Finite Group Databasebeta

← Group #10705318

Character table — Group #10705318

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122234444444444666888888881212121224668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616888824242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i11-1-1
χ61111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii-1-111
χ71111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i-1-111
χ81111111-1-11111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii11-1-1
χ911111-1-111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1
χ1011111-1-111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11
χ1111111-1-111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-11-11
χ1211111-1-111-1-11111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1
χ1311111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiii−i−iiii−i−i−i−iii1-1-11
χ1411111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i-111-1
χ1511111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−ii−i−iiii−i−i−i−iii-111-1
χ1611111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-20000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ19222222222-2-2-2-2-2-222200000000-2-2-2-22-222000022-2-222-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ202222222-2-22222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ212222222-2-2-2-2-2-222222000000002222-22-2-2000022-2-2-2-222-2-2000000000000000022−2−222−2−2−2−222−2−2220000000000000000
χ222222222-2-2-2-2-2-222222000000002222-22-2-2000022-2-2-2-222-2-20000000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222-2-22222-2-2-2-222200000000-2-2-2-2-22-2-20000-2-2222222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2422222-2-22222-2-2-2-222200000000-2-2-2-2-22-2-20000-2-2222222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2522222-2-222-2-222222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2622222-2-2-2-222-2-2222220000000022222-2220000-2-222-2-2-2-2-2-2000000000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2722222-2-2-2-222-2-2222220000000022222-2220000-2-222-2-2-2-2-2-20000000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2822222-2-2-2-2-2-222-2-2222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ302222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ312222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ322222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ332222-122-2-22222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000000000003−33−3−33−330000
χ342222-122-2-22222-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−33−333−33−30000
χ352222-122-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i2i−2i−2i−i−i−i−iiiii0000
χ362222-122-2-22222-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i−2i2i2iiiii−i−i−i−i0000
χ372222-1-2-222-2-22222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-1-2-222-2-22222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-1-2-222-2-22222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ402222-1-2-222-2-22222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ412222-1-2-2-2-2-2-222-2-2-1-1-12222-2-2-2-2111122-1-122-2-2111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ422222-1-2-2-2-2-2-222-2-2-1-1-12222-2-2-2-2111122-1-122-2-2111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
