Finite Group Databasebeta

← Group #10693639

Character table — Group #10693639

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222222222444444444488888888888888888888888888121212121212121216161616161624242424242424244848
order12224444223444444666121212124466121212121212888888881212242424242424242424242424242424244444444488242424248888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−iii−i−iii−i−i11-1-11-1
χ101111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i11-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiii−iii−i−i−i−iii-1-111-11
χ111111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−ii−i−iii−i−iii11-1-1-11
χ121111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111ii−i−i-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii−i−iiiii−i−i-1-1111-1
χ131111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−ii−i−iiiii−i−i-1-111-11
χ141111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii11-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii−ii−i−iii−i−iii11-1-11-1
χ151111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−ii−iii−i−i−i−iii-1-1111-1
χ161111-1-1-1-1-1-11111-1-11111-1-1-1-11-1-1-111-1-111−i−iii-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiii−iii−i−iii−i−i11-1-1-11
χ17222222222222-2-2-2-222222222-2-22222-2-2-2-200000000-2-2000000000000000022-2-222-2-20000000000000000
χ18222222222222-2-2-2-222222222-2-22222-2-2-2-200000000-2-20000000000000000-2-222-2-2220000000000000000
χ192222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111100000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-100000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-111111111111111110000000022-1-1-1-10000000000
χ2322222222-2-22-22222-22222222-2-2-2-2-2-222222-22-20000-2-222-2-222-2-200000000000000000000000000000000
χ2422222222-2-22-22222-22222222-2-2-2-2-2-22222-22-220000-2-2-2-222-2-22200000000000000000000000000000000
χ2522222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000002i−2i2i−2i00
χ2622222222-2-22-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-200000000220000000000000000000000000000000000−2i2i−2i2i00
χ2722222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-12-22-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000−i3i3−i3i30000000000
χ2822222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-12-22-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000i3−i3i3−i30000000000
χ2922222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-22-2200001111-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000i3−i3i3−i30000000000
χ3022222222-2-2-1-22222-2-1-1-1-1-1-1-1-2-21111-1-1-1-1-22-2200001111-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000−i3i3−i3i30000000000
χ312222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-2-2-2222i−2i−2i2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ322222-2-2-2-2222-222-2-2-2222-2-2-2-2-2222-2-2-2-222−2i2i2i−2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-2222-2-2-222-2222-2-2-2-22-222-2-222-2-2000000002-200000000000000000000000000000000002i−2i−2i2i00
χ342222-2-2-2-2222-2-2-222-2222-2-2-2-22-222-2-222-2-2000000002-20000000000000000000000000000000000−2i2i2i−2i00
χ352222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-11111-1-12i−2i−2i2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000003−3−330000000000
χ362222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-11111-1-12i−2i−2i2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000000000−333−30000000000
χ372222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-11111-1-1−2i2i2i−2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000000000−333−30000000000
χ382222-2-2-2-222-1-222-2-2-2-1-1-11111-22-1-11111-1-1−2i2i2i−2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000003−3−330000000000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22222-2-200000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-22-2-22222-2-200000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-12i2i−2i−2i22-2-2-11−i−i−i−iiiii-1-1-1-11111000000002i−2i−i−iii0000000000
χ422222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-12i2i−2i−2i-2-222-11−i−i−i−iiiii1111-1-1-1-100000000−2i2iii−i−i0000000000
