Finite Group Databasebeta

← Group #10695088

Character table — Group #10695088

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12224444223444444444466612121212668888888812121212121212121212242424242424242424242424242424244444444488888888444412121212121212128888
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
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-111-1-111-1-1i−ii−i
χ101111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-1-111-1-111−ii−ii
χ111111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-111-1-111-1-1−ii−ii
χ121111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-1-111-1-111i−ii−i
χ131111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii1-1-1111-1-1-1-111i−i−ii
χ141111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-111-1-1-11111-1-1−iii−i
χ151111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i1-1-1111-1-1-1-111−iii−i
χ161111-1-1-1-1-1-111111-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-111-1-1-11111-1-1i−i−ii
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
χ2322222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ2422222222-2-22-2-222-2-2-2-2222222222-2-200000000-2-22222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ2522222222-2-22-2-2-2-22222-2-22222222-2-222-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-22-2-2-2-22222-2-22222222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-11122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-11122-2-222-2-2111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-111-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-2-2-1-2-2-2-22222-2-2-1-1-1-1-1-1-111-2-222-2-222111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ312222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-2222-2-22222-2-2-2-2222-2-2-2-22200000000-2-222-2-222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-2-2-22222222-2-2-2-222-2-22222-2-2-2-2-2-222-2-222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ362222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-122-2-2-2-2221111-1-111-1-1-1-1-1-111111111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ372222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i3−i3i30000
χ382222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1-2-22222-2-21111-1-111-1-11111-1-1-1-1-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i3i3−i30000
χ392222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-20000000022-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-20000000022-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002-22-2-1-111-1-1110000
χ422222-2-2-2-2-2-2-12222-2-222-2-2-1-1-11111112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000-22-2211-1-111-1-10000
χ432222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000002-2-22-1-11111-1-10000
χ442222-2-2-2-2-2-2-12222-2-222-2-2-1-1-1111111-2-2-2-22222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-10000000000000000-222-211-1-1-1-1110000
χ4522-2-222-2-22-222-2000000002-2-222-2-22-22−22−22−22−22-20000000022−2−222−2−222−2−222−2−2002-2002-22−22−22−22−20000000000000000
χ4622-2-222-2-22-222-2000000002-2-222-2-22-22−22−22−22−22-20000000022−2−222−2−222−2−222−2−200-2200-22−22−22−22−220000000000000000
χ4722-2-222-2-22-222-2000000002-2-222-2-22-2−22−22−22−222-200000000−2−222−2−222−2−222−2−222002-2002-2−22−22−22−220000000000000000
χ4822-2-222-2-22-222-2000000002-2-222-2-22-2−22−22−22−222-200000000−2−222−2−222−2−222−2−22200-2200-222−22−22−22−20000000000000000
χ4922-2-222-2-2-222-22000000002-2-222-2-2-222−2−222−2−22-220000000022−2−2−2−22222−2−2−2−2222-2002-2002−2−222−2−220000000000000000
χ5022-2-222-2-2-222-22000000002-2-222-2-2-222−2−222−2−22-220000000022−2−2−2−22222−2−2−2−222-2200-2200−222−2−222−20000000000000000
χ5122-2-222-2-2-222-22000000002-2-222-2-2-22−222−2−222−2-2200000000−2−22222−2−2−2−22222−2−22-2002-200−222−2−222−20000000000000000
χ5222-2-222-2-2-222-22000000002-2-222-2-2-22−222−2−222−2-2200000000−2−22222−2−2−2−22222−2−2-2200-22002−2−222−2−220000000000000000
χ5322-2-2-2-2222-22-22000000002-2-2-2-2222-22−2−22−222−2-220000000022−2−2−2−222−2−22222−2−22i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ5422-2-2-2-2222-22-22000000002-2-2-2-2222-22−2−22−222−2-220000000022−2−2−2−222−2−22222−2−2−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ5522-2-2-2-2222-22-22000000002-2-2-2-2222-2−222−22−2−22-2200000000−2−22222−2−222−2−2−2−2222i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ5622-2-2-2-2222-22-22000000002-2-2-2-2222-2−222−22−2−22-2200000000−2−22222−2−222−2−2−2−222−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ5722-2-2-2-222-2222-2000000002-2-2-2-222-222−22−2−22−222-20000000022−2−222−2−2−2−222−2−222002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ5822-2-2-2-222-2222-2000000002-2-2-2-222-222−22−2−22−222-20000000022−2−222−2−2−2−222−2−22200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ5922-2-2-2-222-2222-2000000002-2-2-2-222-22−22−222−22−22-200000000−2−222−2−22222−2−222−2−2002