Finite Group Databasebeta

← Group #10711743

Character table — Group #10711743

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222222234444666888812121212446666668888881212121212122424242424242424242424242424242488882424242424242424444444441616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111-1-1-1-1111-1-11111111-1-1-1-11-111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ6111111-1-1-1-1111-1-11111111-1-1-1-11-111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ7111111-1-1-1-1111-1-11111111-1-1-1-11-111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ8111111-1-1-1-1111-1-11111111-1-1-1-11-111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ91111-1-111-1-1111-1-11111111-1-1-1-1-11-1-111-1-1-1-111-1-11-1-11111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-111-1-1111-1-11111111-1-1-1-1-11-1-111-1-1-1-111-1-11-1-11111111-1-1-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-111-1-1111-1-11111111-1-1-1-1-11-1-111-1-1-1-111-1-11-1-11111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-111-1-1111-1-11111111-1-1-1-1-11-1-111-1-1-1-111-1-11-1-11111111-1-1-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2222222222222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-22220000-2-2-2-2-2-2222222000000-2-2-2-2-2-2000000000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ1922222222222-2-2-2-22220000-2-2-2-2-2-2222222000000-2-2-2-2-2-2000000000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222222-12222-1-1-12222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ212222222222-12222-1-1-12222-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ222222222222-12222-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ232222222222-12222-1-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ24222222-2-2-2-2222-2-2222-2-2-2-2-2-2-2-22-222-2-2-2-2-2-22222222-2-22-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ25222222-2-2-2-22-2-22222200002222-2222-2-2-2-2000000-2-2-222-2000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ26222222-2-2-2-22-2-22222200002222-2222-2-2-2-2000000-2-2-222-2000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ27222222-2-2-2-2-122-2-2-1-1-1222211112-2-1-1111122-2-2-2-2-1-1-111-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i−i−i−i−iiiii0000000000000000
χ28222222-2-2-2-2-122-2-2-1-1-1222211112-2-1-1111122-2-2-2-2-1-1-111-1-1-1-1-1-1-1-1-111111111−2i−2i2i2iiiii−i−i−i−i0000000000000000
χ29222222-2-2-2-2-122-2-2-1-1-1-2-2-2-211112-2-1-11111-2-22222-1-1-111-111111111-1-1-1-1-1-1-1-100003−33−3−33−330000000000000000
χ30222222-2-2-2-2-122-2-2-1-1-1-2-2-2-211112-2-1-11111-2-22222-1-1-111-111111111-1-1-1-1-1-1-1-10000−33−333−33−30000000000000000
χ312222-2-222-2-2222-2-2222-2-2-2-2-2-2-2-2-22-2-222-2-222-2-2222-2-2222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ322222-2-222-2-22-2-222222000022222-2-2-222-2-2000000-222-2-2-2000000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ332222-2-222-2-22-2-222222000022222-2-2-222-2-2000000-222-2-2-2000000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342222-2-222-2-2-122-2-2-1-1-122221111-2211-1-111-2-222-2-2-111-1-1-1-1-1-1-11111-1-1-1-111112i−2i2i−2i−i−iii−i−iii0000000000000000
χ352222-2-222-2-2-122-2-2-1-1-122221111-2211-1-111-2-222-2-2-111-1-1-1-1-1-1-11111-1-1-1-11111−2i2i−2i2iii−i−iii−i−i0000000000000000
χ362222-2-222-2-2-122-2-2-1-1-1-2-2-2-21111-2211-1-11122-2-222-111-1-1-11111-1-1-1-11111-1-1-1-100003−3−333−3−330000000000000000
χ372222-2-222-2-2-122-2-2-1-1-1-2-2-2-21111-2211-1-11122-2-222-111-1-1-11111-1-1-1-11111-1-1-1-10000−333−3−333−30000000000000000
