Finite Group Databasebeta

← Group #10694894

Character table — Group #10694894

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111222222222222224444444444444444444466666666888888888812121212121212121212121216161616161616161616161648484848
order12222222344444466624666688888888121212121212888888886122424242424242424444444448888448812121212242424244488
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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1
χ9111111-1-111-1-1-1-11111-1111-1-1iiii−i−i−i−i11-1-1-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-11-1i−i11-1-1ii−i−i1-1i−i
χ10111111-1-111-1-1-1-11111-1111-1-1iiii−i−i−i−i11-1-1-1-11111-1-1-1-1-11iiii−i−i−i−iiiii−i−i−i−i11-1-1-11−ii-1-111−i−iii-11−ii
χ11111111-1-111-1-1-1-11111-1111-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-1111-1i−i11-1-1ii−i−i-11−ii
χ12111111-1-111-1-1-1-11111-1111-1-1iiii−i−i−i−i11-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii-1-111-11−ii-1-111−i−iii1-1i−i
χ13111111-1-111-1-1-1-11111-1111-1-1−i−i−i−iiiii11-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-11-1−ii11-1-1−i−iii1-1−ii
χ14111111-1-111-1-1-1-11111-1111-1-1−i−i−i−iiiii11-1-1-1-11111-1-1-1-1-11−i−i−i−iiiii−i−i−i−iiiii11-1-1-11i−i-1-111ii−i−i-11i−i
χ15111111-1-111-1-1-1-11111-1111-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1−ii11-1-1−i−iii-11i−i
χ16111111-1-111-1-1-1-11111-1111-1-1−i−i−i−iiiii11-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i-1-111-11i−i-1-111ii−i−i1-1−ii
χ17222222222-2-2-2-2-2-22222-222222i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2000000002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ18222222222-2-2-2-2-2-22222-22222−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-2000000002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ1922222222-1222222-1-1-122-1-1-1-122222222-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-10000
χ2022222222-1222222-1-1-122-1-1-1-122222222-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-2111111110000
χ2122222222-1222222-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-1-11111111100000000000022-2-2-1-1-1-111110000
χ2222222222-1222222-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100000000-1-111111111000000000000-2-2221111-1-1-1-10000
χ2322222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-12i2i−2i−2i2i2i−2i−2i11111100000000-11−i−iii−i−iii0000000000000000−i3i3−i3i33−33−30000
χ2422222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-12i2i−2i−2i2i2i−2i−2i11111100000000-11−i−iii−i−iii0000000000000000i3−i3i3−i3−33−330000
χ2522222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1−2i−2i2i2i−2i−2i2i2i11111100000000-11ii−i−iii−i−i0000000000000000−i3i3−i3i3−33−330000
χ2622222222-1-2-2-2-2-2-2-1-1-12-2-1-1-1-1−2i−2i2i2i−2i−2i2i2i11111100000000-11ii−i−iii−i−i0000000000000000i3−i3i3−i33−33−30000
χ27222222-2-22-22222-2222-2-222-2-222-2-2-2-222-2-2222200000000-2-222-2-2-2-2220000000000000000000000000000
χ28222222-2-22-22222-2222-2-222-2-2-2-22222-2-2-2-2222200000000-2-2-2-22222-2-20000000000000000000000000000
χ29222222-2-2-12-2-2-2-22-1-1-1-22-1-1112i2i2i2i−2i−2i−2i−2i-1-11111000000001-1−i−i−i−iiiii0000000000002-22i−2i-1-111−i−iii0000
χ30222222-2-2-12-2-2-2-22-1-1-1-22-1-1112i2i2i2i−2i−2i−2i−2i-1-11111000000001-1−i−i−i−iiiii000000000000-22−2i2i11-1-1ii−i−i0000
χ31222222-2-2-12-2-2-2-22-1-1-1-22-1-111−2i−2i−2i−2i2i2i2i2i-1-11111000000001-1iiii−i−i−i−i0000000000002-2−2i2i-1-111ii−i−i0000
χ32222222-2-2-12-2-2-2-22-1-1-1-22-1-111−2i−2i−2i−2i2i2i2i2i-1-11111000000001-1iiii−i−i−i−i000000000000-222i−2i11-1-1−i−iii0000
χ33222222-2-2-1-22222-2-1-1-1-2-2-1-11122-2-2-2-22211-1-1-1-10000000011-1-11111-1-10000000000000000−i3i3i3−i3−i3i3i3−i30000
χ34222222-2-2-1-22222-2-1-1-1-2-2-1-11122-2-2-2-22211-1-1-1-10000000011-1-11111-1-10000000000000000i3−i3−i3i3i3−i3−i3i30000