χ432222-1-2-2-2-2-2-222-2-2-1-1-1-2-2-2-22222111122-1-1-2-222111111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ442222-1-2-2-2-2-2-222-2-2-1-1-1-2-2-2-22222111122-1-1-2-222111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ452-22-22002i−2i002-22i−2i2-2-200002i2i−2i−2i2i2i−2i−2i00002-20000002i−2i002-222-2-200002i2i−2i−2i00000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ462-22-22002i−2i002-22i−2i2-2-200002i2i−2i−2i2i2i−2i−2i00002-20000002i−2i002-222-2-200002i2i−2i−2i000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ472-22-22002i−2i002-22i−2i2-2-20000−2i−2i2i2i2i2i−2i−2i0000-220000002i−2i002-2-2-2220000−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ482-22-22002i−2i002-22i−2i2-2-20000−2i−2i2i2i2i2i−2i−2i0000-220000002i−2i002-2-2-2220000−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ492-22-22002i−2i00-22−2i2i2-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-22000022-2-200002i2i−2i−2i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i0000000000000000
χ502-22-22002i−2i00-22−2i2i2-2-22i2i−2i−2i0000−2i−2i2i2i0000002-200002i−2i00-22000022-2-200002i2i−2i−2i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i0000000000000000
χ512-22-22002i−2i00-22−2i2i2-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-220000-2-2220000−2i−2i2i2i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i0000000000000000
χ522-22-22002i−2i00-22−2i2i2-2-2−2i−2i2i2i0000−2i−2i2i2i000000-2200002i−2i00-220000-2-2220000−2i−2i2i2i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i0000000000000000
χ532-22-2200−2i2i002-2−2i2i2-2-200002i2i−2i−2i−2i−2i2i2i0000-22000000−2i2i002-2-2-22200002i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ542-22-2200−2i2i002-2−2i2i2-2-200002i2i−2i−2i−2i−2i2i2i0000-22000000−2i2i002-2-2-22200002i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ552-22-2200−2i2i002-2−2i2i2-2-20000−2i−2i2i2i−2i−2i2i2i00002-2000000−2i2i002-222-2-20000−2i−2i2i2i000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ562-22-2200−2i2i002-2−2i2i2-2-20000−2i−2i2i2i−2i−2i2i2i00002-2000000−2i2i002-222-2-20000−2i−2i2i2i00000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ572-22-2200−2i2i00-222i−2i2-2-22i2i−2i−2i00002i2i−2i−2i000000-220000−2i2i00-220000-2-22200002i2i−2i−2i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1−i1+i0000000000000000
χ582-22-2200−2i2i00-222i−2i2-2-22i2i−2i−2i00002i2i−2i−2i000000-220000−2i2i00-220000-2-22200002i2i−2i−2i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1+i−1−i0000000000000000
χ592-22-2200−2i2i00-222i−2i2-2-2−2i−2i2i2i00002i2i−2i−2i0000002-20000−2i2i00-22000022-2-20000−2i−2i2i2i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i0000000000000000
χ602-22-2200−2i2i00-222i−2i2-2-2−2i−2i2i2i00002i2i−2i−2i0000002-20000−2i2i00-22000022-2-20000−2i−2i2i2i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i0000000000000000
χ614444-24444-4-4-4-4-4-4-2-2-20000000022224-4-2-20000-2-222-2-22222000000000000000000000000000000000000000000000000
χ624444-244-4-4-4-4-4-444-2-2-200000000-2-2-2-2-44220000-2-22222-2-222000000000000000000000000000000000000000000000000
χ634444-2-4-44444-4-4-4-4-2-2-2000000002222-4422000022-2-2-2-2-2-222000000000000000000000000000000000000000000000000
χ644444-2-4-4-4-444-4-444-2-2-200000000-2-2-2-24-4-2-2000022-2-2222222000000000000000000000000000000000000000000000000
χ6544-4-444-400000000-44-422−2222−2222−2222−220000000000004-4000000000000000022−2222−2222−2222−2200000000000000000000000000000000
χ6644-4-444-400000000-44-4−2222−2222−2222−22220000000000004-40000000000000000−2222−2222−2222−222200000000000000000000000000000000
χ6744-4-44-4400000000-44-422−2222−22−2222−2222000000000000-440000000000000000−2222−222222−2222−2200000000000000000000000000000000
χ6844-4-44-4400000000-44-4−2222−222222−2222−22000000000000-44000000000000000022−2222−22−2222−222200000000000000000000000000000000
χ6944-4-4-24-4000000002-2222−2222−2222−2222−2223−2323−2300000000-22000023−23006−66−66−66−6−22−22−22−2200000000000000000000000000000000
χ7044-4-4-24-4000000002-2222−2222−2222−2222−22−2323−232300000000-220000−232300−66−66−66−66−22−22−22−2200000000000000000000000000000000
