Finite Group Databasebeta

← Group #10691997

Character table — Group #10691997

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222444444444444444444444888888888812121212121212121212121212121212161616161616161616161616242424244848
order122234444444466624488888888121212121212121212126122424242424242424224444448888888888882424242424242424888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ61111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111111111-1-1
χ91111111-1-1-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1-1-111iiii−i−i−i−ii−i1-1ii−i−i11-1-1ii−i−i1-1
χ101111111-1-1-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i11-1-1-1-111iiii−i−i−i−i−ii-11−i−iii-1-111−i−iii-11
χ111111111-1-1-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i-1-11111-1-1−i−i−i−iiiiii−i1-1ii−i−i11-1-1−i−iii-11
χ121111111-1-1-1-1-1-1111-111iiii−i−i−i−i11-1-111-1-1-1-1-11iiii−i−i−i−i-1-11111-1-1−i−i−i−iiiii−ii-11−i−iii-1-111ii−i−i1-1
χ131111111-1-1-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1-1-111−i−i−i−iiiiii−i-11ii−i−i-1-111ii−i−i-11
χ141111111-1-1-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii11-1-1-1-111−i−i−i−iiiii−ii1-1−i−iii11-1-1−i−iii1-1
χ151111111-1-1-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−ii−i-11ii−i−i-1-111−i−iii1-1
χ161111111-1-1-1-1-1-1111-111−i−i−i−iiiii11-1-111-1-1-1-1-11−i−i−i−iiiii-1-11111-1-1iiii−i−i−i−i−ii1-1−i−iii11-1-1ii−i−i-11
χ1722222222222-2-2222-2-2-200000000-2-2222222-2-2-2-2000000002222-2-2-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-200000000-2-2222222-2-2-2-200000000-2-2-2-2222200000000000000000000000000
χ192222222-2-2-2-2222222-2-200000000-2-2-2-222-2-2222-20000000022-2-222-2-200000000000000000000000000
χ202222222-2-2-2-2222222-2-200000000-2-2-2-222-2-2222-200000000-2-222-2-22200000000000000000000000000
χ2122222-2-222-2-222222-2-2200000000-2-2-2-2-2-22222-22000000000000000022-2-222-2-2000000000000000000
χ2222222-2-222-2-222222-2-2200000000-2-2-2-2-2-22222-220000000000000000-2-222-2-222000000000000000000
χ2322222-2-222-2-2-2-222222-22i2i−2i−2i2i2i−2i−2i22-2-2-2-222-2-22-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ2422222-2-222-2-2-2-222222-2−2i−2i2i2i−2i−2i2i2i22-2-2-2-222-2-22-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ2522222-2-2-2-22222222-22-222-2-2-2-2222222-2-2-2-222-2-222-2-2-2-2220000000000000000000000000000000000
χ2622222-2-2-2-22222222-22-2-2-22222-2-22222-2-2-2-222-2-2-2-22222-2-20000000000000000000000000000000000
χ2722222-2-2-2-222-2-22222-2200000000-2-222-2-2-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2822222-2-2-2-222-2-22222-2200000000-2-222-2-2-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ292222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-1000000
χ302222-122222222-1-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-211111111000000
χ312222-122222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111000000000000000022-2-2-1-1-1-11111000000
χ322222-122222222-1-1-1222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000-2-2221111-1-1-1-1000000
χ332222-122-2-2-2-2-2-2-1-1-1-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111111-1−i−i−i−iiiii00000000000000002i−2i2-2−i−iii-1-111000000
χ342222-122-2-2-2-2-2-2-1-1-1-2222i2i2i2i−2i−2i−2i−2i-1-111-1-111111-1−i−i−i−iiiii0000000000000000−2i2i-22ii−i−i11-1-1000000
χ352222-122-2-2-2-2-2-2-1-1-1-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111111-1iiii−i−i−i−i00000000000000002i−2i-22−i−iii11-1-1000000
χ362222-122-2-2-2-2-2-2-1-1-1-222−2i−2i−2i−2i2i2i2i2i-1-111-1-111111-1iiii−i−i−i−i0000000000000000−2i2i2-2ii−i−i-1-111000000
χ372222-1-2-222-2-2-2-2-1-1-122-22i2i−2i−2i2i2i−2i−2i-1-11111-1-111-11−i−iii−i−iii00000000000000000000−i3i3−i3i33−33−3000000
χ382222-1-2-222-2-2-2-2-1-1-122-22i2i−2i−2i2i2i−2i−2i-1-11111-1-111-11−i−iii−i−iii00000000000000000000i3−i3i3−i3−33−33000000
χ392222-1-2-222-2-2-2-2-1-1-122-2−2i−2i2i2i−2i−2i2i2i-1-11111-1-111-11ii−i−iii−i−i00000000000000000000−i3i3−i3i3−33−33000000
χ402222-1-2-222-2-2-2-2-1-1-122-2−2i−2i2i2i−2i−2i2i2i-1-11111-1-111-11ii−i−iii−i−i00000000000000000000i3−i3i3−i33−33−3000000
χ412222-1-2-2-2-22222-1-1-1-22-222-2-2-2-222-1-1-1-11111-1-111-1-11111-1-1000000000000000000003−3−33−333−3000000
χ422222-1-2-2-2-22222-1-1-1-22-222-2-2-2-222-1-1-1-11111-1-111-1-11111-1-100000000000000000000−333−33−3−33000000
χ432222-1-2-2-2-22222-1-1-1-22-2-2-22222-2-2-1-1-1-11111-1-11111-1-1-1-111000000000000000000003−3−333−3−33000000
χ442222-1-2-2-2-22222-1-1-1-22-2-2-22222-2-2-1-1-1-11111-1-11111-1-1-1-11100000000000000000000−333−3−333−3000000
χ4522-2-222-22i−2i2i−2i002-2-20001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i2-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i00002-22i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4622-2-222-22i−2i2i−2i002-2-20001+i−1−i1+i−1−i1−i−1+i1−i−1+i002i−2i2-22i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000-22−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4722-2-222-22i−2i2i−2i002-2-2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i2-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002-22i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000000000
