Finite Group Databasebeta

← Group #10690157

Character table — Group #10690157

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222222222444444448888888888888888888888888888888888888824242424242424242424242424242424
order1222444422344666666612121212121212122222444422444444446666666612121212121212121212121212121212121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-11111-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-11111-1-111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-1-111-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222222222-2-2-2-22200-2-2000000-2-2220000-2-2-2-200000000-2-22200000000000000000000
χ182222222222222222222222222222-2-2-2-2-2-2-2-20022000000-2-2-2-20000222200000000-2-2-2-200000000000000000000
χ192222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-2-222-2-2-2-2-2-2-1-1-1-11111-1-1-1-111111111-1-1-1-111110000000000000000
χ212222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22200-2-200000011-1-1−i3−i3i3i31111−i3−i3i3i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000
χ222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-22200-2-200000011-1-1i3i3−i3−i31111i3i3−i3−i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000
χ232222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-222-2-222-2-2-2-2-1-111-1-1-1-1111111111111-1-111-1-1-1-10000000000000000
χ242222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-2-2-22222-1-11111111111-1-1-1-1-1-1-1-1-1-11111110000000000000000
χ252222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200220000001111−i3−i3i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i31111−i3−i3i3i30000000000000000
χ262222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200220000001111i3i3−i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i31111i3i3−i3−i30000000000000000
χ2722222222-2-22-2-222-2-2-2-222222-2-2-2-2002-22-20000000000002-20000000000000000002-2000000000000002-22-20000
χ2822222222-2-22-2-222-2-2-2-222222-2-2-2-2002-22-20000000000002-20000000000000000002-200000000000000-22-220000
χ2922222222-2-22-2-222-2-2-2-222222-2-2-2-200-22-22000000000000-22000000000000000000-220000000000000000002-22-2
χ3022222222-2-22-2-222-2-2-2-222222-2-2-2-200-22-22000000000000-22000000000000000000-22000000000000000000-22-22
χ312222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-200-2200000022220000-2-22200000000-2-2-2-200000000000000000000
χ322222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-2-222-2-222002-200000022-2-2000022-2-200000000-2-22200000000000000000000
χ332222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112222-2-2-2-200-22000000-1-1-1-1−i3−i3i3i311-1-1−i3−i3i3i3i3i3−i3−i31111i3i3−i3−i30000000000000000
χ342222-2-2-2-222-1-2-2-1-1-1-1-1-1-1111111112222-2-2-2-200-22000000-1-1-1-1i3i3−i3−i311-1-1i3i3−i3−i3−i3−i3i3i31111−i3−i3i3i30000000000000000
χ352222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-222-2-2222-2-2-222-2-211-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111110000000000000000
χ362222-2-2-2-222-1-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-2-22-222-2-22211-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-10000000000000000
χ372222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-222-2-222002-2000000-1-111−i3−i3i3i3-1-111i3i3−i3−i3−i3−i3i3i311-1-1i3i3−i3−i30000000000000000
χ382222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-222-2-222002-2000000-1-111i3i3−i3−i3-1-111−i3−i3i3i3i3i3−i3−i311-1-1−i3−i3i3i30000000000000000
χ392222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-2222222-22-2-2-2-2221111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ402222-2-2-2-222-1-2-2-1-1-1-1-1-1-111111111-2-2-2-22222-2-2-222222-2-21111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-10000000000000000
