Finite Group Databasebeta

← Group #10690077

Character table — Group #10690077

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order122244442234444446661212121244668888121212121212888888121224242424242424242424242424242424224488888888246612124488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−i1111-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-11-1ii−i−i11-1-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−i1111-1-1i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1-11−i−iii-1-111
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−i1111-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−i−i−iiiii-11-1-1111-1ii−i−i-1-111
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1ii−i−i1111-1-1i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii-1-111iiii−i−i−i−i-11-1-111-11−i−iii11-1-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii1111-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1iiii−i−i−i−i-11-1-1111-1−i−iii-1-111
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii1111-1-1−iiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−i−i−iiiii-11-1-111-11ii−i−i11-1-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii1111-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-11-1−i−iii11-1-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-1−i−iii1111-1-1−ii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1-11ii−i−i-1-111
χ1722222222222-2-22-2-222222222-2-2220000-2-222-2-2000000-2-20000000000000000222200000000000000-2-200000000
χ1822222222222-2-22-2-222222222-2-2220000-2-222-2-2000000-2-20000000000000000-2-2-2-2000000000000002200000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-2-2-2-2-2-2-1-1111111111111111100000000000022-1-1-1-10000000000
χ2322222222-2-2222-222-22222222-2-2-2-2222222-2-222-2-20000-2-222-2-222-2-2000000000000000000000000000000000000
χ2422222222-2-2222-222-22222222-2-2-2-2-2-2-2-222-2-222220000-2-2-2-222-2-222000000000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-20000-2-2-2-2-2-2000000220000000000000000000000000000000000002-22-20000
χ2622222222-2-22-2-2-2-2-2-2222222222-2-20000-2-2-2-2-2-200000022000000000000000000000000000000000000-22-220000
χ2722222222-2-2-122-222-2-1-1-1-1-1-1-1-2-2112222-1-111-1-1-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ2822222222-2-2-122-222-2-1-1-1-1-1-1-1-2-2112222-1-111-1-1-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ2922222222-2-2-122-222-2-1-1-1-1-1-1-1-2-211-2-2-2-2-1-111-1-12200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ3022222222-2-2-122-222-2-1-1-1-1-1-1-1-2-211-2-2-2-2-1-111-1-12200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-2-22222i2i−2i−2i22-2-2-2-2−2i2i0000-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-2-2222−2i−2i2i2i22-2-2-2-22i−2i0000-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-2220000-2-2-2-2220000002-20000000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-2220000-2-2-2-2220000002-2000000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-12i2i−2i−2i-1-11111−2i2i00001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ362222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-12i2i−2i−2i-1-11111−2i2i00001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ372222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1−2i−2i2i2i-1-111112i−2i00001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ382222-2-2-2-222-122-2-2-2-2-1-1-11111-22-1-1−2i−2i2i2i-1-111112i−2i00001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ392222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-20000-2-22222000000-22000000000000000022-2-200000000000000-2200000000
χ402222-2-2-2-2-2-22-2-22222222-2-2-2-2-22-2-20000-2-22222000000-220000000000000000-2-222000000000000002-200000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i-1-1-1-1112i−2i2i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ422222-2-2-2-2-2-2-1222-2-22-1-1-111112-2112i2i−2i−2i-1-1-1-1112i−2i−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ432222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i-1-1-1-111−2i2i2i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ442222-2-2-2-2-2-2-1222-2-22-1-1-111112-211−2i−2i2i2i-1-1-1-111−2i2i−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ4522-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-2002i−2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000002−2−i2i2
χ4622-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-2002i−2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000−22i2−i2
χ4722-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-2002i−2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000−22i2−i2
χ4822-2-22i−2i2i−2i0022-202i−2i02-2-22i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-2002i−2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000002−2−i2i2
χ4922-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-200−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000002−2i2−i2
χ5022-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-200−2i2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000−22−i2i2
