Finite Group Databasebeta

← Group #10694969

Character table — Group #10694969

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222222344444444444466666668888888812121212121212121212121224242424242424242424242424242424888888888888888822446666121212124444
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1i−i11-1-1ii−i−ii−i1-1
χ101-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−ii-1-111−i−iii−ii-11
χ111-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1i−i11-1-1ii−i−i−ii-11
χ121-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1iiii−i−i−i−i111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11−ii-1-111−i−iiii−i1-1
χ131-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-111111-1−ii11-1-1−i−iiii−i-11
χ141-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-11i−i-1-111ii−i−i−ii1-1
χ151-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-11-1−ii11-1-1−i−iii−ii1-1
χ161-1-111-1-11111-1-111-1-111-1-1-1-1-1111-1−i−i−i−iiiii111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-11i−i-1-111ii−i−ii−i-11
χ1722222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-222-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-22222222220000000022-2-2-2-222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222-2-222-2-2-2-222-2-2222222200000000-2-222-2-2-2-222-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222-2-2-2-222-2-2222222200000000-2-222-2-2-2-222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-22222-2-2-2-2222222222-2-222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ22222222222-2-2-2-22222-2-2-2-22222222-2-222-2-222-2-2-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2722222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ3122-22-22-2-222-2000000002-22-2-22-2-222−22−22−22−22-200002-2000022−2−222−2−222−2−222−2−2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3222-22-22-2-222-2000000002-22-2-22-2-222−22−22−22−22-200002-2000022−2−222−2−222−2−222−2−200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3322-22-22-2-222-2000000002-22-2-22-2-22−22−22−22−222-200002-20000−2−222−2−222−2−222−2−222002i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ3422-22-22-2-222-2000000002-22-2-22-2-22−22−22−22−222-200002-20000−2−222−2−222−2−222−2−22200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ3522-22-22-2-22-2200000000-222-2-22-2-222−2−222−2−22-220000-22000022−2−2−2−22222−2−2−2−2222i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ3622-22-22-2-22-2200000000-222-2-22-2-222−2−222−2−22-220000-22000022−2−2−2−22222−2−2−2−222−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ3722-22-22-2-22-2200000000-222-2-22-2-22−222−2−222−2-220000-220000−2−22222−2−2−2−22222−2−22i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ3822-22-22-2-22-2200000000-222-2-22-2-22−222−2−222−2-220000-220000−2−22222−2−2−2−22222−2−2−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ392-222-2-22-222-200000000-22-2222-2-2-2−i2i2−i2i2i2−i2i2−i22-20000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2002-200-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ402-222-2-22-222-200000000-22-2222-2-2-2−i2i2−i2i2i2−i2i2−i22-20000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200-22002-2i2−i2i2−i2−i2i2−i2i20000000000000000
χ412-222-2-22-222-200000000-22-2222-2-2-2i2−i2i2−i2−i2i2−i2i22-20000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2002-200-22i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-222-2-22-222-200000000-22-2222-2-2-2i2−i2i2−i2−i2i2−i2i22-20000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200-22002-2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-222-2-22-22-22000000002-2-2222-2-2-2−i2i2i2−i2i2−i2−i2i2-2200002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i20000000000000000
χ442-222-2-22-22-22000000002-2-2222-2-2-2−i2i2i2−i2i2−i2−i2i2-2200002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i20000000000000000
χ452-222-2-22-22-22000000002-2-2222-2-2-2i2−i2−i2i2−i2i2i2−i2-2200002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i20000000000000000
χ462-222-2-22-22-22000000002-2-2222-2-2-2i2−i2−i2i2−i2i2i2−i2-2200002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i20000000000000000
χ472-2-222-2-2222222-2-222-2-2-2-2-2-2-2222-20000000022-2-2-2-2-2-2222200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ482-2-222-2-2222222-2-222-2-2-2-2-2-2-2222-20000000022-2-2-2-2-2-222220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ492-2-222-2-222-2-22222-2-2-2-222-2-2-2222-22i2i−2i−2i−2i−2i2i2i-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ502-2-222-2-222-2-22222-2-2-2-222-2-2-2222-2−2i−2i2i2i2i2i−2i−2i-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ512-2-222-2-222-2-2-2-2-2-2222222-2-2-2222-200000000-2-222-2-222-2-22200000000000000000000000022-2-2-2-2220000000000000000
χ522-2-222-2-222-2-2-2-2-2-2222222-2-2-2222-200000000-2-222-2-222-2-222000000000000000000000000-2-22222-2-20000000000000000
χ532-2-222-2-22-122-2-222-2-222-2-2111-1-1-112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i-1-111−i−iii0000
χ542-2-222-2-22-122-2-222-2-222-2-2111-1-1-112i2i2i2i−2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2i11-1-1ii−i−i0000