χ412222-2-2-2-2-2-222222-2-2-2-22-2-2-2-22222002-2-220000000000002-2000000000000000000-220000000000000000002i−2i−2i2i
χ422222-2-2-2-2-2-222222-2-2-2-22-2-2-2-22222002-2-220000000000002-2000000000000000000-22000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-222222-2-2-2-22-2-2-2-2222200-222-2000000000000-220000000000000000002-2000000000000002i−2i−2i2i0000
χ442222-2-2-2-2-2-222222-2-2-2-22-2-2-2-2222200-222-2000000000000-220000000000000000002-200000000000000−2i2i2i−2i0000
χ4522-2-22i2i−2i−2i2-222i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i2-200002i−2i0000000000002-20000000000000000002i−2i00001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ4622-2-22i2i−2i−2i2-222i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i2-200002i−2i0000000000002-20000000000000000002i−2i0000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ4722-2-22i2i−2i−2i2-222i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i-220000−2i2i000000000000-22000000000000000000−2i2i00001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ4822-2-22i2i−2i−2i2-222i−2i2-222-2-2-22i2i−2i−2i2i2i−2i−2i-220000−2i2i000000000000-22000000000000000000−2i2i0000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ4922-2-2−2i−2i2i2i2-22−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i2-20000−2i2i0000000000002-2000000000000000000−2i2i00001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ5022-2-2−2i−2i2i2i2-22−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i2-20000−2i2i0000000000002-2000000000000000000−2i2i0000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ5122-2-2−2i−2i2i2i2-22−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i-2200002i−2i000000000000-220000000000000000002i−2i00001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ5222-2-2−2i−2i2i2i2-22−2i2i2-222-2-2-2−2i−2i2i2i−2i−2i2i2i-2200002i−2i000000000000-220000000000000000002i−2i0000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ5344444444-4-4-2-4-4-2-22222-2-2-2-2-22222004-44-4000000000000-22000000000000000000-220000000000000000000000
χ5444444444-4-4-2-4-4-2-22222-2-2-2-2-2222200-44-440000000000002-20000000000000000002-20000000000000000000000
χ554444-4-4-4-4-4-4-244-2-22222-22222-2-2-2-2004-4-44000000000000-220000000000000000002-20000000000000000000000
χ564444-4-4-4-4-4-4-244-2-22222-22222-2-2-2-200-444-40000000000002-2000000000000000000-220000000000000000000000
χ5744-4-44i4i−4i−4i4-4-24i−4i-22-2-2222−2i−2i2i2i−2i−2i2i2i4-400004i−4i000000000000-22000000000000000000−2i2i00000000000000000000
χ5844-4-44i4i−4i−4i4-4-24i−4i-22-2-2222−2i−2i2i2i−2i−2i2i2i-440000−4i4i0000000000002-20000000000000000002i−2i00000000000000000000
χ5944-4-44i4i−4i−4i-444−4i4i4-4-4-444-44i4i−4i−4i−4i−4i4i4i00000000000000000000000000000000000000000000000000000000000000
χ6044-4-44i4i−4i−4i-44-2−4i4i-2222-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000023−23−2i32i300000000000000000000000000000000
χ6144-4-44i4i−4i−4i-44-2−4i4i-2222-2-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000−23232i3−2i300000000000000000000000000000000
χ6244-4-4−4i−4i4i4i4-4-2−4i4i-22-2-22222i2i−2i−2i2i2i−2i−2i4-40000−4i4i000000000000-220000000000000000002i−2i00000000000000000000
χ6344-4-4−4i−4i4i4i4-4-2−4i4i-22-2-22222i2i−2i−2i2i2i−2i−2i-4400004i−4i0000000000002-2000000000000000000−2i2i00000000000000000000
χ6444-4-4−4i−4i4i4i-4444i−4i4-4-4-444-4−4i−4i4i4i4i4i−4i−4i00000000000000000000000000000000000000000000000000000000000000
χ6544-4-4−4i−4i4i4i-44-24i−4i-2222-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000023−232i3−2i300000000000000000000000000000000
