Finite Group Databasebeta

← Group #10692993

Character table — Group #10692993

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
χ3111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
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−i11-1-111-1-111-1-1-111111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−ii−iii−i−i1-1i−i
χ10111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-111-1-1-111111-1-1-1-1iiii−i−i−i−i-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−i11-1-111-1-1-1-111-11-1-1-1-11111iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−ii−i−iii-11−ii
χ12111111-1-11-1-1-1-1111-1-1-1-1-111iiii−i−i−i−i11-1-111-1-1-1-111-11-1-1-1-11111iiii−i−i−i−i-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−iiiii11-1-111-1-111-1-1-111111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−ii−i−iii1-1−ii
χ14111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-111-1-1-111111-1-1-1-1−i−i−i−iiiii-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−iiiii11-1-111-1-1-1-111-11-1-1-1-11111−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiii−iii−i−i-11i−i
χ16111111-1-11-1-1-1-1111-1-1-1-1-111−i−i−i−iiiii11-1-111-1-1-1-111-11-1-1-1-11111−i−i−i−iiiii-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
χ2022222222-12222-1-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-1-1-1-1-1-1-1-10000000000000000-2-211110000
χ2122222222-12222-1-1-1-1-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-211110000
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-1-111-1-11122-2-21-1-1-1-1-11111−i−i−i−iiiii00000000000000002i−2i−i−iii0000
χ26222222-2-2-1-2-2-2-2-1-1-11111-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111-2-2221-11111-1-1-1-1−i−i−i−iiiii0000000000000000−2i2iii−i−i0000
χ27222222-2-2-1-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-111-1-11122-2-21-1-1-1-1-11111iiii−i−i−i−i0000000000000000−2i2iii−i−i0000
χ28222222-2-2-1-2-2-2-2-1-1-11111-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111-2-2221-11111-1-1-1-1iiii−i−i−i−i00000000000000002i−2i−i−iii0000
χ292222-2-222222-2-22222222-22-222-2-222-2-2-2-22222-2-20000-2-20000000022-2-222-2-200000000000000000000000000
χ302222-2-222222-2-22222222-22-2-2-222-2-222-2-22222-2-20000-2-200000000-2-222-2-22200000000000000000000000000
χ312222-2-2222-2-222222-2-2-2-2-2-2200000000-2-222-2-2220000-2200000000000000000000000022-2-222-2-20000000000
χ322222-2-2222-2-222222-2-2-2-2-2-2200000000-2-222-2-2220000-22000000000000000000000000-2-222-2-2220000000000
χ332222-2-222-122-2-2-1-1-1-1-1-1-1-22-222-2-222-2-211-1-1-1-111000011−i3−i3i3i3−i3−i3i3i3-1-111-1-111000000000000000000−i3i3−i3i30000
χ342222-2-222-122-2-2-1-1-1-1-1-1-1-22-222-2-222-2-211-1-1-1-111000011i3i3−i3−i3i3i3−i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000
χ352222-2-222-122-2-2-1-1-1-1-1-1-1-22-2-2-222-2-22211-1-1-1-111000011−i3−i3i3i3−i3−i3i3i311-1-111-1-1000000000000000000i3−i3i3−i30000
χ362222-2-222-122-2-2-1-1-1-1-1-1-1-22-2-2-222-2-22211-1-1-1-111000011i3i3−i3−i3i3i3−i3−i311-1-111-1-1000000000000000000−i3i3−i3i30000
χ372222-2-2-2-2222-2-222222222-2200000000-2-2-2-2-2-2-2-20000220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000
χ382222-2-2-2-2222-2-222222222-2200000000-2-2-2-2-2-2-2-2000022000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000
χ392222-2-2-2-22-2-222222-2-2-2-222-22i2i−2i−2i−2i−2i2i2i-2-2-2-2222200002-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000
χ402222-2-2-2-22-2-222222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i-2-2-2-2222200002-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000
χ412222-2-2-2-2-1-2-222-1-1-1111122-22i2i−2i−2i−2i−2i2i2i1111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000000000003−3−330000
χ422222-2-2-2-2-1-2-222-1-1-1111122-22i2i−2i−2i−2i−2i2i2i1111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i000000000000000000−333−30000
χ432222-2-2-2-2-1-2-222-1-1-1111122-2−2i−2i2i2i2i2i−2i−2i1111-1-1-1-10000-11−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii000000000000000000−333−30000
χ442222-2-2-2-2-1-2-222-1-1-1111122-2−2i−2i2i2i2i2i−2i−2i1111-1-1-1-10000-11i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000000000003−3−330000
