Finite Group Databasebeta

← Group #10690041

Character table — Group #10690041

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order12224444223444444666121212124444446612121212121244888812121212121212121212242424242424242488888888888844121212124444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ51111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111
χ91111-1-1-1-1-1-1111-1-111111-1-1-1-1111-1-1-1-1-111-1-1111-111-1-11-11111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−ii−iii−i−i
χ101111-1-1-1-1-1-1111-1-111111-1-1-1-1111-1-1-1-1-111-1-1111-111-1-11-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii−ii−i−iii
χ111111-1-1-1-1-1-1111-1-111111-1-1-1-1111-1-1-1-1-111-1-1111-1-1-1111-11111-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-11-1-111−i−iiii−iii−i−i
χ121111-1-1-1-1-1-1111-1-111111-1-1-1-1111-1-1-1-1-111-1-1111-1-1-1111-11111-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-11-1-111ii−i−i−ii−i−iii
χ131111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-111-1-1-111-1-111-1111-1-11-1-1-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-111−i−iiii−i−i−iii
χ141111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-111-1-1-111-1-111-1111-1-11-1-1-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-11-1-111ii−i−i−iiii−i−i
χ151111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-111-1-1-111-1-111-11-1-1111-1-1-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii1-111-1-1ii−i−ii−i−i−iii
χ161111-1-1-1-1-1-1111-1-111111-1-1-1-11-1-111-1-1-111-1-111-11-1-1111-1-1-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−i1-111-1-1−i−iii−iiii−i−i
χ172222222222222-2-2-2-22222222-20000-22222-2-2-2-2000000-2-200000000000000002222000000000000000000-2-20000
χ182222222222222-2-2-2-22222222-20000-22222-2-2-2-2000000-2-20000000000000000-2-2-2-2000000000000000000220000
χ192222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-12-2-2-2-22-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-12-2-2-2-22-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2322222222-2-22-2-222222222222-22222-2-2-2-2-22222-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-22-2-222222222222-2-2-2-2-2-2-2-2-2-22222220000-2-2-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-20000002200000000000000000000000000000000000000002-22-2
χ2622222222-2-22-2-2-2-2-2-22222222200002-2-2-2-2-2-2-2-2000000220000000000000000000000000000000000000000-22-22
χ2722222222-2-2-1-2-22222-1-1-1-1-1-1-1-22222-21111-1-1-1-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-2-22222-1-1-1-1-1-1-1-22222-21111-1-1-1-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-2-222-2-2222-2-2-2-220000-222-2-222-2-20000002-200000000000000000000000000000000000000002i−2i−2i2i
χ322222-2-2-2-2222-2-222-2-2222-2-2-2-220000-222-2-222-2-20000002-20000000000000000000000000000000000000000−2i2i2i−2i
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-2-222-2-2222-2-2-2-222-220000-2222-2-2-2-222000000000000000000000000000000000000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-222222-2-2-2-2222-20000-22-2-22222-2-2000000000000000000000000000000000000
χ352222-2-2-2-222-1-2-2-2-222-1-1-11111-222-2-22-1-11111-1-1-2200001-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ362222-2-2-2-222-1-2-2-2-222-1-1-11111-222-2-22-1-11111-1-1-2200001-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ372222-2-2-2-222-1-2-2-2-222-1-1-11111-2-2-2222-1-11111-1-12-200001-111-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ382222-2-2-2-222-1-2-2-2-222-1-1-11111-2-2-2222-1-11111-1-12-200001-111-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ392222-2-2-2-2-2-222222-2-2222-2-2-2-2-200002-2-22222-2-2000000-2200000000000000002i2i−2i−2i000000000000000000−2i2i0000
χ402222-2-2-2-2-2-222222-2-2222-2-2-2-2-200002-2-22222-2-2000000-220000000000000000−2i−2i2i2i0000000000000000002i−2i0000
χ412222-2-2-2-2-2-2-122-2-222-1-1-11111222-2-2-211-1-111-1-12-222-2-2-11-1-1-1-11111-1-1-1-111110000000000002-2-1-1110000000000
χ422222-2-2-2-2-2-2-122-2-222-1-1-11111222-2-2-211-1-111-1-12-2-2-222-11-1-1-1-111111111-1-1-1-1000000000000-2211-1-10000000000
χ432222-2-2-2-2-2-2-122-2-222-1-1-111112-2-222-211-1-111-1-1-2222-2-2-111111-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ442222-2-2-2-2-2-2-122-2-222-1-1-111112-2-222-211-1-111-1-1-22-2-222-111111-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ4522-2-222-2-22-222-200002-2-222-2-20000002-22-20000002−22−200000000002−22−22−22−22-22-222−2−222−2−20000000000000000
χ4622-2-222-2-22-222-200002-2-222-2-20000002-22-20000002−22−200000000002−22−22−22−2-22-22−2−222−2−2220000000000000000
χ4722-2-222-2-22-222-200002-2-222-2-20000002-22-2000000−22−220000000000−22−22−22−222-22-2−2−222−2−2220000000000000000
χ4822-2-222-2-22-222-200002-2-222-2-20000002-22-2000000−22−220000000000−22−22−22−22-22-2222−2−222−2−20000000000000000
χ4922-2-2-2-222-2222-200002-2-2-2-222000000-222-20000002−2−2200000000002−22−2−22−222i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ5022-2-2-2-222-2222-200002-2-2-2-222000000-222-20000002−2−2200000000002−22−2−22−22−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ5122-2-2-2-222-2222-200002-2-2-2-222000000-222-2000000−222−20000000000−22−222−22−22i−2i−2i2i−i2−i2i2i2i2i2−i2−i20000000000000000