χ4822-2-222-22i−2i2i−2i002-2-2000−1−i1+i−1−i1+i−1+i1−i−1+i1−i002i−2i2-22i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000-22−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000000000
χ4922-2-222-2−2i2i−2i2i002-2-20001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i2-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i00002-2−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5022-2-222-2−2i2i−2i2i002-2-20001−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2i2i2-2−2i2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000-222i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5122-2-222-2−2i2i−2i2i002-2-2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i2-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002-2−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000000000
χ5222-2-222-2−2i2i−2i2i002-2-2000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2i2i2-2−2i2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000-222i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000000000
χ5322-2-22-222i−2i−2i2i002-2-20001−i−1+i−1+i1−i−1−i1+i1+i−1−i00−2i2i-222i−2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i2-22i−2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5422-2-22-222i−2i−2i2i002-2-20001−i−1+i−1+i1−i−1−i1+i1+i−1−i00−2i2i-222i−2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i-22−2i2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5522-2-22-222i−2i−2i2i002-2-2000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−2i2i-222i−2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i2-22i−2i0000−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000000000
χ5622-2-22-222i−2i−2i2i002-2-2000−1+i1−i1−i−1+i1+i−1−i−1−i1+i00−2i2i-222i−2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i-22−2i2i00001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000000000
χ5722-2-22-22−2i2i2i−2i002-2-20001+i−1−i−1−i1+i−1+i1−i1−i−1+i002i−2i-22−2i2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i2-2−2i2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ5822-2-22-22−2i2i2i−2i002-2-20001+i−1−i−1−i1+i−1+i1−i1−i−1+i002i−2i-22−2i2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i-222i−2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ5922-2-22-22−2i2i2i−2i002-2-2000−1−i1+i1+i−1−i1−i−1+i−1+i1−i002i−2i-22−2i2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i2-2−2i2i0000−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000000000
χ6022-2-22-22−2i2i2i−2i002-2-2000−1−i1+i1+i−1−i1−i−1+i−1+i1−i002i−2i-22−2i2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i-222i−2i00001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000000000
χ614444-2444444-4-4-2-2-2-4-4-40000000022-2-2-2-2-2-22222000000000000000000000000000000000000000000
χ624444-244-4-4-4-444-2-2-24-4-4000000002222-2-222-2-2-22000000000000000000000000000000000000000000
χ634444-2-4-444-4-444-2-2-2-4-4400000000222222-2-2-2-22-2000000000000000000000000000000000000000000
χ644444-2-4-4-4-444-4-4-2-2-24-440000000022-2-2222222-2-2000000000000000000000000000000000000000000
χ6544-4-4-24-44i−4i4i−4i00-2220002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00−2i2i-22−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000000000000000
χ6644-4-4-24-44i−4i4i−4i00-222000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00−2i2i-22−2i2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000000000000000
χ6744-4-4-24-4−4i4i−4i4i00-2220002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i002i−2i-222i−2i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000000000000000
χ6844-4-4-24-4−4i4i−4i4i00-222000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i002i−2i-222i−2i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000000000000000
χ6944-4-4-2-444i−4i−4i4i00-2220002−2i−2+2i−2+2i2−2i−2−2i2+2i2+2i−2−2i002i−2i2-2−2i2i0000−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000000000000000000000
χ7044-4-4-2-444i−4i−4i4i00-222000−2+2i2−2i2−2i−2+2i2+2i−2−2i−2−2i2+2i002i−2i2-2−2i2i00001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000000000000000000000
χ7144-4-4-2-44−4i4i4i−4i00-2220002+2i−2−2i−2−2i2+2i−2+2i2−2i2−2i−2+2i00−2i2i2-22i−2i0000−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000000000000000000000
χ7244-4-4-2-44−4i4i4i−4i00-222000−2−2i2+2i2+2i−2−2i2−2i−2+2i−2+2i2−2i00−2i2i2-22i−2i00001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000000000000000000000
χ734-44-440000004i−4i-44-400000000000000000004i−4i000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ744-44-440000004i−4i-44-400000000000000000004i−4i00000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ754-44-44000000−4i4i-44-40000000000000000000−4i4i00000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ764-44-44000000−4i4i-44-40000000000000000000−4i4i000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ778-88-8-40000008i−8i4-440000000000000000000−4i4i00000000000000000000000000000000000000000000
χ788-88-8-4000000−8i8i4-4400000000000000000004i−4i00000000000000000000000000000000000000000000
χ798-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000000000
χ808-8-88-40000000044-40000000000043−430000000000000000000000000000000000000000000000000000
χ818-8-88-40000000044-400000000000−43430000000000000000000000000000000000000000000000000000

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