χ4522-2-22-20022i−2i2i−2i2-2-22i2i−2i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002-22i−2i001−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−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00-22−2i2i00−1+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−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002-22i−2i00−1+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−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00-22−2i2i001−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−i2-20000−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i002-2−2i2i001+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−i2-20000−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00-222i−2i00−1−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+i2-20000−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i002-2−2i2i00−1−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+i2-20000−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00-222i−2i001+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-220000−2i2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i2-200002i−2i1+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-220000−2i2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i−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-220000−2i2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i2-200002i−2i−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-220000−2i2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i1+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−2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i2-20000−2i2i1−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−2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−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−2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i2-20000−2i2i−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−2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i1−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
χ634444-4-444-2-4-444-2-2-22222-4-440000000022-2-222-2-200002-2000000000000000000000000000000000000000000
χ644444-4-4-4-4-244-4-4-2-2-2-2-2-2-24-4400000000222222220000-2-2000000000000000000000000000000000000000000
χ6544-4-44-400-24i−4i4i−4i-222−2i−2i2i2i0002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-220000−2i2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000000000000000
χ6644-4-44-400-24i−4i4i−4i-222−2i−2i2i2i000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-220000−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000000000000000
χ6744-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i0002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-2200002i−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000000000000000
χ6844-4-44-400-2−4i4i−4i4i-2222i2i−2i−2i000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-2200002i−2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000000000000000
χ6944-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i0002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2-200002i−2i00000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000000000000000000000
χ7044-4-4-4400-24i−4i−4i4i-222−2i−2i2i2i000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2-200002i−2i000000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000000000000000000000
χ7144-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i0002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2-20000−2i2i00000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000000000000000000000
χ7244-4-4-4400-2−4i4i4i−4i-2222i2i−2i−2i000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2-20000−2i2i000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000000000000000000000
χ734-44-4004-440000-44-4000000000000000004-400002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ744-44-4004-440000-44-4000000000000000004-40000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ754-44-4004-4-200002-22−2i32i3−2i32i30000000000000-22−2i32i3002i−2i2i−2i002ζ7−2ζ72ζ11−2ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
χ764-44-4004-4-200002-22−2i32i3−2i32i30000000000000-22−2i32i300−2i2i−2i2i00−2ζ72ζ7−2ζ112ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000000000000000
χ774-44-4004-4-200002-222i3−2i32i3−2i30000000000000-222i3−2i3002i−2i2i−2i002ζ11−2ζ112ζ7−2ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000000000000000
χ784-44-4004-4-200002-222i3−2i32i3−2i30000000000000-222i3−2i300−2i2i−2i2i00−2ζ112ζ11−2ζ72ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000000000000000
χ794-44-400-4440000-44-400000000000000000-4400002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000
χ804-44-400-4440000-44-400000000000000000-440000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000
χ814-44-400-44-200002-22−2i32i3−2i32i300000000000002-22i3−2i3002i−2i−2i2i002ζ11−2ζ112ζ7−2ζ7−2ζ112ζ11−2ζ72ζ70000000000000000000000000000000000
χ824-44-400-44-200002-22−2i32i3−2i32i300000000000002-22i3−2i300−2i2i2i−2i00−2ζ112ζ11−2ζ72ζ72ζ11−2ζ112ζ7−2ζ70000000000000000000000000000000000
χ834-44-400-44-200002-222i3−2i32i3−2i300000000000002-2−2i32i3002i−2i−2i2i002ζ7−2ζ72ζ11−2ζ11−2ζ72ζ7−2ζ112ζ110000000000000000000000000000000000
χ844-44-400-44-200002-222i3−2i32i3−2i300000000000002-2−2i32i300−2i2i2i−2i00−2ζ72ζ7−2ζ112ζ112ζ7−2ζ72ζ11−2ζ110000000000000000000000000000000000
χ858-8-88000080000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ868-8-880000-4000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ878-8-880000-4000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000

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