Finite Group Databasebeta

← Group #10688981

Character table — Group #10688981

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212124444
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
χ91-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−ii−i
χ101-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii−ii
χ111-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−iii−i−iii−i−i−ii−ii
χ121-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-11111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−ii−i−iii−i−iiii−ii−i
χ131-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ141-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ151-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ161-1111-1-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ1722222222222-2-2-2-222-2-2-2-2222222222-2-222-2-2-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-22222222-2-222-2-222-2-2-2-222-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ19222222222-2-222-2-2-2-222-2-222222220000000022-2-2-2-222-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222-2-2-2-222-2-222222220000000022-2-2-2-222-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-222-2-2-2-222222222200000000-2-222-2-2-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ22222222222-2-2-2-222-2-2-2-222222222200000000-2-222-2-2-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
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
χ2722222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-21111-1-11111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-2221111-1-11111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ31222-2-22-2-2200002-200002-22-2-22-2-222−22−22−22−2002-200002-20022−2−222−2−222−2−222−2−2002i−2i002i−2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ32222-2-22-2-2200002-200002-22-2-22-2-222−22−22−22−2002-200002-20022−2−222−2−222−2−222−2−200−2i2i00−2i2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ33222-2-22-2-2200002-200002-22-2-22-2-22−22−22−22−22002-200002-200−2−222−2−222−2−222−2−222002i−2i002i−2ii2−i2i2−i2i2−i2i2−i20000000000000000
χ34222-2-22-2-2200002-200002-22-2-22-2-22−22−22−22−22002-200002-200−2−222−2−222−2−222−2−22200−2i2i00−2i2i−i2i2−i2i2−i2i2−i2i20000000000000000
χ35222-2-22-2-220000-220000-222-2-22-2-222−2−222−2−2200-220000-220022−2−2−2−22222−2−2−2−2222i−2i002i−2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ36222-2-22-2-220000-220000-222-2-22-2-222−2−222−2−2200-220000-220022−2−2−2−22222−2−2−2−222−2i2i00−2i2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ37222-2-22-2-220000-220000-222-2-22-2-22−222−2−222−200-220000-2200−2−22222−2−2−2−22222−2−22i−2i002i−2i00i2−i2−i2i2i2−i2−i2i20000000000000000
χ38222-2-22-2-220000-220000-222-2-22-2-22−222−2−222−200-220000-2200−2−22222−2−2−2−22222−2−2−2i2i00−2i2i00−i2i2i2−i2−i2i2i2−i20000000000000000
χ392-2222-2-2-222222-2-2-2-2-2-222-2-2-2222-200000000-2-2222222-2-2-2-2000000000000000022-2-2-2-222000000000000000000000000
χ402-2222-2-2-222222-2-2-2-2-2-222-2-2-2222-200000000-2-2222222-2-2-2-20000000000000000-2-22222-2-2000000000000000000000000
χ412-2222-2-2-2222-2-222-2-222-2-2-2-2-2222-20000000022-2-222-2-222-2-200000000000000000000000022-2-2-2-2220000000000000000
χ422-2222-2-2-2222-2-222-2-222-2-2-2-2-2222-20000000022-2-222-2-222-2-2000000000000000000000000-2-22222-2-20000000000000000
χ432-2222-2-2-22-2-2222222-2-2-2-2-2-2-2222-222-2-2-2-222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ442-2222-2-2-22-2-2222222-2-2-2-2-2-2-2222-2-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ452-2222-2-2-2-1-2-2222222-2-2-2-2111-1-1-1122-2-2-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−330000
χ462-2222-2-2-2-1-2-2222222-2-2-2-2111-1-1-1122-2-2-2-222111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−30000
χ472-2222-2-2-2-1-2-2222222-2-2-2-2111-1-1-11-2-22222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ482-2222-2-2-2-1-2-2222222-2-2-2-2111-1-1-11-2-22222-2-2111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ492-2222-2-2-2-1-2-2-2-2-2-2222222111-1-1-112222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ502-2222-2-2-2-1-2-2-2-2-2-2222222111-1-1-112222-2-2-2-2-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ512-2222-2-2-2-1-2-2-2-2-2-2222222111-1-1-11-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ522-2222-2-2-2-1-2-2-2-2-2-2222222111-1-1-11-2-2-2-22222-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ532-22-2-2-222200002-20000-22-2222-2-2-22−2−22−222−200-2200002-20022−2−2−2−222−2−22222−2−22i−2i00−2i2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ542-22-2-2-222200002-20000-22-2222-2-2-22−2−22−222−200-2200002-20022−2−2−2−222−2−22222−2−2−2i2i002i−2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ552-22-2-2-222200002-20000-22-2222-2-2-2−222−22−2−2200-2200002-200−2−22222−2−222−2−2−2−2222i−2i00−2i2i00i2−i2−i2i2−i2i2i2−i20000000000000000
χ562-22-2-2-222200002-20000-22-2222-2-2-2−222−22−2−2200-2200002-200−2−22222−2−222−2−2−2−222−2i2i002i−2i00−i2i2i2−i2i2−i2−i2i20000000000000000
