Finite Group Databasebeta

← Group #10694776

Character table — Group #10694776

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order12222234444444466688888888121212124466888812121212121212121212242424242424242424242424242424248888888888888888888824242424242424244444
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
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-1
χ101111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11
χ111111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11
χ121111111-111-1-1-1-1-11111111-1-1-1-1-1-1-1-11-11111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-1
χ131111111-111-1-1-1-1-1111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ141111111-111-1-1-1-1-1111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ151111111-111-1-1-1-1-1111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ161111111-111-1-1-1-1-1111-1-1-1-11111-1-1-1-11-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ1722222222-2-222-2-22222000000002222-2-2220000-2-222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ1822222222-2-222-2-22222000000002222-2-2220000-2-222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ192222222-2-2-2-2-222-222200000000-2-2-2-2-22220000-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ202222222-2-2-2-2-222-222200000000-2-2-2-2-22220000-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ21222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ22222222-122222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ23222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ24222222-122222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ25222222-1-222-2-2-2-2-2-1-1-12222-2-2-2-211112-2-1-122-2-2-1-1111111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i−2i2i−2i−i−iii−i−iii0000
χ26222222-1-222-2-2-2-2-2-1-1-12222-2-2-2-211112-2-1-122-2-2-1-1111111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i2i−2i2iii−i−iii−i−i0000
χ27222222-1-222-2-2-2-2-2-1-1-1-2-2-2-2222211112-2-1-1-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ28222222-1-222-2-2-2-2-2-1-1-1-2-2-2-2222211112-2-1-1-2-222-1-1111111-1-111111111-1-1-1-1-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ292222-2-22222-2-2-2-222222222-2-2-2-22222-22-2-2-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ302222-2-22222-2-2-2-22222-2-2-2-222222222-22-2-222-2-2-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-222-2-2-2-22222220000000022222-2-2-2000022-2-2-2-222-2-2000000000000000022-2-222-2-2000000000000000000000000
χ322222-2-222-2-2-2-22222220000000022222-2-2-2000022-2-2-2-222-2-20000000000000000-2-222-2-222000000000000000000000000
χ332222-2-22-2222222-222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ342222-2-22-2222222-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-222-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ352222-2-22-2-2-222-2-2-222200000000-2-2-2-222-2-20000222222-2-2-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ362222-2-22-2-2-222-2-2-222200000000-2-2-2-222-2-20000222222-2-2-2-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ372222-2-2-1222-2-2-2-22-1-1-12222-2-2-2-2-1-1-1-1-2211-2-2221111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ382222-2-2-1222-2-2-2-22-1-1-12222-2-2-2-2-1-1-1-1-2211-2-2221111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ392222-2-2-1222-2-2-2-22-1-1-1-2-2-2-22222-1-1-1-1-221122-2-21111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ402222-2-2-1222-2-2-2-22-1-1-1-2-2-2-22222-1-1-1-1-221122-2-21111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ412222-2-2-1-2222222-2-1-1-1222222221111-2-211-2-2-2-211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1000000000000000000003−3−333−3−330000
χ422222-2-2-1-2222222-2-1-1-1222222221111-2-211-2-2-2-211-1-111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000−333−3−333−30000