χ35222222-2-2-1-22222-2-1-1-1-2-2-1-111-2-22222-2-211-1-1-1-1000000001111-1-1-1-1110000000000000000−i3i3i3−i3i3−i3−i3i30000
χ36222222-2-2-1-22222-2-1-1-1-2-2-1-111-2-22222-2-211-1-1-1-1000000001111-1-1-1-1110000000000000000i3−i3−i3i3−i3i3i3−i30000
χ372222-2-2222222-2-22222-2-2-2-222000000002222-2-222222222-2-20000000000000000-2-2-2-20000000000000000
χ382222-2-2222222-2-22222-2-2-2-222000000002222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022220000000000000000
χ392222-2-2222-2-2-222-2222-22-2-22200000000-2-2-2-22200000000-220000000022-2-222-2-200000000000000000000
χ402222-2-2222-2-2-222-2222-22-2-22200000000-2-2-2-22200000000-2200000000-2-222-2-22200000000000000000000
χ412222-2-2-2-222-2-22222222-2-2-2-2-20000000022-2-2222222-2-2-2-22-20000000000000000-2-2220000000000000000
χ422222-2-2-2-222-2-22222222-2-2-2-2-20000000022-2-222-2-2-2-222222-2000000000000000022-2-20000000000000000
χ432222-2-2-2-22-222-2-2-222222-2-2-2-200000000-2-222-2-20000000022000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ442222-2-2-2-22-222-2-2-222222-2-2-2-200000000-2-222-2-2000000002200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ452-22-22-200202i−2i2i−2i0-22-2002-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i2i−2i22−2−2−i2−i2i2i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23001−i−1+i1−i−1+i1+i−1−i1+i−1−i2−2−i2i20000000000000000
χ462-22-22-200202i−2i2i−2i0-22-2002-20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i2i−2i−2−222i2i2−i2−i20000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−1+i1−i−1+i1−i−1−i1+i−1−i1+i−22i2−i20000000000000000
χ472-22-22-200202i−2i2i−2i0-22-2002-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i2i−2i22−2−2−i2−i2i2i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−1+i1−i−1+i1−i−1−i1+i−1−i1+i2−2−i2i20000000000000000
χ482-22-22-200202i−2i2i−2i0-22-2002-200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i2i−2i−2−222i2i2−i2−i200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23001−i−1+i1−i−1+i1+i−1−i1+i−1−i−22i2−i20000000000000000
χ492-22-22-20020−2i2i−2i2i0-22-2002-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i−2i2i22−2−2i2i2−i2−i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i2−2i2−i20000000000000000
χ502-22-22-20020−2i2i−2i2i0-22-2002-200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i−2i2i−2−222−i2−i2i2i200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i−22−i2i20000000000000000
χ512-22-22-20020−2i2i−2i2i0-22-2002-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i−2i2i22−2−2i2i2−i2−i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−1−i1+i−1−i1+i−1+i1−i−1+i1−i2−2i2−i20000000000000000
χ522-22-22-20020−2i2i−2i2i0-22-2002-20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i−2i2i−2−222−i2−i2i2i20000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13001+i−1−i1+i−1−i1−i−1+i1−i−1+i−22−i2i20000000000000000
χ532-22-2-2200202i−2i−2i2i0-22-200-22002ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13002i−2i−2i2i22−2−2−i2−i2i2i2002ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ131+i−1−i−1−i1+i1−i−1+i−1+i1−i−22i2−i20000000000000000
χ542-22-2-2200202i−2i−2i2i0-22-200-22002ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13002i−2i−2i2i−2−222i2i2−i2−i2002ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ13−1−i1+i1+i−1−i−1+i1−i1−i−1+i2−2−i2i20000000000000000
χ552-22-2-2200202i−2i−2i2i0-22-200-2200−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13002i−2i−2i2i22−2−2−i2−i2i2i200−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13−1−i1+i1+i−1−i−1+i1−i1−i−1+i−22i2−i20000000000000000
χ562-22-2-2200202i−2i−2i2i0-22-200-2200−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ13002i−2i−2i2i−2−222i2i2−i2−i200−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ131+i−1−i−1−i1+i1−i−1+i−1+i1−i2−2−i2i20000000000000000
