Finite Group Databasebeta

← Group #10695007

Character table — Group #10695007

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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111-1-1
χ91-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i11-1-11-1i−i
χ101-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11−ii−i−iii-1-111-11−ii
χ111-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-1i−iii−i−i11-1-1-11−ii
χ121-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11iiii−i−i−i−i1111-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11−ii−i−iii-1-1111-1i−i
χ131-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii11-1-11-1−ii
χ141-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11i−iii−i−i-1-111-11i−i
χ151-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-1−ii−i−iii11-1-1-11i−i
χ161-1-1-1111-111111-1-1-1-1-1-111-1-1-111-11−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11i−iii−i−i-1-1111-1−ii
χ1722222222222-2-2-2-2-2-222-2-222222220000000022-2-222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ1822222222222-2-2-2-2-2-222-2-222222220000000022-2-222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ19222222222-2-222-2-222-2-2-2-2222222222-2-222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222-2-222-2-222-2-2-2-22222222-2-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ21222222222-2-2-2-222-2-2-2-222222222200000000-2-222-2-222-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ22222222222-2-2-2-222-2-2-2-222222222200000000-2-222-2-222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
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
χ2522222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-21111-1-1-1-10000
χ2622222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-222-1-1-1-111110000
χ2722222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-1-2-222-2-222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211111111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ31222-22-2-2-222-20000002-20022-22-2-2-22−22−22−22−22-2002-200000022−2−222−2−222−2−222−2−22−22−22−22−2002-2002-20000000000000000
χ32222-22-2-2-222-20000002-20022-22-2-2-22−22−22−22−22-2002-200000022−2−222−2−222−2−222−2−2−22−22−22−2200-2200-220000000000000000
χ33222-22-2-2-222-20000002-20022-22-2-2-2−22−22−22−222-2002-2000000−2−222−2−222−2−222−2−2222−22−22−22−200-2200-220000000000000000
χ34222-22-2-2-222-20000002-20022-22-2-2-2−22−22−22−222-2002-2000000−2−222−2−222−2−222−2−222−22−22−22−22002-2002-20000000000000000
χ35222-22-2-2-22-22000000-220022-22-2-2-22−2−222−2−22-2200-2200000022−2−2−2−22222−2−2−2−2222−2−222−2−222-2002-2000000000000000000
χ36222-22-2-2-22-22000000-220022-22-2-2-22−2−222−2−22-2200-2200000022−2−2−2−22222−2−2−2−222−222−2−222−2-2200-22000000000000000000
χ37222-22-2-2-22-22000000-220022-22-2-2-2−222−2−222−2-2200-22000000−2−22222−2−2−2−22222−2−22−2−222−2−22-2200-22000000000000000000
χ38222-22-2-2-22-22000000-220022-22-2-2-2−222−2−222−2-2200-22000000−2−22222−2−2−2−22222−2−2−222−2−222−22-2002-2000000000000000000
χ392-2-222-2-2222-2000000-2200-2-222-22-2−i2i2−i2i2i2−i2i2−i22-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22−22−2−22−2200−2i2i002i−2i0000000000000000
χ402-2-222-2-2222-2000000-2200-2-222-22-2−i2i2−i2i2i2−i2i2−i22-200-22000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−22−222−22−2002i−2i00−2i2i0000000000000000
χ412-2-222-2-2222-2000000-2200-2-222-22-2i2−i2i2−i2−i2i2−i2i22-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22−22−2−22−22002i−2i00−2i2i0000000000000000
χ422-2-222-2-2222-2000000-2200-2-222-22-2i2−i2i2−i2−i2i2−i2i22-200-22000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−22−222−22−200−2i2i002i−2i0000000000000000
χ432-2-222-2-222-220000002-200-2-222-22-2−i2i2i2−i2i2−i2−i2i2-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22−2−22−222−2−2i2i002i−2i000000000000000000
χ442-2-222-2-222-220000002-200-2-222-22-2−i2i2i2−i2i2−i2−i2i2-22002-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−222−22−2−222i−2i00−2i2i000000000000000000
χ452-2-222-2-222-220000002-200-2-222-22-2i2−i2−i2i2−i2i2i2−i2-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22−2−22−222−22i−2i00−2i2i000000000000000000
χ462-2-222-2-222-220000002-200-2-222-22-2i2−i2−i2i2−i2i2i2−i2-22002-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−222−22−2−22−2i2i002i−2i000000000000000000
χ472-2-2-2222-2222-2-22222-2-2-2-2-2-2-222-220000000022-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ482-2-2-2222-2222-2-22222-2-2-2-2-2-2-222-220000000022-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ492-2-2-2222-22-2-22222-2-222-2-2-2-2-222-222i2i−2i−2i−2i−2i2i2i-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ502-2-2-2222-22-2-22222-2-222-2-2-2-2-222-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ512-2-2-2222-22-2-2-2-2-2-2222222-2-2-222-2200000000-2-22222-2-2-2-222000000000000000022-2-2-2-222000000000000000000000000
χ522-2-2-2222-22-2-2-2-2-2-2222222-2-2-222-2200000000-2-22222-2-2-2-2220000000000000000-2-22222-2-2000000000000000000000000
χ532-2-2-2222-2-12222-2-2-2-2-2-222111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002-22i−2i−i−iii-1-1110000
χ542-2-2-2222-2-12222-2-2-2-2-2-222111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000-22−2i2iii−i−i11-1-10000
