−66−6−66−666−66−600000000000000000000000000000000
χ7144-4-4-4-4444-44-44000000004-4-444-4-44-400000000-4400000000000000000000000000000000000000000000000000000000
χ7244-4-4-4-4444-4-2-4400000000-222-2-222-22000000002-200000000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ7344-4-4-4-4444-4-2-4400000000-222-2-222-22000000002-200000000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ7444-4-4-4-444-4444-4000000004-4-444-4-4-44000000004-400000000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-44-24-400000000-222-2-2222-200000000-2200000000i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ7644-4-4-4-444-44-24-400000000-222-2-2222-200000000-2200000000−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.