χ572-22-2-220020−2i2i2i−2i0-22-200-2200−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ2300−2i2i2i−2i22−2−2i2i2−i2−i200−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ231−i−1+i−1+i1−i1+i−1−i−1−i1+i−22−i2i20000000000000000
χ582-22-2-220020−2i2i2i−2i0-22-200-2200−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ2300−2i2i2i−2i−2−222−i2−i2i2i200−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−1+i1−i1−i−1+i−1−i1+i1+i−1−i2−2i2−i20000000000000000
χ592-22-2-220020−2i2i2i−2i0-22-200-22002ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ2300−2i2i2i−2i22−2−2i2i2−i2−i2002ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ23−1+i1−i1−i−1+i−1−i1+i1+i−1−i−22−i2i20000000000000000
χ602-22-2-220020−2i2i2i−2i0-22-200-22002ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ2300−2i2i2i−2i−2−222−i2−i2i2i2002ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ231−i−1+i−1+i1−i1+i−1−i−1−i1+i2−2i2−i20000000000000000
χ614444-4-444-2444-4-44-2-2-2-4-422-2-200000000-2-2-2-2220000000022000000000000000000000000000000000000
χ624444-4-444-2-4-4-444-4-2-2-2-4422-2-2000000002222-2-2000000002-2000000000000000000000000000000000000
χ634444-4-4-4-4-24-4-4444-2-2-24-4222200000000-2-222-2-200000000-22000000000000000000000000000000000000
χ644444-4-4-4-4-2-444-4-4-4-2-2-24422220000000022-2-22200000000-2-2000000000000000000000000000000000000
χ6544-4-4004-440000004-4-400004-40000000000000022−2222−2222−2222−2200000000000000000000000000000000000000
χ6644-4-4004-440000004-4-400004-400000000000000−2222−2222−2222−222200000000000000000000000000000000000000
χ6744-4-400-4440000004-4-40000-440000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ6844-4-400-4440000004-4-40000-4400000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ694-44-44-400-204i−4i4i−4i02-2200-220000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000−2i2i−2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000
χ704-44-44-400-204i−4i4i−4i02-2200-2200004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ230000−2i2i−2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000
χ714-44-44-400-20−4i4i−4i4i02-2200-2200004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ1300002i−2i2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000
χ724-44-44-400-20−4i4i−4i4i02-2200-220000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ1300002i−2i2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000
χ734-44-4-4400-204i−4i−4i4i02-22002-2004ζ7+4ζ23−4ζ7−4ζ230000−4ζ5−4ζ134ζ5+4ζ1300−2i2i2i−2i0000000000−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ744-44-4-4400-204i−4i−4i4i02-22002-200−4ζ7−4ζ234ζ7+4ζ2300004ζ5+4ζ13−4ζ5−4ζ1300−2i2i2i−2i00000000002ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ754-44-4-4400-20−4i4i4i−4i02-22002-200−4ζ5−4ζ134ζ5+4ζ1300004ζ7+4ζ23−4ζ7−4ζ23002i−2i−2i2i00000000002ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ764-44-4-4400-20−4i4i4i−4i02-22002-2004ζ5+4ζ13−4ζ5−4ζ130000−4ζ7−4ζ234ζ7+4ζ23002i−2i−2i2i0000000000−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ774-4-440000440000-4-4-44000000000000004-4000000004i−4i−4i4i00000000000000000000000000000000000000
χ784-4-440000440000-4-4-44000000000000004-400000000−4i4i4i−4i00000000000000000000000000000000000000
χ794-4-4400004-400004-4-4400000000000000-4400004-4-44000000000000000000000000000000000000000000
χ804-4-4400004-400004-4-4400000000000000-440000-444-4000000000000000000000000000000000000000000
χ8188-8-8008-8-4000000-4440000-44000000000000000000000000000000000000000000000000000000000000
χ8288-8-800-88-4000000-44400004-4000000000000000000000000000000000000000000000000000000000000
χ838-8-880000-480000-844-400000000000000-4400000000000000000000000000000000000000000000000000
χ848-8-880000-4-80000844-4000000000000004-400000000000000000000000000000000000000000000000000

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