Finite Group Databasebeta

← Group #10692621

Character table — Group #10692621

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888881212121212121212121212121212121216161616161648484848
order12222222344446661212121224444444444666612121212444461212121212121212121212121212121212222244444444444488242424244488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ9111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-111-1-1-11iiii−i−i−i−i1111-1-1-1-111-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ10111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-111-1-1-11iiii−i−i−i−i1111-1-1-1-1-1-111-1-111−i−i−i−iiiiii−iii−i−i-11−ii
χ11111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-1-1-111-11iiii−i−i−i−i-1-1-1-1111111-1-111-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ12111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-1-1-111-11iiii−i−i−i−i-1-1-1-11111-1-111-1-111−i−i−i−iiiii−ii−i−iii1-1i−i
χ13111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-111-1-1-11−i−i−i−iiiii1111-1-1-1-111-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ14111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-111-1-1-11−i−i−i−iiiii1111-1-1-1-1-1-111-1-111iiii−i−i−i−i−ii−i−iii-11i−i
χ15111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-1-1-111-11−i−i−i−iiiii-1-1-1-1111111-1-111-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ16111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-1-1-111-11−i−i−i−iiiii-1-1-1-11111-1-111-1-111iiii−i−i−i−ii−iii−i−i1-1−ii
χ17222222222-2-2-2-2222-2-2-2-22-2-2000000002222-2-2-2-200002-200000000000000002222-2-2-2-2000000000000000000
χ18222222222-2-2-2-2222-2-2-2-22-2-2000000002222-2-2-2-200002-20000000000000000-2-2-2-22222000000000000000000
χ1922222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-10000
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ2222222222-12222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111111111111000000000000000022-1-1-1-10000
χ23222222-2-2222222222222-2-2-20000000022-2-2-2-2220000-2-2000000000000000022-2-2-2-222000000000000000000
χ24222222-2-2222222222222-2-2-20000000022-2-2-2-2220000-2-20000000000000000-2-22222-2-2000000000000000000
χ25222222-2-2-1-2-2-2-2-1-1-11111-2222i2i2i2i−2i−2i−2i−2i-1-111-1-11122-2-21-1−i−i−i−iiiii-1-1-1-1111100000000000000002i−2i−i−iii0000
χ26222222-2-2-1-2-2-2-2-1-1-11111-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111-2-2221-1−i−i−i−iiiii1111-1-1-1-10000000000000000−2i2iii−i−i0000
χ27222222-2-2-1-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-111-1-11122-2-21-1iiii−i−i−i−i-1-1-1-111110000000000000000−2i2iii−i−i0000
χ28222222-2-2-1-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111-2-2221-1iiii−i−i−i−i1111-1-1-1-100000000000000002i−2i−i−iii0000
χ292222-2-222222-2-22222222-22-200000000-2-22222-2-20000-2-200000000000000000000000022-2-222-2-20000000000
χ302222-2-222222-2-22222222-22-200000000-2-22222-2-20000-2-2000000000000000000000000-2-222-2-2220000000000
χ312222-2-2222-2-222222-2-2-2-2-2-2222-2-222-2-2-2-222-2-2220000-2222-2-222-2-20000000000000000000000000000000000
χ322222-2-2222-2-222222-2-2-2-2-2-22-2-222-2-222-2-222-2-2220000-22-2-222-2-2220000000000000000000000000000000000
χ332222-2-222-1-2-222-1-1-11111-2-2222-2-222-2-211-1-111-1-100001-1-1-111-1-11133−3−333−3−30000000000000000003−33−30000
χ342222-2-222-1-2-222-1-1-11111-2-2222-2-222-2-211-1-111-1-100001-1-1-111-1-111−3−333−3−333000000000000000000−33−330000
χ352222-2-222-1-2-222-1-1-11111-2-22-2-222-2-22211-1-111-1-100001-111-1-111-1-133−3−333−3−3000000000000000000−33−330000
χ362222-2-222-1-2-222-1-1-11111-2-22-2-222-2-22211-1-111-1-100001-111-1-111-1-1−3−333−3−3330000000000000000003−33−30000
χ372222-2-2-2-2222-2-222222222-222i2i−2i−2i−2i−2i2i2i-2-2-2-2-2-2-2-20000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ382222-2-2-2-2222-2-222222222-22−2i−2i2i2i2i2i−2i−2i-2-2-2-2-2-2-2-2000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000
χ392222-2-2-2-22-2-222222-2-2-2-222-200000000-2-2-2-2222200002-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ402222-2-2-2-22-2-222222-2-2-2-222-200000000-2-2-2-2222200002-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ412222-2-2-2-2-122-2-2-1-1-1-1-1-1-12-222i2i−2i−2i−2i−2i2i2i111111110000-1-1−i−iiiii−i−i33−3−3−3−333000000000000000000i3−i3−i3i30000
χ422222-2-2-2-2-122-2-2-1-1-1-1-1-1-12-222i2i−2i−2i−2i−2i2i2i111111110000-1-1−i−iiiii−i−i−3−33333−3−3000000000000000000−i3i3i3−i30000
χ432222-2-2-2-2-122-2-2-1-1-1-1-1-1-12-22−2i−2i2i2i2i2i−2i−2i111111110000-1-1ii−i−i−i−iii33−3−3−3−333000000000000000000−i3i3i3−i30000
χ442222-2-2-2-2-122-2-2-1-1-1-1-1-1-12-22−2i−2i2i2i2i2i−2i−2i111111110000-1-1ii−i−i−i−iii−3−33333−3−3000000000000000000i3−i3−i3i30000
