Finite Group Databasebeta

← Group #10694897

Character table — Group #10694897

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order122222223444444666244444444466661212121212128888888861212121212121212128888888888882466881212242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ9111111-1-111-1-1-1-11111-11iiii−i−i−i−i11-1-111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-11-111i−i-1-1ii−i−i1-1i−i
χ10111111-1-111-1-1-1-11111-11iiii−i−i−i−i11-1-111-1-1-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-1-11-1-1−ii11−i−iii-11−ii
χ11111111-1-111-1-1-1-11111-11iiii−i−i−i−i11-1-111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-1111-111i−i-1-1ii−i−i-11−ii
χ12111111-1-111-1-1-1-11111-11iiii−i−i−i−i11-1-111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1−ii11−i−iii1-1i−i
χ13111111-1-111-1-1-1-11111-11−i−i−i−iiiii11-1-111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-11-111−ii-1-1−i−iii1-1−ii
χ14111111-1-111-1-1-1-11111-11−i−i−i−iiiii11-1-111-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-1-11-1-1i−i11ii−i−i-11i−i
χ15111111-1-111-1-1-1-11111-11−i−i−i−iiiii11-1-111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-1111-111−ii-1-1−i−iii-11i−i
χ16111111-1-111-1-1-1-11111-11−i−i−i−iiiii11-1-111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1i−i11ii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-2000000002222-2-2-2-2-2-2000000002-2000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ18222222222-2-2-2-2-2-22222-2000000002222-2-2-2-2-2-2000000002-200000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ1922222222-1222222-1-1-12222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-100000000000022-1-122-1-1-1-1-1-10000
χ2022222222-1222222-1-1-12222222222-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-211-2-21111110000
χ2122222222-1222222-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-1-11111111100000000000022-1-1-2-2-1-111110000
χ2222222222-1222222-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-1-111111111000000000000-2-2112211-1-1-1-10000
χ23222222-2-22-22222-2222-2-20000000022-2-2-2-2222200000000-2-20000000022-2-2-2-22200000000000000000000
χ24222222-2-22-22222-2222-2-20000000022-2-2-2-2222200000000-2-200000000-2-22222-2-200000000000000000000
χ25222222-2-2-12-2-2-2-22-1-1-1-222i2i2i2i−2i−2i−2i−2i-1-111-1-11111000000001-1−i−i−i−iiiii0000000000002-2-1-12i−2i11−i−iii0000
χ26222222-2-2-12-2-2-2-22-1-1-1-222i2i2i2i−2i−2i−2i−2i-1-111-1-11111000000001-1−i−i−i−iiiii000000000000-2211−2i2i-1-1ii−i−i0000
χ27222222-2-2-12-2-2-2-22-1-1-1-22−2i−2i−2i−2i2i2i2i2i-1-111-1-11111000000001-1iiii−i−i−i−i0000000000002-2-1-1−2i2i11ii−i−i0000
χ28222222-2-2-12-2-2-2-22-1-1-1-22−2i−2i−2i−2i2i2i2i2i-1-111-1-11111000000001-1iiii−i−i−i−i000000000000-22112i−2i-1-1−i−iii0000
χ292222-2-2222222-2-22222-2-200000000-2-2222222-2-222222222-2-20000000000000000-2-2-2-20000000000000000
χ302222-2-2222222-2-22222-2-200000000-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ312222-2-2222-2-2-222-2222-2222-2-222-2-2-2-222-2-2-2-22200000000-2222-2-222-2-20000000000000000000000000000
χ322222-2-2222-2-2-222-2222-22-2-222-2-222-2-222-2-2-2-22200000000-22-2-222-2-2220000000000000000000000000000
χ332222-2-222-1-2-2-222-2-1-1-1-2222-2-222-2-211-1-11111-1-1000000001-1-1-111-1-11100000000000000−i3i300−i3i3−i3i3−i3i30000
χ342222-2-222-1-2-2-222-2-1-1-1-2222-2-222-2-211-1-11111-1-1000000001-1-1-111-1-11100000000000000i3−i300i3−i3i3−i3i3−i30000
χ352222-2-222-1-2-2-222-2-1-1-1-22-2-222-2-22211-1-11111-1-1000000001-111-1-111-1-100000000000000−i3i300−i3i3i3−i3i3−i30000
χ362222-2-222-1-2-2-222-2-1-1-1-22-2-222-2-22211-1-11111-1-1000000001-111-1-111-1-100000000000000i3−i300i3−i3−i3i3−i3i30000
χ372222-2-2-2-222-2-22222222-200000000-2-2-2-222-2-2222222-2-2-2-22-20000000000000000-2-2220000000000000000
χ382222-2-2-2-222-2-22222222-200000000-2-2-2-222-2-222-2-2-2-222222-2000000000000000022-2-20000000000000000
χ392222-2-2-2-22-222-2-2-2222222i2i−2i−2i−2i−2i2i2i-2-2-2-2-2-222-2-200000000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-2-22-222-2-2-222222−2i−2i2i2i2i2i−2i−2i-2-2-2-2-2-222-2-20000000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-2-2-1-222-2-2-2-1-1-1222i2i−2i−2i−2i−2i2i2i111111-1-11100000000-1-1−i−iiiii−i−i00000000000000−i3i300i3−i33−3−330000
χ422222-2-2-2-2-1-222-2-2-2-1-1-1222i2i−2i−2i−2i−2i2i2i111111-1-11100000000-1-1−i−iiiii−i−i00000000000000i3−i300−i3i3−333−30000
χ432222-2-2-2-2-1-222-2-2-2-1-1-122−2i−2i2i2i2i2i−2i−2i111111-1-11100000000-1-1ii−i−i−i−iii00000000000000−i3i300i3−i3−333−30000
χ442222-2-2-2-2-1-222-2-2-2-1-1-122−2i−2i2i2i2i2i−2i−2i111111-1-11100000000-1-1ii−i−i−i−iii00000000000000i3−i300−i3i33−3−330000
χ4522-2-22-200202i−2i2i−2i02-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i2i−2i22−2−2−i2−i2i2i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002−2−i2i20000000000000000
χ4622-2-22-200202i−2i2i−2i02-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-200002i−2i2i−2i−2−222i2i2−i2−i2001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−22i2−i20000000000000000
χ4722-2-22-200202i−2i2i−2i02-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i2i−2i22−2−2−i2−i2i2i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002−2−i2i20000000000000000
χ4822-2-22-200202i−2i2i−2i02-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200002i−2i2i−2i−2−222i2i2−i2−i200−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−22i2−i20000000000000000