χ7144-4-4-24-4000000002-22−2222−2222−2222−222223−2323−2300000000-22000023−2300−66−66−66−662−22−22−22−200000000000000000000000000000000
χ7244-4-4-24-4000000002-22−2222−2222−2222−2222−2323−232300000000-220000−2323006−66−66−66−62−22−22−22−200000000000000000000000000000000
χ7344-4-4-2-44000000002-2222−2222−22−2222−222223−2323−23000000002-20000−232300−66−666−66−62−22−2−22−2200000000000000000000000000000000
χ7444-4-4-2-44000000002-2222−2222−22−2222−2222−2323−2323000000002-2000023−23006−66−6−66−662−22−2−22−2200000000000000000000000000000000
χ7544-4-4-2-44000000002-22−2222−222222−2222−2223−2323−23000000002-20000−2323006−66−6−66−66−22−222−22−200000000000000000000000000000000
χ7644-4-4-2-44000000002-22−2222−222222−2222−22−2323−2323000000002-2000023−2300−66−666−66−6−22−222−22−200000000000000000000000000000000
χ774-44-4-2004i−4i004-44i−4i-22200004i4i−4i−4i−2i−2i2i2i00004-4000000−2i2i00-22-2-2220000−2i−2i2i2i000000000000000000000000000000000000
χ784-44-4-2004i−4i004-44i−4i-2220000−4i−4i4i4i−2i−2i2i2i0000-44000000−2i2i00-2222-2-200002i2i−2i−2i000000000000000000000000000000000000
χ794-44-4-2004i−4i00-44−4i4i-2224i4i−4i−4i00002i2i−2i−2i0000004-40000−2i2i002-20000-2-2220000−2i−2i2i2i00000000000000000000000000000000
χ804-44-4-2004i−4i00-44−4i4i-222−4i−4i4i4i00002i2i−2i−2i000000-440000−2i2i002-2000022-2-200002i2i−2i−2i00000000000000000000000000000000
χ814-44-4-200−4i4i004-4−4i4i-22200004i4i−4i−4i2i2i−2i−2i0000-440000002i−2i00-2222-2-20000−2i−2i2i2i000000000000000000000000000000000000
χ824-44-4-200−4i4i004-4−4i4i-2220000−4i−4i4i4i2i2i−2i−2i00004-40000002i−2i00-22-2-22200002i2i−2i−2i000000000000000000000000000000000000
χ834-44-4-200−4i4i00-444i−4i-2224i4i−4i−4i0000−2i−2i2i2i000000-4400002i−2i002-2000022-2-20000−2i−2i2i2i00000000000000000000000000000000
χ844-44-4-200−4i4i00-444i−4i-222−4i−4i4i4i0000−2i−2i2i2i0000004-400002i−2i002-20000-2-22200002i2i−2i−2i00000000000000000000000000000000
χ854-4-44400004-40000-4-44−2i22i22i2−2i2−2i22i22i2−2i2000000000000004-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ864-4-44400004-40000-4-442i2−2i2−2i22i22i2−2i2−2i22i2000000000000004-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ874-4-4440000-440000-4-44−2i22i22i2−2i22i2−2i2−2i22i200000000000000-44000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ884-4-4440000-440000-4-442i2−2i2−2i22i2−2i22i22i2−2i200000000000000-4400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ894-4-44-200004-4000022-2−2i22i22i2−2i2−2i22i22i2−2i2−2i32i32i3−2i300−2i32i3000000-220000006−6−66−666−6i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ904-4-44-200004-4000022-2−2i22i22i2−2i2−2i22i22i2−2i22i3−2i3−2i32i3002i3−2i3000000-22000000−666−66−6−66i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ914-4-44-200004-4000022-22i2−2i2−2i22i22i2−2i2−2i22i2−2i32i32i3−2i300−2i32i3000000-22000000−666−66−6−66−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ924-4-44-200004-4000022-22i2−2i2−2i22i22i2−2i2−2i22i22i3−2i3−2i32i3002i3−2i3000000-220000006−6−66−666−6−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ934-4-44-20000-44000022-2−2i22i22i2−2i22i2−2i2−2i22i2−2i32i32i3−2i3002i3−2i30000002-2000000−666−6−666−6−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ944-4-44-20000-44000022-2−2i22i22i2−2i22i2−2i2−2i22i22i3−2i3−2i32i300−2i32i30000002-20000006−6−666−6−66−i2i2i2−i2i2−i2−i2i200000000000000000000000000000000
χ954-4-44-20000-44000022-22i2−2i2−2i22i2−2i22i22i2−2i2−2i32i32i3−2i3002i3−2i30000002-20000006−6−666−6−66i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000
χ964-4-44-20000-44000022-22i2−2i2−2i22i2−2i22i22i2−2i22i3−2i3−2i32i300−2i32i30000002-2000000−666−6−666−6i2−i2−i2i2−i2i2i2−i200000000000000000000000000000000

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