χ4522-2-22-20022i−2i2i−2i2-2-22i2i−2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002-200002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ4622-2-22-20022i−2i2i−2i2-2-22i2i−2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000-220000−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ4722-2-22-20022i−2i2i−2i2-2-22i2i−2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002-200002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ4822-2-22-20022i−2i2i−2i2-2-22i2i−2i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000-220000−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ4922-2-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002-20000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ5022-2-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000-2200002i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ5122-2-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002-20000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ5222-2-22-2002−2i2i−2i2i2-2-2−2i−2i2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000-2200002i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ5322-2-2-220022i−2i−2i2i2-2-22i2i−2i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i-220000−2i2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000002-22i−2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5422-2-2-220022i−2i−2i2i2-2-22i2i−2i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i-220000−2i2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000-22−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5522-2-2-220022i−2i−2i2i2-2-22i2i−2i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-220000−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000002-22i−2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ5622-2-2-220022i−2i−2i2i2-2-22i2i−2i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-220000−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000-22−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ5722-2-2-22002−2i2i2i−2i2-2-2−2i−2i2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200002i−2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000002-2−2i2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ5822-2-2-22002−2i2i2i−2i2-2-2−2i−2i2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i-2200002i−2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000-222i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ5922-2-2-22002−2i2i2i−2i2-2-2−2i−2i2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200002i−2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000002-2−2i2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ6022-2-2-22002−2i2i2i−2i2-2-2−2i−2i2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-2200002i−2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000-222i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ6144444444-2-4-4-4-4-2-2-222224-4-400000000-2-2-2-222220000-22000000000000000000000000000000000000000000
χ62444444-4-4-24444-2-2-2-2-2-2-2-4-4-400000000-2-22222-2-2000022000000000000000000000000000000000000000000
χ634444-4-444-244-4-4-2-2-2-2-2-2-2-44-40000000022-2-2-2-222000022000000000000000000000000000000000000000000
χ644444-4-4-4-4-2-4-444-2-2-2222244-4000000002222-2-2-2-20000-22000000000000000000000000000000000000000000
χ6544-4-44-400-24i−4i4i−4i-222−2i−2i2i2i0002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-220000−2i2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000000000
χ6644-4-44-400-24i−4i4i−4i-222−2i−2i2i2i000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-220000−2i2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000000000
χ6744-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i0002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-2200002i−2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000000000
χ6844-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-2200002i−2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000000000
χ6944-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2-200002i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000000000000000000000
χ7044-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2-200002i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000000000000000000000
χ7144-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2-20000−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000000000000000000000
χ7244-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2-20000−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000000000000000000000
χ734-44-4004-440000-44-4000000000000000004-400002i−2i2i−2i00000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ744-44-4004-440000-44-4000000000000000004-40000−2i2i−2i2i0000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ754-44-4004-4-200002-2223−2323−230000000000000-2223−23002i−2i2i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ764-44-4004-4-200002-2223−2323−230000000000000-2223−2300−2i2i−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ774-44-4004-4-200002-22−2323−23230000000000000-22−2323002i−2i2i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ784-44-4004-4-200002-22−2323−23230000000000000-22−232300−2i2i−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ794-44-400-4440000-44-400000000000000000-4400002i−2i−2i2i00000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ804-44-400-4440000-44-400000000000000000-440000−2i2i2i−2i0000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ814-44-400-44-200002-2223−2323−2300000000000002-2−2323002i−2i−2i2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ824-44-400-44-200002-2223−2323−2300000000000002-2−232300−2i2i2i−2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ834-44-400-44-200002-22−2323−232300000000000002-223−23002i−2i−2i2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ844-44-400-44-200002-22−2323−232300000000000002-223−2300−2i2i2i−2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ858-8-88000080000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-880000-4000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000000
χ878-8-880000-4000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000000

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