χ552-2-2-2222-2-12222-2-2-2-2-2-222111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002-2−2i2iii−i−i-1-1110000
χ562-2-2-2222-2-12222-2-2-2-2-2-222111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000-222i−2i−i−iii11-1-10000
χ572-2-2-2222-2-1-2-22222-2-222-2-2111-1-11-12i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000003−3−33−i3i3i3−i30000
χ582-2-2-2222-2-1-2-22222-2-222-2-2111-1-11-12i2i−2i−2i−2i−2i2i2i1111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−333−3i3−i3−i3i30000
χ592-2-2-2222-2-1-2-22222-2-222-2-2111-1-11-1−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii000000000000000000003−3−33i3−i3−i3i30000
χ602-2-2-2222-2-1-2-22222-2-222-2-2111-1-11-1−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−333−3−i3i3i3−i30000
χ6144444444-244-4-4-4-4-4-444-4-4-2-2-2-2-2-2-200000000-2-222-2-2222222000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4-444-4-4-4-444-2-2-2-2-2-2-20000000022-2-222-2-22222000000000000000000000000000000000000000000000000
χ63444-44-4-4-4-24-40000004-400-2-22-222222−2222−2222−2222−22-2200-22000000−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ64444-44-4-4-4-24-40000004-400-2-22-2222−2222−2222−2222−2222-2200-2200000022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ65444-44-4-4-4-2-44000000-4400-2-22-222222−22−222222−22−22222-2002-2000000−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ66444-44-4-4-4-2-44000000-4400-2-22-2222−222222−22−222222−222-2002-200000022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ6744-44-44-4-44004-4004-400004-44-4-4-4400000000000000004-44-4000000000000000000000000000000000000000000000000
χ6844-44-44-4-4400-4400-4400004-44-4-4-440000000000000000-44-44000000000000000000000000000000000000000000000000
χ6944-44-44-4-4-2004-4004-40000-22-2222-20000000000000000-22-22000023−2323−23000023−2323−2300000000000000000000000000000000
χ7044-44-44-4-4-2004-4004-40000-22-2222-20000000000000000-22-220000−2323−23230000−2323−232300000000000000000000000000000000
χ7144-44-44-4-4-200-4400-440000-22-2222-200000000000000002-22-223−2323−23000023−2323−23000000000000000000000000000000000000
χ7244-44-44-4-4-200-4400-440000-22-2222-200000000000000002-22-2−2323−23230000−2323−2323000000000000000000000000000000000000
χ7344-4-4-4-444400004-400004-44-4-4-444-400000000004-4004-40000000000000000000000000000000000000000000000000000
χ7444-4-4-4-44440000-440000-444-4-4-444-40000000000-4400-440000000000000000000000000000000000000000000000000000
χ7544-4-4-4-444-200004-400004-4-2222-2-220000000000-2200-2200006−6−666−6−666−6−666−6−6600000000000000000000000000000000
χ7644-4-4-4-444-200004-400004-4-2222-2-220000000000-2200-220000−666−6−666−6−666−6−666−600000000000000000000000000000000
χ7744-4-4-4-444-20000-440000-44-2222-2-2200000000002-2002-200006−6−66−666−66−6−66−666−600000000000000000000000000000000
χ7844-4-4-4-444-20000-440000-44-2222-2-2200000000002-2002-20000−666−66−6−66−666−66−6−6600000000000000000000000000000000
χ794-444-4-44-4400004-40000-44-444-44-4-40000000000-44004-40000000000000000000000000000000000000000000000000000
χ804-444-4-44-440000-4400004-4-444-44-4-400000000004-400-440000000000000000000000000000000000000000000000000000
χ814-444-4-44-4-200004-40000-442-2-22-22200000000002-200-220000i6−i6−i6i6−i6i6i6−i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ824-444-4-44-4-200004-40000-442-2-22-22200000000002-200-220000−i6i6i6−i6i6−i6−i6i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ834-444-4-44-4-20000-4400004-42-2-22-2220000000000-22002-20000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ844-444-4-44-4-20000-4400004-42-2-22-2220000000000-22002-20000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ854-44-4-44-444004-400-440000-44-4-4-44400000000000000004-4-44000000000000000000000000000000000000000000000000
χ864-44-4-44-44400-44004-40000-44-4-4-4440000000000000000-444-4000000000000000000000000000000000000000000000000
χ874-44-4-44-44-2004-400-4400002-2222-2-20000000000000000-222-20000−2i32i3−2i32i300002i3−2i32i3−2i300000000000000000000000000000000
χ884-44-4-44-44-2004-400-4400002-2222-2-20000000000000000-222-200002i3−2i32i3−2i30000−2i32i3−2i32i300000000000000000000000000000000
χ894-44-4-44-44-200-44004-400002-2222-2-200000000000000002-2-22−2i32i3−2i32i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ904-44-4-44-44-200-44004-400002-2222-2-200000000000000002-2-222i3−2i32i3−2i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ914-4-444-4-44-24-4000000-440022-2-22-22−2i22i2−2i22i22i2−2i22i2−2i2-22002-2000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ924-4-444-4-44-24-4000000-440022-2-22-222i2−2i22i2−2i2−2i22i2−2i22i2-22002-2000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ934-4-444-4-44-2-440000004-40022-2-22-22−2i22i22i2−2i22i2−2i2−2i22i22-200-22000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ944-4-444-4-44-2-440000004-40022-2-22-222i2−2i2−2i22i2−2i22i22i2−2i22-200-22000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ954-4-4-4444-4-244-4-44444-4-4-4-4222-2-22-200000000-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ964-4-4-4444-4-2-4-4-4-4-4-4444444222-2-22-20000000022-2-2-2-22222-2-2000000000000000000000000000000000000000000000000

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