χ5122-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-200−2i2i000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000−22−i2i2
χ5222-2-2−2i2i−2i2i0022-20−2i2i02-2-2−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-200−2i2i000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000002−2i2−i2
χ532-2-2222-2-22-2200-2002-2-2222-2-2002-20000002-20000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i20000000000000000
χ542-2-2222-2-22-2200-2002-2-2222-2-2002-20000002-20000−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2-22-22i2−i2i2−i2i2−i2i2−i20000000000000000
χ552-2-2222-2-22-2200-2002-2-2222-2-2002-20000002-20000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i20000000000000000
χ562-2-2222-2-22-2200-2002-2-2222-2-2002-20000002-20000i2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2-22-22−i2i2−i2i2−i2i2−i2i20000000000000000
χ572-2-22-2-222-22200-2002-2-22-2-22200-220000002-200002−2−2200000000002−22−2−22−222-2-222−22−2−22−220000000000000000
χ582-2-22-2-222-22200-2002-2-22-2-22200-220000002-200002−2−2200000000002−22−2−22−22-222-2−22−222−22−20000000000000000
χ592-2-22-2-222-22200-2002-2-22-2-22200-220000002-20000−222−20000000000−22−222−22−22-2-22−22−222−22−20000000000000000
χ602-2-22-2-222-22200-2002-2-22-2-22200-220000002-20000−222−20000000000−22−222−22−2-222-22−22−2−22−220000000000000000
χ614444444444-2-4-44-4-44-2-2-2-2-2-2-2-4-4-2-2000022-2-2220000002200000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-244220000222222000000-2-200000000000000000000000000000000000000000000
χ634444-4-4-4-444-2-4-4-444-4-2-2-222224-4-2-200002222-2-2000000-2200000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-4-2-4-44444-2-2-22222-4422000022-2-2-2-20000002-200000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i004-440−4i4i04-4-44i−4i4i−4i00000000-4400−4i4i0000000000000000000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i00-24-404i−4i0-222−2i2i−2i2i00004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-2200−2i2i00000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000000000
χ6744-4-44i−4i4i−4i00-24-404i−4i0-222−2i2i−2i2i0000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-2200−2i2i000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000000000
χ6844-4-44i−4i4i−4i00-2-440−4i4i0-222−2i2i−2i2i000000002-2002i−2i00000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000000000000000
χ6944-4-44i−4i4i−4i00-2-440−4i4i0-222−2i2i−2i2i000000002-2002i−2i0000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000000000000000
χ7044-4-4−4i4i−4i4i004-4404i−4i04-4-4−4i4i−4i4i00000000-44004i−4i0000000000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-24-40−4i4i0-2222i−2i2i−2i0000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ23-22002i−2i000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-24-40−4i4i0-2222i−2i2i−2i00004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-22002i−2i00000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000000000
χ7344-4-4−4i4i−4i4i00-2-4404i−4i0-2222i−2i2i−2i000000002-200−2i2i0000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000000000000000
χ7444-4-4−4i4i−4i4i00-2-4404i−4i0-2222i−2i2i−2i000000002-200−2i2i00000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000000000000000
χ754-44-44i−4i−4i4i004000000-44-44i−4i−4i4i000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ764-44-44i−4i−4i4i004000000-44-44i−4i−4i4i0000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ774-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i0000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ784-44-4−4i4i4i−4i004000000-44-4−4i4i4i−4i000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ794-4-4444-4-44-4-200-400422-2-2-22200-22000000-220000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000000000000000
χ804-4-4444-4-44-4-200-400422-2-2-22200-22000000-2200002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000000000000000
χ814-4-4444-4-4-44400400-4-4-4444-4-400-44000000-44000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-44-200400-422-2-2-222002-20000002-20000000000000000006−6−666−6−660000000000000000000000000000
χ834-4-4444-4-4-44-200400-422-2-2-222002-20000002-2000000000000000000−666−6−666−60000000000000000000000000000
χ844-4-44-4-4444-4400400-4-4-44-4-444004-4000000-44000000000000000000000000000000000000000000000000000000
χ854-4-44-4-4444-4-200400-422-222-2-200-220000002-2000000000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ864-4-44-4-4444-4-200400-422-222-2-200-220000002-2000000000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ874-4-44-4-444-44-200-400422-222-2-2002-2000000-22000022−22−22220000000000−22−222−22−20000000000000000000000000000
χ884-4-44-4-444-44-200-400422-222-2-2002-2000000-220000−222222−2200000000002−22−2−22−220000000000000000000000000000
χ898-88-88i−8i−8i8i00-40000004-44−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i8i−8i00-40000004-444i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000

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