Finite Group Databasebeta

← Group #10691413

Character table — Group #10691413

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444412121212121212122244888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ91-1-1-111-1111-111-11-1-1-1-1-111-111-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−ii−i1-1ii−i−i11-1-11-11-1ii−i−i11-1-1ii−i−i
χ101-1-1-111-1111-111-11-1-1-1-1-111-111-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−ii−i1-1ii−i−i11-1-1-11-11−i−iii-1-111−i−iii
χ111-1-1-111-1111-111-11-1-1-1-1-111-111-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii-11−i−iii-1-1111-11-1−i−iii-1-111ii−i−i
χ121-1-1-111-1111-111-11-1-1-1-1-111-111-1ii−i−iii−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii-11−i−iii-1-111-11-11ii−i−i11-1-1−i−iii
χ131-1-1-111-1111-111-11-1-1-1-1-111-111-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiii−i-11ii−i−i-1-1111-11-1ii−i−i-1-111−i−iii
χ141-1-1-111-1111-111-11-1-1-1-1-111-111-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiiii−i-11ii−i−i-1-111-11-11−i−iii11-1-1ii−i−i
χ151-1-1-111-1111-111-11-1-1-1-1-111-111-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii1-1−i−iii11-1-11-11-1−i−iii11-1-1−i−iii
χ161-1-1-111-1111-111-11-1-1-1-1-111-111-1−i−iii−i−iii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii1-1−i−iii11-1-1-11-11ii−i−i-1-111ii−i−i
χ1722222222222-2-2-222-22222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000000000000022-2-2000000000000
χ1822222222222-2-2-222-22222222-2-20000000022-2-222-2-2-2-2-2-20000000000000000000000000000-2-222000000000000
χ19222222222-2-2222-2-222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ20222222222-2-2222-2-222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-222-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-222-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ2722222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3−i3i30000000000000000
χ2822222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3i3−i30000000000000000
χ2922222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3i3−i30000000000000000
χ3022222222-1-2-2222-2-22-1-1-1-1-1-1-1-2-2-2-2-2-2222211111111-1-1-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3−i3i30000000000000000
χ31222-2-2-2-222002-2200-222-2-2-2-220000002i−2i2i−2i000000002-22-200002i2i−2i−2i00002i2i−2i−2i0000000000000000−i2i2−i2i22−22−20000
χ32222-2-2-2-222002-2200-222-2-2-2-220000002i−2i2i−2i000000002-22-200002i2i−2i−2i00002i2i−2i−2i0000000000000000i2−i2i2−i2−22−220000
χ33222-2-2-2-222002-2200-222-2-2-2-22000000−2i2i−2i2i000000002-22-20000−2i−2i2i2i0000−2i−2i2i2i0000000000000000−i2i2−i2i2−22−220000
χ34222-2-2-2-222002-2200-222-2-2-2-22000000−2i2i−2i2i000000002-22-20000−2i−2i2i2i0000−2i−2i2i2i0000000000000000i2−i2i2−i22−22−20000
χ352-2-22-2-2222002-2-2002-2-22-2-2220000002-2-22000000002-2-22000022-2-20000-2-22200000000000000002−2−22−222−20000
χ362-2-22-2-2222002-2-2002-2-22-2-2220000002-2-22000000002-2-22000022-2-20000-2-2220000000000000000−222−22−2−220000
χ372-2-22-2-2222002-2-2002-2-22-2-222000000-222-2000000002-2-220000-2-222000022-2-200000000000000002−2−222−2−220000
χ382-2-22-2-2222002-2-2002-2-22-2-222000000-222-2000000002-2-220000-2-222000022-2-20000000000000000−222−2−222−20000
χ392-2-2-222-2222-2-2-222-22-2-2-222-22-220000000022-2-2-2-222-2-22200000000000000000000000000002-2-22000000000000
χ402-2-2-222-2222-2-2-222-22-2-2-222-22-220000000022-2-2-2-222-2-2220000000000000000000000000000-222-2000000000000
χ412-2-2-222-222-2222-2-22-2-2-2-222-22-222i2i−2i−2i−2i−2i2i2i-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ422-2-2-222-222-2222-2-22-2-2-2-222-22-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ432-2-2-222-222-22-2-22-222-2-2-222-222-200000000-2-22222-2-2-2-22200000000000000000000000000000000000000002-2-22
χ442-2-2-222-222-22-2-22-222-2-2-222-222-200000000-2-22222-2-2-2-2220000000000000000000000000000000000000000-222-2
χ452-2-2-222-22-12-222-22-2-2111-1-11-12-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii2i−2i2-2−i−iii-1-1110000000000000000
χ462-2-2-222-22-12-222-22-2-2111-1-11-12-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii−2i2i-22ii−i−i11-1-10000000000000000
χ472-2-2-222-22-12-222-22-2-2111-1-11-12-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i2i−2i-22−i−iii11-1-10000000000000000
χ482-2-2-222-22-12-222-22-2-2111-1-11-12-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i−2i2i2-2ii−i−i-1-1110000000000000000
χ492-2-2-222-22-1-2222-2-22-2111-1-11-1-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i00003−3−33−i3i3i3−i30000000000000000
χ502-2-2-222-22-1-2222-2-22-2111-1-11-1-222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i0000−333−3i3−i3−i3i30000000000000000