χ382222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-2222222-2-22-2-2-2-22-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ392222-2-2-2-2222-2-2-2-22220000-2-2-2-222-2-2-2-222000000-22222-2000000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ402222-2-2-2-2222-2-2-2-22220000-2-2-2-222-2-2-2-222000000-22222-2000000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ412222-2-2-2-222-12222-1-1-12222-1-1-1-1-2-21111-1-1-2-2-2-222-11111-1-1-1-1-111111111-1-1-1-12-2-22-1-11111-1-10000000000000000
χ422222-2-2-2-222-12222-1-1-12222-1-1-1-1-2-21111-1-1-2-2-2-222-11111-1-1-1-1-111111111-1-1-1-1-222-211-1-1-1-1110000000000000000
χ432222-2-2-2-222-12222-1-1-1-2-2-2-2-1-1-1-1-2-21111-1-12222-2-2-11111-11111-1-1-1-1-1-1-1-111110000−i3i3i3−i3i3−i3−i3i30000000000000000
χ442222-2-2-2-222-12222-1-1-1-2-2-2-2-1-1-1-1-2-21111-1-12222-2-2-11111-11111-1-1-1-1-1-1-1-111110000i3−i3−i3i3−i3i3i3−i30000000000000000
χ452-2-2200002-22-222-2-2-2222-2-222-2-20000002-200002-2-20000222-2-20000000022-2-2000000000000002i−2i2i−2i0000000000
χ462-2-2200002-22-222-2-2-2222-2-222-2-20000002-200002-2-20000222-2-20000000022-2-200000000000000−2i2i−2i2i0000000000
χ472-2-2200002-22-222-2-2-22-2-22222-2-20000002-20000-22-200002-2-22200000000-2-2220000000000002i−2i00002i−2i00000000
χ482-2-2200002-22-222-2-2-22-2-22222-2-20000002-20000-22-200002-2-22200000000-2-222000000000000−2i2i0000−2i2i00000000
χ492-2-220000-222-22-22-2-2222-2-2-2-222000000-220000-22-20000222-2-200000000-2-222000000000000002-2-220000000000
χ502-2-220000-222-22-22-2-2222-2-2-2-222000000-220000-22-20000222-2-200000000-2-22200000000000000-222-20000000000
χ512-2-220000-222-22-22-2-22-2-222-2-222000000-2200002-2-200002-2-2220000000022-2-20000000000002-20000-2200000000
χ522-2-220000-222-22-22-2-22-2-222-2-222000000-2200002-2-200002-2-2220000000022-2-2000000000000-2200002-200000000
χ534444444444-2-4-4-4-4-2-2-200002222-4-4-2-2-2-2-2-200000022222200000000000000000000000000000000000000000000
χ54444444-4-4-4-4-2-4-444-2-2-20000-2-2-2-2-44-2-22222000000222-2-2200000000000000000000000000000000000000000000
χ554444-4-444-4-4-2-4-444-2-2-20000-2-2-2-24-422-2-2220000002-2-222200000000000000000000000000000000000000000000
χ564444-4-4-4-444-2-4-4-4-4-2-2-200002222442222-2-20000002-2-2-2-2200000000000000000000000000000000000000000000
χ5744-4-4004-400400004-4-4−2i22i2−2i22i2000000004-40000−2i22i200000000−2i22i2−2i22i20000−2i2−2i22i22i200000000000000000000000000000000
χ5844-4-4004-400400004-4-42i2−2i22i2−2i2000000004-400002i2−2i2000000002i2−2i22i2−2i200002i22i2−2i2−2i200000000000000000000000000000000
χ5944-4-4004-400-20000-222−2i22i2−2i22i223−2323−230000-220000−2i22i200023−23000i2−i2i2−i2i6i6−i6−i6i2i2−i2−i2i6−i6i6−i60000000000000000000000000000
χ6044-4-4004-400-20000-222−2i22i2−2i22i2−2323−23230000-220000−2i22i2000−2323000i2−i2i2−i2−i6−i6i6i6i2i2−i2−i2−i6i6−i6i60000000000000000000000000000
χ6144-4-4004-400-20000-2222i2−2i22i2−2i223−2323−230000-2200002i2−2i200023−23000−i2i2−i2i2−i6−i6i6i6−i2−i2i2i2−i6i6−i6i60000000000000000000000000000
χ6244-4-4004-400-20000-2222i2−2i22i2−2i2−2323−23230000-2200002i2−2i2000−2323000−i2i2−i2i2i6i6−i6−i6−i2−i2i2i2i6−i6i6−i60000000000000000000000000000
χ6344-4-400-4400400004-4-4−2i22i2−2i22i200000000-4400002i2−2i200000000−2i22i2−2i22i200002i22i2−2i2−2i200000000000000000000000000000000
χ6444-4-400-4400400004-4-42i2−2i22i2−2i200000000-440000−2i22i2000000002i2−2i22i2−2i20000−2i2−2i22i22i200000000000000000000000000000000