χ6644-4-4−4i−4i4i4i-44-24i−4i-2222-2-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000−2323−2i32i300000000000000000000000000000000
χ674-44-44i−4i4i−4i00400-440000-44i−4i4i−4i0000000000000000002-22i−2i0000000000002-22-22i−2i2i−2i000000000000000000000000
χ684-44-44i−4i4i−4i00400-440000-44i−4i4i−4i000000000000000000-22−2i2i000000000000-22-22−2i2i−2i2i000000000000000000000000
χ694-44-44i−4i4i−4i00-2002-2−2i32i3−2i32i32−2i2i−2i2i23−2323−23000000000000002-22i−2i000000000000−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ704-44-44i−4i4i−4i00-2002-2−2i32i3−2i32i32−2i2i−2i2i23−2323−2300000000000000-22−2i2i0000000000001+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ714-44-44i−4i4i−4i00-2002-22i3−2i32i3−2i32−2i2i−2i2i−2323−2323000000000000002-22i−2i000000000000−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ724-44-44i−4i4i−4i00-2002-22i3−2i32i3−2i32−2i2i−2i2i−2323−232300000000000000-22−2i2i0000000000001−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ734-44-4−4i4i−4i4i00400-440000-4−4i4i−4i4i0000000000000000002-2−2i2i0000000000002-22-2−2i2i−2i2i000000000000000000000000
χ744-44-4−4i4i−4i4i00400-440000-4−4i4i−4i4i000000000000000000-222i−2i000000000000-22-222i−2i2i−2i000000000000000000000000
χ754-44-4−4i4i−4i4i00-2002-2−2i32i3−2i32i322i−2i2i−2i−2323−2323000000000000002-2−2i2i000000000000−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ7000000000000000000000000
χ764-44-4−4i4i−4i4i00-2002-2−2i32i3−2i32i322i−2i2i−2i−2323−232300000000000000-222i−2i0000000000001+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ7000000000000000000000000
χ774-44-4−4i4i−4i4i00-2002-22i3−2i32i3−2i322i−2i2i−2i23−2323−23000000000000002-2−2i2i000000000000−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ11000000000000000000000000
χ784-44-4−4i4i−4i4i00-2002-22i3−2i32i3−2i322i−2i2i−2i23−2323−2300000000000000-222i−2i0000000000001−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ11000000000000000000000000
χ794-4-444-4-4400400-4-4000044-4-440000000000002-2002-2000000002-22-200000000000000002-22-20000000000000000
χ804-4-444-4-4400400-4-4000044-4-44000000000000-2200-2200000000-22-220000000000000000-22-220000000000000000
χ814-4-444-4-4400-20022−2i32i32i3−2i3-2-222-2−2i32i32i3−2i3000000002-2002-200000000−1−i31+i3−1+i31−i30000000000000000−1−i31+i3−1+i31−i30000000000000000
χ824-4-444-4-4400-20022−2i32i32i3−2i3-2-222-2−2i32i32i3−2i300000000-2200-22000000001+i3−1−i31−i3−1+i300000000000000001+i3−1−i31−i3−1+i30000000000000000
χ834-4-444-4-4400-200222i3−2i3−2i32i3-2-222-22i3−2i3−2i32i3000000002-2002-200000000−1+i31−i3−1−i31+i30000000000000000−1+i31−i3−1−i31+i30000000000000000
χ844-4-444-4-4400-200222i3−2i3−2i32i3-2-222-22i3−2i3−2i32i300000000-2200-22000000001−i3−1+i31+i3−1−i300000000000000001−i3−1+i31+i3−1−i30000000000000000
χ854-4-44-444-400400-4-400004-444-40000000000002-200-22000000002-22-20000000000000000-22-220000000000000000
χ864-4-44-444-400400-4-400004-444-4000000000000-22002-200000000-22-2200000000000000002-22-20000000000000000
χ874-4-44-444-400-20022−2i32i32i3−2i3-22-2-222i3−2i3−2i32i3000000002-200-2200000000−1−i31+i3−1+i31−i300000000000000001+i3−1−i31−i3−1+i30000000000000000
χ884-4-44-444-400-20022−2i32i32i3−2i3-22-2-222i3−2i3−2i32i300000000-22002-2000000001+i3−1−i31−i3−1+i30000000000000000−1−i31+i3−1+i31−i30000000000000000
χ894-4-44-444-400-200222i3−2i3−2i32i3-22-2-22−2i32i32i3−2i3000000002-200-2200000000−1+i31−i3−1−i31+i300000000000000001−i3−1+i31+i3−1−i30000000000000000
χ904-4-44-444-400-200222i3−2i3−2i32i3-22-2-22−2i32i32i3−2i300000000-22002-2000000001−i3−1+i31+i3−1−i30000000000000000−1+i31−i3−1−i31+i30000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.