χ512-2-2-222-22-1-2222-2-22-2111-1-11-1-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii00003−3−33i3−i3−i3i30000000000000000
χ522-2-2-222-22-1-2222-2-22-2111-1-11-1-22−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii0000−333−3−i3i3i3−i30000000000000000
χ5344444444-244-4-4-444-4-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022-2-222-2-2222200000000000000000000000000000000000000000000
χ55444-4-4-4-44400-44-400444-4-4-4-44000000000000000000-44-4400000000000000000000000000000000000000000000
χ56444-4-4-4-44-2004-4400-4-2-22222-20000004i−4i4i−4i00000000-22-220000−2i−2i2i2i0000−2i−2i2i2i0000000000000000000000000000
χ57444-4-4-4-44-2004-4400-4-2-22222-2000000−4i4i−4i4i00000000-22-2200002i2i−2i−2i00002i2i−2i−2i0000000000000000000000000000
χ58444-4-4-4-44-200-44-4004-2-22222-20000000000000000002-22-22323−23−2300002323−23−2300000000000000000000000000000000
χ59444-4-4-4-44-200-44-4004-2-22222-20000000000000000002-22-2−23−2323230000−23−23232300000000000000000000000000000000
χ6044-444-4-4-44000000004-444-4-4-40022−2222−22000000000000000022−2222−22000022−2222−2200000000000000000000000000000000
χ6144-444-4-4-44000000004-444-4-4-400−2222−22220000000000000000−2222−22220000−2222−222200000000000000000000000000000000
χ6244-444-4-4-4-200000000-22-2-22220022−2222−22000000−2i32i300−2i32i30000−22−22i6−i6i6−i6−22−22i6−i6i6−i60000000000000000000000000000
χ6344-444-4-4-4-200000000-22-2-22220022−2222−220000002i3−2i3002i3−2i30000−22−22−i6i6−i6i6−22−22−i6i6−i6i60000000000000000000000000000
χ6444-444-4-4-4-200000000-22-2-222200−2222−2222000000−2i32i300−2i32i300002−22−2−i6i6−i6i62−22−2−i6i6−i6i60000000000000000000000000000
χ6544-444-4-4-4-200000000-22-2-222200−2222−22220000002i3−2i3002i3−2i300002−22−2i6−i6i6−i62−22−2i6−i6i6−i60000000000000000000000000000
χ6644-4-4-444-4444000-4-404-4-4-444-400000000004-4004-400000000000000000000000000000000000000000000000000
χ6744-4-4-444-44-4-40004404-4-4-444-40000000000-4400-4400000000000000000000000000000000000000000000000000
χ6844-4-4-444-4-244000-4-40-2222-2-220000000000-2200-220000006−6−666−6−666−6−666−6−660000000000000000000000000000
χ6944-4-4-444-4-244000-4-40-2222-2-220000000000-2200-22000000−666−6−666−6−666−6−666−60000000000000000000000000000
χ7044-4-4-444-4-2-4-4000440-2222-2-2200000000002-2002-20000006−6−66−666−66−6−66−666−60000000000000000000000000000
χ7144-4-4-444-4-2-4-4000440-2222-2-2200000000002-2002-2000000−666−66−6−66−666−66−6−660000000000000000000000000000
χ724-444-44-4-444-4000-440-444-44-4-400000000004-400-4400000000000000000000000000000000000000000000000000
χ734-444-44-4-44-440004-40-444-44-4-40000000000-44004-400000000000000000000000000000000000000000000000000
χ744-444-44-4-4-24-4000-4402-2-22-2220000000000-22002-2000000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ754-444-44-4-4-24-4000-4402-2-22-2220000000000-22002-2000000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ764-444-44-4-4-2-440004-402-2-22-22200000000002-200-22000000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ774-444-44-4-4-2-440004-402-2-22-22200000000002-200-22000000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ784-44-44-44-4400000000-44-44-44-400−2i22i22i2−2i20000000000000000−2i22i2−2i22i200002i2−2i22i2−2i200000000000000000000000000000000
χ794-44-44-44-4400000000-44-44-44-4002i2−2i2−2i22i200000000000000002i2−2i22i2−2i20000−2i22i2−2i22i200000000000000000000000000000000
χ804-44-44-44-4-2000000002-22-22-2200−2i22i22i2−2i2000000−2i32i3002i3−2i30000i2−i2i2−i26−66−6−i2i2−i2i2−66−660000000000000000000000000000
χ814-44-44-44-4-2000000002-22-22-2200−2i22i22i2−2i20000002i3−2i300−2i32i30000i2−i2i2−i2−66−66−i2i2−i2i26−66−60000000000000000000000000000
χ824-44-44-44-4-2000000002-22-22-22002i2−2i2−2i22i2000000−2i32i3002i3−2i30000−i2i2−i2i2−66−66i2−i2i2−i26−66−60000000000000000000000000000
χ834-44-44-44-4-2000000002-22-22-22002i2−2i2−2i22i20000002i3−2i300−2i32i30000−i2i2−i2i26−66−6i2−i2i2−i2−66−660000000000000000000000000000
χ844-4-44-4-444400-44400-4-4-44-4-444000000000000000000-444-400000000000000000000000000000000000000000000
χ854-4-44-4-444-2004-4-400422-222-2-20000004-4-4400000000-222-20000-2-222000022-2-20000000000000000000000000000
χ864-4-44-4-444-2004-4-400422-222-2-2000000-444-400000000-222-2000022-2-20000-2-2220000000000000000000000000000
χ874-4-44-4-444-200-44400-422-222-2-20000000000000000002-2-22−2i3−2i32i32i300002i32i3−2i3−2i300000000000000000000000000000000
χ884-4-44-4-444-200-44400-422-222-2-20000000000000000002-2-222i32i3−2i3−2i30000−2i3−2i32i32i300000000000000000000000000000000
χ894-4-4-444-44-24-4-4-444-44222-2-22-2-4400000000-2-22222-2-222-2-200000000000000000000000000000000000000000000
χ904-4-4-444-44-2-44-4-44-444222-2-22-24-40000000022-2-2-2-22222-2-200000000000000000000000000000000000000000000

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