χ5222-2-2-2-222-2222-200002-2-2-2-222000000-222-2000000−222−20000000000−22−222−22−2−2i2i2i−2ii2i2−i2−i2−i2−i2i2i20000000000000000
χ532-22-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i02-22i−2i000002i−2i2-2000000002-2002i−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000001+i−1−i1−i−1+i000000
χ542-22-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i02-22i−2i000002i−2i2-2000000002-2002i−2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000−1−i1+i−1+i1−i000000
χ552-22-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i0-22−2i2i000002i−2i2-200000000-2200−2i2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000−1−i1+i−1+i1−i000000
χ562-22-22i−2i2i−2i002002i−2i2-2-22-22i−2i2i−2i0-22−2i2i000002i−2i2-200000000-2200−2i2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000001+i−1−i1−i−1+i000000
χ572-22-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i02-2−2i2i00000−2i2i2-2000000002-200−2i2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000001−i−1+i1+i−1−i000000
χ582-22-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i02-2−2i2i00000−2i2i2-2000000002-200−2i2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−1+i1−i−1−i1+i000000
χ592-22-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i0-222i−2i00000−2i2i2-200000000-22002i−2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−1+i1−i−1−i1+i000000
χ602-22-2−2i2i−2i2i00200−2i2i2-2-22-2−2i2i−2i2i0-222i−2i00000−2i2i2-200000000-22002i−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000001−i−1+i1+i−1−i000000
χ614444444444-244-4-4-4-4-2-2-2-2-2-2-2-40000-4-2-2-2-222220000002200000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-240000422222222000000-2-200000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-444-4-4-2-2-2222240000-4-2-222-2-222000000-2200000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-24444-4-4-2-2-22222-40000422-2-2-2-2220000002-200000000000000000000000000000000000000000000
χ6544-4-444-4-44-4-24-40000-222-2-222000000-22-2200000022−2222−220000000000−22−22−22−220000000000000000000000000000
χ6644-4-444-4-44-4-24-40000-222-2-222000000-22-22000000−2222−222200000000002−22−22−22−20000000000000000000000000000
χ6744-4-444-4-4-444-4400004-4-444-4-4000000-44-4400000000000000000000000000000000000000000000000000000000
χ6844-4-444-4-4-44-2-440000-222-2-2220000002-22-200000000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ6944-4-444-4-4-44-2-440000-222-2-2220000002-22-200000000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ7044-4-4-4-4444-44-4400004-4-4-4-4440000004-4-4400000000000000000000000000000000000000000000000000000000
χ7144-4-4-4-4444-4-2-440000-22222-2-2000000-222-200000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ7244-4-4-4-4444-4-2-440000-22222-2-2000000-222-200000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ7344-4-4-4-444-44-24-40000-22222-2-20000002-2-2200000022−22−22220000000000−22−222−22−20000000000000000000000000000
χ7444-4-4-4-444-44-24-40000-22222-2-20000002-2-22000000−222222−2200000000002−22−2−22−220000000000000000000000000000
χ754-44-44i−4i4i−4i00400−4i4i-44-44-44i−4i4i−4i0000000000−4i4i-440000000000000000000000000000000000000000000000000000
χ764-44-44i−4i4i−4i00-2004i−4i4-42-22−2i2i−2i2i04-44i−4i00000−2i2i-2200000000-2200−2i2i00000000000000000000000000000000000000
χ774-44-44i−4i4i−4i00-2004i−4i4-42-22−2i2i−2i2i0-44−4i4i00000−2i2i-22000000002-2002i−2i00000000000000000000000000000000000000
χ784-44-44i−4i4i−4i00-200−4i4i-442-22−2i2i−2i2i00000000002i−2i2-2000000000023−2300−2i32i3000000000000000000000000000000000000
χ794-44-44i−4i4i−4i00-200−4i4i-442-22−2i2i−2i2i00000000002i−2i2-20000000000−2323002i3−2i3000000000000000000000000000000000000
χ804-44-4−4i4i−4i4i004004i−4i-44-44-4−4i4i−4i4i00000000004i−4i-440000000000000000000000000000000000000000000000000000
χ814-44-4−4i4i−4i4i00-2004i−4i-442-222i−2i2i−2i0000000000−2i2i2-2000000000023−23002i3−2i3000000000000000000000000000000000000
χ824-44-4−4i4i−4i4i00-2004i−4i-442-222i−2i2i−2i0000000000−2i2i2-20000000000−232300−2i32i3000000000000000000000000000000000000
χ834-44-4−4i4i−4i4i00-200−4i4i4-42-222i−2i2i−2i04-4−4i4i000002i−2i-2200000000-22002i−2i00000000000000000000000000000000000000
χ844-44-4−4i4i−4i4i00-200−4i4i4-42-222i−2i2i−2i0-444i−4i000002i−2i-22000000002-200−2i2i00000000000000000000000000000000000000
χ854-4-444i−4i−4i4i004000000-4-444i−4i−4i4i0000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ864-4-444i−4i−4i4i004000000-4-444i−4i−4i4i000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ874-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ884-4-44−4i4i4i−4i004000000-4-44−4i4i4i−4i0000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ898-8-888i−8i−8i8i00-400000044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ908-8-88−8i8i8i−8i00-400000044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000

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