χ572-22-2-2-22220000-2200002-2-2222-2-2-22−22−2−22−22002-20000-220022−2−222−2−2−2−222−2−222002i−2i00−2i2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ582-22-2-2-22220000-2200002-2-2222-2-2-22−22−2−22−22002-20000-220022−2−222−2−2−2−222−2−22200−2i2i002i−2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ592-22-2-2-22220000-2200002-2-2222-2-2-2−22−222−22−2002-20000-2200−2−222−2−22222−2−222−2−2002i−2i00−2i2ii2−i2i2−i2−i2i2−i2i20000000000000000
χ602-22-2-2-22220000-2200002-2-2222-2-2-2−22−222−22−2002-20000-2200−2−222−2−22222−2−222−2−200−2i2i002i−2i−i2i2−i2i2i2−i2i2−i20000000000000000
χ6144444444-2-4-444-4-4-4-444-4-4-2-2-2-2-2-2-200000000-2-22222-2-22222000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-20000000022-2-22222-2-222000000000000000000000000000000000000000000000000
χ63444-4-44-4-4-200004-400004-4-222-222-222−2222−2222−2222−2200-220000-2200−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ64444-4-44-4-4-200004-400004-4-222-222-2−2222−2222−2222−222200-220000-220022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ65444-4-44-4-4-20000-440000-44-222-222-222−22−222222−22−2222002-200002-200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ66444-4-44-4-4-20000-440000-44-222-222-2−222222−22−222222−22002-200002-20022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ6744-44-4-44-44004-400004-40044-4-44-4-4000000004-400004-40000000000000000000000000000000000000000000000000000
χ6844-44-4-44-4400-440000-440044-4-44-4-400000000-440000-440000000000000000000000000000000000000000000000000000
χ6944-44-4-44-4-2004-400004-400-2-222-22200000000-220000-220000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ7044-44-4-44-4-2004-400004-400-2-222-22200000000-220000-220000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ7144-44-4-44-4-200-440000-4400-2-222-222000000002-200002-20000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ7244-44-4-44-4-200-440000-4400-2-222-222000000002-200002-20000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ7344-4-44-4-4444-400004-400004-44-4-44-40000000000004-400004-4000000000000000000000000000000000000000000000000
χ7444-4-44-4-444-440000-4400004-44-4-44-4000000000000-440000-44000000000000000000000000000000000000000000000000
χ7544-4-44-4-44-24-400004-40000-22-222-22000000000000-220000-22−2i32i32i3−2i30000−2i32i32i3−2i3000000000000000000000000000000000000
χ7644-4-44-4-44-24-400004-40000-22-222-22000000000000-220000-222i3−2i3−2i32i300002i3−2i3−2i32i3000000000000000000000000000000000000
χ7744-4-44-4-44-2-440000-440000-22-222-220000000000002-200002-20000−2i32i32i3−2i30000−2i32i32i3−2i300000000000000000000000000000000
χ7844-4-44-4-44-2-440000-440000-22-222-220000000000002-200002-200002i3−2i3−2i32i300002i3−2i3−2i32i300000000000000000000000000000000
χ794-4444-4-4-4-24444-4-4-4-4-4-444222-2-2-220000000022-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ804-4444-4-4-4-244-4-444-4-444-4-4222-2-2-2200000000-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ814-44-4-4-444-200004-40000-442-2-2-222222−22−2222−222222−22002-20000-2200−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ824-44-4-4-444-200004-40000-442-2-2-2222−222222−2222−22−2222002-20000-220022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ834-44-4-4-444-20000-4400004-42-2-2-222222−2222−22−2222−222200-2200002-200−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ844-44-4-4-444-20000-4400004-42-2-2-2222−2222−222222−2222−2200-2200002-20022−2−222−2−2−2−222−2−22200000000000000000000000000000000
χ854-4-44-44-444004-40000-4400-4-44-44-4400000000-4400004-40000000000000000000000000000000000000000000000000000
χ864-4-44-44-44400-4400004-400-4-44-44-44000000004-40000-440000000000000000000000000000000000000000000000000000
χ874-4-44-44-44-2004-40000-440022-22-22-2000000002-20000-220000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000
χ884-4-44-44-44-2004-40000-440022-22-22-2000000002-20000-220000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000
χ894-4-44-44-44-200-4400004-40022-22-22-200000000-2200002-20000i6−i6i6−i6i6−i6i6−i6−i6i6−i6i6−i6i6−i6i600000000000000000000000000000000
χ904-4-44-44-44-200-4400004-40022-22-22-200000000-2200002-20000−i6i6−i6i6−i6i6−i6i6i6−i6i6−i6i6−i6i6−i600000000000000000000000000000000
χ914-4-4-4444-444-40000-440000-44-4-4-4440000000000004-40000-44000000000000000000000000000000000000000000000000
χ924-4-4-4444-44-4400004-40000-44-4-4-444000000000000-4400004-4000000000000000000000000000000000000000000000000
χ934-4-4-4444-4-24-40000-4400002-2222-2-2000000000000-2200002-20000−2i32i32i3−2i300002i3−2i3−2i32i300000000000000000000000000000000
χ944-4-4-4444-4-24-40000-4400002-2222-2-2000000000000-2200002-200002i3−2i3−2i32i30000−2i32i32i3−2i300000000000000000000000000000000
χ954-4-4-4444-4-2-4400004-400002-2222-2-20000000000002-20000-22−2i32i32i3−2i300002i3−2i3−2i32i3000000000000000000000000000000000000
χ964-4-4-4444-4-2-4400004-400002-2222-2-20000000000002-20000-222i3−2i3−2i32i30000−2i32i32i3−2i3000000000000000000000000000000000000

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