χ6544-4-400-4400-20000-222−2i22i2−2i22i223−2323−2300002-200002i2−2i2000−2323000i2−i2i2−i2−i6−i6i6i6−i2−i2i2i2i6−i6i6−i60000000000000000000000000000
χ6644-4-400-4400-20000-222−2i22i2−2i22i2−2323−232300002-200002i2−2i200023−23000i2−i2i2−i2i6i6−i6−i6−i2−i2i2i2−i6i6−i6i60000000000000000000000000000
χ6744-4-400-4400-20000-2222i2−2i22i2−2i223−2323−2300002-20000−2i22i2000−2323000−i2i2−i2i2i6i6−i6−i6i2i2−i2−i2−i6i6−i6i60000000000000000000000000000
χ6844-4-400-4400-20000-2222i2−2i22i2−2i2−2323−232300002-20000−2i22i200023−23000−i2i2−i2i2−i6−i6i6i6i2i2−i2−i2i6−i6i6−i60000000000000000000000000000
χ694-44-44-4000040000-44-4−2i22i22i2−2i20000004-40000−2i22i20000000000−2i22i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000000000
χ704-44-44-4000040000-44-42i2−2i2−2i22i20000004-400002i2−2i200000000002i2−2i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000000000
χ714-44-44-40000-200002-22−2i22i22i2−2i223−23−232300-220000−2i22i2000000023−230i2−i2−i2i2i2−i2i2−i2i6−i6i6−i6i6−i6−i6i60000000000000000000000000000
χ724-44-44-40000-200002-22−2i22i22i2−2i2−232323−2300-220000−2i22i20000000−23230i2−i2−i2i2i2−i2i2−i2−i6i6−i6i6−i6i6i6−i60000000000000000000000000000
χ734-44-44-40000-200002-222i2−2i2−2i22i223−23−232300-2200002i2−2i2000000023−230−i2i2i2−i2−i2i2−i2i2−i6i6−i6i6−i6i6i6−i60000000000000000000000000000
χ744-44-44-40000-200002-222i2−2i2−2i22i2−232323−2300-2200002i2−2i20000000−23230−i2i2i2−i2−i2i2−i2i2i6−i6i6−i6i6−i6−i6i60000000000000000000000000000
χ754-44-4-44000040000-44-4−2i22i22i2−2i2000000-4400002i2−2i20000000000−2i22i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000000000
χ764-44-4-44000040000-44-42i2−2i2−2i22i2000000-440000−2i22i200000000002i2−2i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000000000
χ774-44-4-440000-200002-22−2i22i22i2−2i223−23−2323002-200002i2−2i20000000−23230i2−i2−i2i2−i2i2−i2i2−i6i6−i6i6i6−i6−i6i60000000000000000000000000000
χ784-44-4-440000-200002-22−2i22i22i2−2i2−232323−23002-200002i2−2i2000000023−230i2−i2−i2i2−i2i2−i2i2i6−i6i6−i6−i6i6i6−i60000000000000000000000000000
χ794-44-4-440000-200002-222i2−2i2−2i22i223−23−2323002-20000−2i22i20000000−23230−i2i2i2−i2i2−i2i2−i2i6−i6i6−i6−i6i6i6−i60000000000000000000000000000
χ804-44-4-440000-200002-222i2−2i2−2i22i2−232323−23002-20000−2i22i2000000023−230−i2i2i2−i2i2−i2i2−i2−i6i6−i6i6i6−i6−i6i60000000000000000000000000000
χ814-4-4400004-444-4-44-4-440000-4-4440000004-400000040000-400000000000000000000000000000000000000000000
χ824-4-4400004-4-24-4-4422-2000022-2-2000000-22000000-200002000023−23−232323−23−232300000000000000000000000000000000
χ834-4-4400004-4-24-4-4422-2000022-2-2000000-22000000-2000020000−232323−23−232323−2300000000000000000000000000000000
χ844-4-4400004-4-2-444-422-244-4-4-2-222000000-2200004-420000-2-2-22200000000-2-2220000000000000000000000000000
χ854-4-4400004-4-2-444-422-2-4-444-2-222000000-220000-4420000-222-2-20000000022-2-20000000000000000000000000000
χ864-4-440000-4444-44-4-4-44000044-4-4000000-4400000040000-400000000000000000000000000000000000000000000
χ874-4-440000-44-24-44-422-20000-2-2220000002-2000000-200002000023−23−2323−232323−2300000000000000000000000000000000
χ884-4-440000-44-24-44-422-20000-2-2220000002-2000000-2000020000−232323−2323−23−232300000000000000000000000000000000
χ894-4-440000-44-2-44-4422-244-4-422-2-20000002-20000-4420000-2-2-2220000000022-2-20000000000000000000000000000
χ904-4-440000-44-2-44-4422-2-4-44422-2-20000002-200004-420000-222-2-200000000-2-2220000000000000000000000000000

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