χ432222-2-2-1-2222222-2-1-1-1-2-2-2-2-2-2-2-21111-2-211222211-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ442222-2-2-1-2222222-2-1-1-1-2-2-2-2-2-2-2-21111-2-211222211-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ4522-2-22-222002-200-22-2-222−2−222−2−222-2-2002-22−22−2002-200000022−2−222−2−222−2−222−2−22−22−22−22−2002-2002-20000000000000000
χ4622-2-22-222002-200-22-2-222−2−222−2−222-2-2002-22−22−2002-200000022−2−222−2−222−2−222−2−2−22−22−22−2200-2200-220000000000000000
χ4722-2-22-222002-200-22-2-2−2−222−2−22222-2-2002-2−22−22002-2000000−2−222−2−222−2−222−2−2222−22−22−22−200-2200-220000000000000000
χ4822-2-22-222002-200-22-2-2−2−222−2−22222-2-2002-2−22−22002-2000000−2−222−2−222−2−222−2−222−22−22−22−22002-2002-20000000000000000
χ4922-2-22-22-200-220022-2-222−2−2−2−222-2-222002-22−2−2200-2200000022−2−222−2−2−2−222−2−222−i2i2−i2i2i2−i2i2−i200−2i2i002i−2i0000000000000000
χ5022-2-22-22-200-220022-2-222−2−2−2−222-2-222002-22−2−2200-2200000022−2−222−2−2−2−222−2−222i2−i2i2−i2−i2i2−i2i2002i−2i00−2i2i0000000000000000
χ5122-2-22-22-200-220022-2-2−2−22222−2−2-2-222002-2−222−200-22000000−2−222−2−22222−2−222−2−2−i2i2−i2i2i2−i2i2−i2002i−2i00−2i2i0000000000000000
χ5222-2-22-22-200-220022-2-2−2−22222−2−2-2-222002-2−222−200-22000000−2−222−2−22222−2−222−2−2i2−i2i2−i2−i2i2−i2i200−2i2i002i−2i0000000000000000
χ5322-2-2-222200-2200-22-2-222−2−2−2−22222-2-200-22−222−200-2200000022−2−2−2−22222−2−2−2−2222−2−222−2−222-2002-2000000000000000000
χ5422-2-2-222200-2200-22-2-222−2−2−2−22222-2-200-22−222−200-2200000022−2−2−2−22222−2−2−2−222−222−2−222−2-2200-22000000000000000000
χ5522-2-2-222200-2200-22-2-2−2−22222−2−222-2-200-222−2−2200-22000000−2−22222−2−2−2−22222−2−22−2−222−2−22-2200-22000000000000000000
χ5622-2-2-222200-2200-22-2-2−2−22222−2−222-2-200-222−2−2200-22000000−2−22222−2−2−2−22222−2−2−222−2−222−22-2002-2000000000000000000
χ5722-2-2-222-2002-20022-2-222−2−222−2−2-2-22200-22−22−22002-200000022−2−2−2−222−2−22222−2−2−i2i2i2−i2i2−i2−i2i2−2i2i002i−2i000000000000000000
χ5822-2-2-222-2002-20022-2-222−2−222−2−2-2-22200-22−22−22002-200000022−2−2−2−222−2−22222−2−2i2−i2−i2i2−i2i2i2−i22i−2i00−2i2i000000000000000000
χ5922-2-2-222-2002-20022-2-2−2−222−2−222-2-22200-222−22−2002-2000000−2−22222−2−222−2−2−2−222−i2i2i2−i2i2−i2−i2i22i−2i00−2i2i000000000000000000
χ6022-2-2-222-2002-20022-2-2−2−222−2−222-2-22200-222−22−2002-2000000−2−22222−2−222−2−2−2−222i2−i2−i2i2−i2i2i2−i2−2i2i002i−2i000000000000000000
χ61444444-24-4-444-4-44-2-2-200000000-2-2-2-2-4-4-2-2000022-2-2222222000000000000000000000000000000000000000000000000
χ62444444-2-4-4-4-4-444-4-2-2-2000000002222-44-2-200002222-2-2-2-222000000000000000000000000000000000000000000000000
χ634444-4-4-24-4-4-4-4444-2-2-200000000-2-2-2-24-4220000-2-22222-2-222000000000000000000000000000000000000000000000000
χ644444-4-4-2-4-4-444-4-4-4-2-2-200000000222244220000-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ6544-4-44-4-24004-400-4-2222222−22−222222−22−22-2-22200-2222−2222−2200-22000000−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ6644-4-44-4-24004-400-4-222−22−222222−22−222222-2-22200-22−2222−222200-2200000022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ6744-4-44-4-2-400-44004-2222222−22−22−22−22222222-2-200-2222−22−2222002-2000000−2−222−2−22222−2−222−2−200000000000000000000000000000000
χ6844-4-44-4-2-400-44004-222−22−2222222222−22−2222-2-200-22−222222−22002-200000022−2−222−2−2−2−222−2−22200000000000000000000000000000000
χ6944-4-4-44-2400-4400-4-2222222−22−22−22−222222-2-222002-2−222222−22002-2000000−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7044-4-4-44-2400-4400-4-222−22−2222222222−22−22-2-222002-222−22−2222002-200000022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ7144-4-4-44-2-4004-4004-2222222−22−222222−22−2222-2-2002-2−2222−222200-22000000−2−22222−2−222−2−2−2−22200000000000000000000000000000000