χ552-2-222-2-22-122-2-222-2-222-2-2111-1-1-11−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2i-1-111ii−i−i0000
χ562-2-222-2-22-122-2-222-2-222-2-2111-1-1-11−2i−2i−2i−2i2i2i2i2i-1-1-1-1-1-1111111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i11-1-1−i−iii0000
χ572-2-222-2-22-1-2-22222-2-2-2-222111-1-1-112i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−i3i3i3−i33−3−330000
χ582-2-222-2-22-1-2-22222-2-2-2-222111-1-1-112i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000i3−i3−i3i3−333−30000
χ592-2-222-2-22-1-2-22222-2-2-2-222111-1-1-11−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−i3i3i3−i3−333−30000
χ602-2-222-2-22-1-2-22222-2-2-2-222111-1-1-11−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000i3−i3−i3i33−3−330000
χ6144444444-244-4-4-4-4-4-4-4-444-2-2-2-2-2-2-200000000-2-22222-2-22222000000000000000000000000000000000000000000000000
χ6244444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-20000000022-2-22222-2-222000000000000000000000000000000000000000000000000
χ63444-44-4-4-44004-400004-40044-4-44-4-400000000004-400004-400000000000000000000000000000000000000000000000000
χ64444-44-4-4-4400-440000-440044-4-44-4-40000000000-440000-4400000000000000000000000000000000000000000000000000
χ65444-44-4-4-4-2004-400004-400-2-222-2220000000000-220000-22006−66−66−66−66−66−66−66−600000000000000000000000000000000
χ66444-44-4-4-4-2004-400004-400-2-222-2220000000000-220000-2200−66−66−66−66−66−66−66−6600000000000000000000000000000000
χ67444-44-4-4-4-200-440000-4400-2-222-22200000000002-200002-2006−66−6−66−666−66−6−66−6600000000000000000000000000000000
χ68444-44-4-4-4-200-440000-4400-2-222-22200000000002-200002-200−66−666−66−6−66−666−66−600000000000000000000000000000000
χ6944-44-44-4-4-24-4000000004-4-222-222-222−2222−2222−2222−22-220000-220000−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ7044-44-44-4-4-24-4000000004-4-222-222-2−2222−2222−2222−2222-220000-22000022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ7144-44-44-4-4-2-4400000000-44-222-222-222−22−222222−22−22222-200002-20000−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7244-44-44-4-4-2-4400000000-44-222-222-2−222222−22−222222−222-200002-2000022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ7344-4-4-4-444400004-44-400004-44-4-44-40000000000004-400004-4000000000000000000000000000000000000000000000000
χ7444-4-4-4-44440000-44-4400004-44-4-44-4000000000000-440000-44000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-200004-44-40000-22-222-22000000000000-220000-22000023−23−2323000023−23−232300000000000000000000000000000000
χ7644-4-4-4-444-200004-44-40000-22-222-22000000000000-220000-220000−232323−230000−232323−2300000000000000000000000000000000
χ7744-4-4-4-444-20000-44-440000-22-222-220000000000002-200002-223−23−2323000023−23−2323000000000000000000000000000000000000
χ7844-4-4-4-444-20000-44-440000-22-222-220000000000002-200002-2−232323−230000−232323−23000000000000000000000000000000000000
χ794-444-4-44-4-24-400000000-442-2-2-2222−2i22i2−2i22i22i2−2i22i2−2i2-2200002-20000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ804-444-4-44-4-24-400000000-442-2-2-22222i2−2i22i2−2i2−2i22i2−2i22i2-2200002-20000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ814-444-4-44-4-2-44000000004-42-2-2-2222−2i22i22i2−2i22i2−2i2−2i22i22-20000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ824-444-4-44-4-2-44000000004-42-2-2-22222i2−2i2−2i22i2−2i22i22i2−2i22-20000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ834-44-4-44-44400004-4-440000-44-4-4-4440000000000004-40000-44000000000000000000000000000000000000000000000000
χ844-44-4-44-4440000-444-40000-44-4-4-444000000000000-4400004-4000000000000000000000000000000000000000000000000
χ854-44-4-44-44-200004-4-4400002-2222-2-2000000000000-2200002-20000−2i32i32i3−2i300002i3−2i3−2i32i300000000000000000000000000000000
χ864-44-4-44-44-200004-4-4400002-2222-2-2000000000000-2200002-200002i3−2i3−2i32i30000−2i32i32i3−2i300000000000000000000000000000000
χ874-44-4-44-44-20000-444-400002-2222-2-20000000000002-20000-22−2i32i32i3−2i300002i3−2i3−2i32i3000000000000000000000000000000000000
χ884-44-4-44-44-20000-444-400002-2222-2-20000000000002-20000-222i3−2i3−2i32i30000−2i32i32i3−2i3000000000000000000000000000000000000
χ894-4-444-4-44-24444-4-444-4-4-4-4222-2-2-2200000000-2-2222222-2-2-2-2000000000000000000000000000000000000000000000000
χ904-4-444-4-44-2-4-4-4-4-4-4444444222-2-2-220000000022-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ914-4-4-4444-44004-40000-4400-4-44-44-440000000000-4400004-400000000000000000000000000000000000000000000000000
χ924-4-4-4444-4400-4400004-400-4-44-44-4400000000004-40000-4400000000000000000000000000000000000000000000000000
χ934-4-4-4444-4-2004-40000-440022-22-22-200000000002-20000-2200i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ944-4-4-4444-4-2004-40000-440022-22-22-200000000002-20000-2200−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ954-4-4-4444-4-200-4400004-40022-22-22-20000000000-2200002-200i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ964-4-4-4444-4-200-4400004-40022-22-22-20000000000-2200002-200−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000

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