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ6022-2-2-2-222-2222-2000000002-2-2-2-222-22−22−222−22−22-200000000−2−222−2−22222−2−222−2−200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ614444444444-244-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-200000000-2-222222222000000000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-444-4-4-4-444-2-2-2-2-2-2-2220000000022-2-2-2-22222000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-44444-4-4-4-4-2-2-22222-2-20000000022-2-222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-244-4-444-4-444-2-2-222222200000000-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ6544-4-444-4-44-4-24-400000000-222-2-222-2222−2222−2222−2222−22-2200000000−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ6644-4-444-4-44-4-24-400000000-222-2-222-22−2222−2222−2222−2222-220000000022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ6744-4-444-4-4-44-2-4400000000-222-2-2222-222−22−222222−22−22222-200000000−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ6844-4-444-4-4-44-2-4400000000-222-2-2222-2−222222−22−222222−222-20000000022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ6944-4-4-4-4444-4-2-4400000000-22222-2-2-2222−22−2222−222222−222-200000000−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ7044-4-4-4-4444-4-2-4400000000-22222-2-2-22−222222−2222−22−22222-20000000022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ7144-4-4-4-444-44-24-400000000-22222-2-22-222−2222−22−2222−2222-2200000000−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ7244-4-4-4-444-44-24-400000000-22222-2-22-2−2222−222222−2222−22-220000000022−2−222−2−2−2−222−2−22200000000000000000000000000000000
χ734-44-44i−4i4i−4i00400004i−4i4-400-44-44i−4i4i−4i00000000000000004i−4i4-4000000000000000000000000000000000000000000000000
χ744-44-44i−4i4i−4i0040000−4i4i-4400-44-44i−4i4i−4i0000000000000000−4i4i-44000000000000000000000000000000000000000000000000
χ754-44-44i−4i4i−4i00-200004i−4i4-4002-22−2i2i−2i2i0000000000000000−2i2i-22−2i32i3−2i32i3000023−2323−23000000000000000000000000000000000000
χ764-44-44i−4i4i−4i00-200004i−4i4-4002-22−2i2i−2i2i0000000000000000−2i2i-222i3−2i32i3−2i30000−2323−2323000000000000000000000000000000000000
χ774-44-44i−4i4i−4i00-20000−4i4i-44002-22−2i2i−2i2i00000000000000002i−2i2-20000−2i32i3−2i32i3000023−2323−2300000000000000000000000000000000
χ784-44-44i−4i4i−4i00-20000−4i4i-44002-22−2i2i−2i2i00000000000000002i−2i2-200002i3−2i32i3−2i30000−2323−232300000000000000000000000000000000
χ794-44-4−4i4i−4i4i00400004i−4i-4400-44-4−4i4i−4i4i00000000000000004i−4i-44000000000000000000000000000000000000000000000000
χ804-44-4−4i4i−4i4i0040000−4i4i4-400-44-4−4i4i−4i4i0000000000000000−4i4i4-4000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i00-200004i−4i-44002-222i−2i2i−2i0000000000000000−2i2i2-20000−2i32i3−2i32i30000−2323−232300000000000000000000000000000000
χ824-44-4−4i4i−4i4i00-200004i−4i-44002-222i−2i2i−2i0000000000000000−2i2i2-200002i3−2i32i3−2i3000023−2323−2300000000000000000000000000000000
χ834-44-4−4i4i−4i4i00-20000−4i4i4-4002-222i−2i2i−2i00000000000000002i−2i-22−2i32i3−2i32i30000−2323−2323000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i00-20000−4i4i4-4002-222i−2i2i−2i00000000000000002i−2i-222i3−2i32i3−2i3000023−2323−23000000000000000000000000000000000000
χ854-4-444i−4i−4i4i004004-400004i−4i-4-444i−4i−4i4i0000000000004-44i−4i0000000000000000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i00400-440000−4i4i-4-444i−4i−4i4i000000000000-44−4i4i0000000000000000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i00-2004-400004i−4i22-2−2i2i2i−2i000000000000-22−2i2i0000i6−i6−i6i6i6−i6−i6i6−666−6−666−600000000000000000000000000000000
χ884-4-444i−4i−4i4i00-2004-400004i−4i22-2−2i2i2i−2i000000000000-22−2i2i0000−i6i6i6−i6−i6i6i6−i66−6−666−6−6600000000000000000000000000000000
χ894-4-444i−4i−4i4i00-200-440000−4i4i22-2−2i2i2i−2i0000000000002-22i−2i0000i6−i6−i6i6−i6i6i6−i6−666−66−6−6600000000000000000000000000000000
χ904-4-444i−4i−4i4i00-200-440000−4i4i22-2−2i2i2i−2i0000000000002-22i−2i0000−i6i6i6−i6i6−i6−i6i66−6−66−666−600000000000000000000000000000000
χ914-4-44−4i4i4i−4i004004-40000−4i4i-4-44−4i4i4i−4i0000000000004-4−4i4i0000000000000000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i00400-4400004i−4i-4-44−4i4i4i−4i000000000000-444i−4i0000000000000000000000000000000000000000000000000000
χ934-4-44−4i4i4i−4i00-2004-40000−4i4i22-22i−2i−2i2i000000000000-222i−2i0000i6−i6−i6i6i6−i6−i6i66−6−666−6−6600000000000000000000000000000000
χ944-4-44−4i4i4i−4i00-2004-40000−4i4i22-22i−2i−2i2i000000000000-222i−2i0000−i6i6i6−i6−i6i6i6−i6−666−6−666−600000000000000000000000000000000
χ954-4-44−4i4i4i−4i00-200-4400004i−4i22-22i−2i−2i2i0000000000002-2−2i2i0000i6−i6−i6i6−i6i6i6−i66−6−66−666−600000000000000000000000000000000
χ964-4-44−4i4i4i−4i00-200-4400004i−4i22-22i−2i−2i2i0000000000002-2−2i2i0000−i6i6i6−i6i6−i6−i6i6−666−66−6−6600000000000000000000000000000000

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