χ7244-4-4-44-2-4004-4004-222−22−222222−22−22222222-2-2002-222−2222−2200-2200000022−2−2−2−222−2−22222−2−200000000000000000000000000000000
χ734-44-4004000004-40-44-4−2i22i2−2i22i2−2i22i2−2i22i20000000000000000004-400−2i22i2−2i22i200000000−2i22i2−2i22i200000000000000000000000000000000
χ744-44-4004000004-40-44-42i2−2i22i2−2i22i2−2i22i2−2i20000000000000000004-4002i2−2i22i2−2i2000000002i2−2i22i2−2i200000000000000000000000000000000
χ754-44-400400000-440-44-4−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000-4400−2i22i2−2i22i2000000002i2−2i22i2−2i200000000000000000000000000000000
χ764-44-400400000-440-44-42i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000-44002i2−2i22i2−2i200000000−2i22i2−2i22i200000000000000000000000000000000
χ774-44-400-2000004-402-22−2i22i2−2i22i2−2i22i2−2i22i223−2323−230000000023−230000-2200i2−i2i2−i2i6−i6i6−i6i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ784-44-400-2000004-402-22−2i22i2−2i22i2−2i22i2−2i22i2−2323−232300000000−23230000-2200i2−i2i2−i2−i6i6−i6i6−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ794-44-400-2000004-402-222i2−2i22i2−2i22i2−2i22i2−2i223−2323−230000000023−230000-2200−i2i2−i2i2−i6i6−i6i6−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ804-44-400-2000004-402-222i2−2i22i2−2i22i2−2i22i2−2i2−2323−232300000000−23230000-2200−i2i2−i2i2i6−i6i6−i6i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ814-44-400-200000-4402-22−2i22i2−2i22i22i2−2i22i2−2i223−2323−2300000000−232300002-200i2−i2i2−i2−i6i6−i6i6i6−i6i6−i6−i2i2−i2i200000000000000000000000000000000
χ824-44-400-200000-4402-22−2i22i2−2i22i22i2−2i22i2−2i2−2323−23230000000023−2300002-200i2−i2i2−i2i6−i6i6−i6−i6i6−i6i6−i2i2−i2i200000000000000000000000000000000
χ834-44-400-200000-4402-222i2−2i22i2−2i2−2i22i2−2i22i223−2323−2300000000−232300002-200−i2i2−i2i2i6−i6i6−i6−i6i6−i6i6i2−i2i2−i200000000000000000000000000000000
χ844-44-400-200000-4402-222i2−2i22i2−2i2−2i22i2−2i22i2−2323−23230000000023−2300002-200−i2i2−i2i2−i6i6−i6i6i6−i6i6−i6i2−i2i2−i200000000000000000000000000000000
χ854-4-4400404-400000-4-4400004i−4i−4i4i000000000000000000004-40000000000004i−4i−4i4i00000000000000000000000000000000
χ864-4-4400404-400000-4-440000−4i4i4i−4i000000000000000000004-4000000000000−4i4i4i−4i00000000000000000000000000000000
χ874-4-440040-4400000-4-444i−4i−4i4i000000000000000000000000-444i−4i−4i4i00000000000000000000000000000000000000000000
χ884-4-440040-4400000-4-44−4i4i4i−4i000000000000000000000000-44−4i4i4i−4i00000000000000000000000000000000000000000000
χ894-4-4400-204-40000022-200004i−4i−4i4i23−23−232300000000000023−2300-220000−2i32i32i3−2i30000−2i2i2i−2i00000000000000000000000000000000
χ904-4-4400-204-40000022-200004i−4i−4i4i−232323−23000000000000−232300-2200002i3−2i3−2i32i30000−2i2i2i−2i00000000000000000000000000000000
χ914-4-4400-204-40000022-20000−4i4i4i−4i23−23−232300000000000023−2300-2200002i3−2i3−2i32i300002i−2i−2i2i00000000000000000000000000000000
χ924-4-4400-204-40000022-20000−4i4i4i−4i−232323−23000000000000−232300-220000−2i32i32i3−2i300002i−2i−2i2i00000000000000000000000000000000
χ934-4-4400-20-440000022-24i−4i−4i4i000023−23−2323000000000000−2323002-2−2i2i2i−2i0000−2i32i32i3−2i3000000000000000000000000000000000000
χ944-4-4400-20-440000022-24i−4i−4i4i0000−232323−2300000000000023−23002-2−2i2i2i−2i00002i3−2i3−2i32i3000000000000000000000000000000000000
χ954-4-4400-20-440000022-2−4i4i4i−4i000023−23−2323000000000000−2323002-22i−2i−2i2i00002i3−2i3−2i32i3000000000000000000000000000000000000
χ964-4-4400-20-440000022-2−4i4i4i−4i0000−232323−2300000000000023−23002-22i−2i−2i2i0000−2i32i32i3−2i3000000000000000000000000000000000000

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