χ4922-2-22-20020−2i2i−2i2i02-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i−2i2i22−2−2i2i2−i2−i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002−2i2−i20000000000000000
χ5022-2-22-20020−2i2i−2i2i02-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20000−2i2i−2i2i−2−222−i2−i2i2i2001−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−22−i2i20000000000000000
χ5122-2-22-20020−2i2i−2i2i02-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i−2i2i22−2−2i2i2−i2−i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002−2i2−i20000000000000000
χ5222-2-22-20020−2i2i−2i2i02-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-20000−2i2i−2i2i−2−222−i2−i2i2i200−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−22−i2i20000000000000000
χ5322-2-2-2200202i−2i−2i2i02-2-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−2i2i22−2−2−i2−i2i2i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−22i2−i20000000000000000
χ5422-2-2-2200202i−2i−2i2i02-2-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i-2200002i−2i−2i2i−2−222i2i2−i2−i2001−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ232−2−i2i20000000000000000
χ5522-2-2-2200202i−2i−2i2i02-2-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i−2i2i22−2−2−i2−i2i2i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−22i2−i20000000000000000
χ5622-2-2-2200202i−2i−2i2i02-2-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i-2200002i−2i−2i2i−2−222i2i2−i2−i200−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232−2−i2i20000000000000000
χ5722-2-2-220020−2i2i2i−2i02-2-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i2i−2i22−2−2i2i2−i2−i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−22−i2i20000000000000000
χ5822-2-2-220020−2i2i2i−2i02-2-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i-220000−2i2i2i−2i−2−222−i2−i2i2i2001+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132−2i2−i20000000000000000
χ5922-2-2-220020−2i2i2i−2i02-2-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i2i−2i22−2−2i2i2−i2−i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−22−i2i20000000000000000
χ6022-2-2-220020−2i2i2i−2i02-2-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i-220000−2i2i2i−2i−2−222−i2−i2i2i200−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ132−2i2−i20000000000000000
χ6144444444-2-4-4-4-4-4-4-2-2-24-400000000-2-2-2-222222200000000-22000000000000000000000000000000000000
χ62444444-4-4-2-44444-4-2-2-2-4-400000000-2-22222-2-2-2-20000000022000000000000000000000000000000000000
χ634444-4-444-2444-4-44-2-2-2-4-40000000022-2-2-2-2-2-2220000000022000000000000000000000000000000000000
χ644444-4-4-4-4-24-4-4444-2-2-24-4000000002222-2-222-2-200000000-22000000000000000000000000000000000000
χ6544-4-44-400-204i−4i4i−4i0-222002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i-220000−2i2i−2i2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000
χ6644-4-44-400-204i−4i4i−4i0-22200−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i-220000−2i2i−2i2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000
χ6744-4-44-400-20−4i4i−4i4i0-222002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i-2200002i−2i2i−2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000
χ6844-4-44-400-20−4i4i−4i4i0-22200−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-2200002i−2i2i−2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000
χ6944-4-4-4400-204i−4i−4i4i0-222002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i2-20000−2i2i2i−2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000000000000000
χ7044-4-4-4400-204i−4i−4i4i0-22200−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i2-20000−2i2i2i−2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000000000000000
χ7144-4-4-4400-20−4i4i4i−4i0-222002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i2-200002i−2i−2i2i0000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000000000000000
χ7244-4-4-4400-20−4i4i4i−4i0-22200−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i2-200002i−2i−2i2i00000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000000000000000
χ734-44-40000440000-4-44-4000000000000004-4000000004i−4i4i−4i00000000000000000000000000000000000000
χ744-44-40000440000-4-44-4000000000000004-400000000−4i4i−4i4i00000000000000000000000000000000000000
χ754-44-400004-400004-44-400000000000000-4400004-44-4000000000000000000000000000000000000000000
χ764-44-400004-400004-44-400000000000000-440000-44-44000000000000000000000000000000000000000000
χ774-4-44004-44000000-4-440000000000004-400000022−22−222222−22−222200000000000000000000000000000000000000
χ784-4-44004-44000000-4-440000000000004-4000000−222222−22−222222−2200000000000000000000000000000000000000
χ794-4-4400-444000000-4-44000000000000-4400000022−22−2222−222222−2200000000000000000000000000000000000000
χ804-4-4400-444000000-4-44000000000000-44000000−222222−2222−22−222200000000000000000000000000000000000000
χ818-88-80000-480000-84-4400000000000000-4400000000000000000000000000000000000000000000000000
χ828-88-80000-4-8000084-44000000000000004-400000000000000000000000000000000000000000000000000
χ838-8-88008-8-400000044-4000000000000-440000000000000000000000000000000000000000000000000000
χ848-8-8800-88-400000044-40000000000004-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.