χ432222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-1−2i−2i2i2i22-2-2-11iiii−i−i−i−i-1-1-1-1111100000000−2i2iii−i−i0000000000
χ442222-2-2-2-2-2-2-1222-2-22-1-1-111112-211-1-111-1-1−2i−2i2i2i-2-222-11iiii−i−i−i−i1111-1-1-1-1000000002i−2i−i−iii0000000000
χ452-2-2222-2-22-22-2000022-2-222-2-2002-22-2000000002−22−200000000002−22−22−22−2002i−2i002i−2i000000−i2i2−i2i2000000
χ462-2-2222-2-22-22-2000022-2-222-2-2002-22-2000000002−22−200000000002−22−22−22−200−2i2i00−2i2i000000i2−i2i2−i2000000
χ472-2-2222-2-22-22-2000022-2-222-2-2002-22-200000000−22−220000000000−22−22−22−22002i−2i002i−2i000000i2−i2i2−i2000000
χ482-2-2222-2-22-22-2000022-2-222-2-2002-22-200000000−22−220000000000−22−22−22−2200−2i2i00−2i2i000000−i2i2−i2i2000000
χ492-2-22-2-222-222-2000022-2-2-2-22200-222-2000000002−2−2200000000002−22−2−22−22002-200-22000000−222−2000000
χ502-2-22-2-222-222-2000022-2-2-2-22200-222-2000000002−2−2200000000002−22−2−22−2200-22002-20000002−2−22000000
χ512-2-22-2-222-222-2000022-2-2-2-22200-222-200000000−222−20000000000−22−222−22−2002-200-220000002−2−22000000
χ522-2-22-2-222-222-2000022-2-2-2-22200-222-200000000−222−20000000000−22−222−22−200-22002-2000000−222−2000000
χ534444444444-24-4-4-4-44-2-2-2-2-2-2-2-4-4-2-2-2-2222200000000220000000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-2442222222200000000-2-20000000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-444-4-2-2-222224-4-2-222-2-22200000000-220000000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-24-4-4444-2-2-22222-4422-2-2-2-222000000002-20000000000000000000000000000000000000000
χ5744-4-44i−4i4i−4i004000000-44-44i−4i4i−4i0000000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ5844-4-44i−4i4i−4i004000000-44-44i−4i4i−4i000000000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ5944-4-4−4i4i−4i4i004000000-44-4−4i4i−4i4i0000000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ6044-4-4−4i4i−4i4i004000000-44-4−4i4i−4i4i000000000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ614-44-44i−4i−4i4i00404-44i−4i0-4-444i−4i−4i4i0000004i−4i4-400000000000000000000000000000000000000000000000000
χ624-44-44i−4i−4i4i0040-44−4i4i0-4-444i−4i−4i4i000000−4i4i-4400000000000000000000000000000000000000000000000000
χ634-44-44i−4i−4i4i00-204-44i−4i022-2−2i2i2i−2i000000−2i2i-2200000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ230000000000000000000000000000000000
χ644-44-44i−4i−4i4i00-204-44i−4i022-2−2i2i2i−2i000000−2i2i-220000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ230000000000000000000000000000000000
χ654-44-44i−4i−4i4i00-20-44−4i4i022-2−2i2i2i−2i0000002i−2i2-2000000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000
χ664-44-44i−4i−4i4i00-20-44−4i4i022-2−2i2i2i−2i0000002i−2i2-20000000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000
χ674-44-4−4i4i4i−4i00404-4−4i4i0-4-44−4i4i4i−4i000000−4i4i4-400000000000000000000000000000000000000000000000000
χ684-44-4−4i4i4i−4i0040-444i−4i0-4-44−4i4i4i−4i0000004i−4i-4400000000000000000000000000000000000000000000000000
χ694-44-4−4i4i4i−4i00-204-4−4i4i022-22i−2i−2i2i0000002i−2i-220000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ130000000000000000000000000000000000
χ704-44-4−4i4i4i−4i00-204-4−4i4i022-22i−2i−2i2i0000002i−2i-2200000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ130000000000000000000000000000000000
χ714-44-4−4i4i4i−4i00-20-444i−4i022-22i−2i−2i2i000000−2i2i2-20000000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000
χ724-44-4−4i4i4i−4i00-20-444i−4i022-22i−2i−2i2i000000−2i2i2-2000000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000
χ734-4-4444-4-44-4-2-400004-222-2-22200-22-220000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ744-4-4444-4-44-4-2-400004-222-2-22200-22-2200000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ754-4-4444-4-4-44440000-44-4-444-4-400-44-44000000000000000000000000000000000000000000000000000000
χ764-4-4444-4-4-44-240000-4-222-2-222002-22-20000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ774-4-4444-4-4-44-240000-4-222-2-222002-22-20000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ784-4-44-4-4444-4440000-44-4-4-4-444004-4-44000000000000000000000000000000000000000000000000000000
χ794-4-44-4-4444-4-240000-4-22222-2-200-222-20000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ804-4-44-4-4444-4-240000-4-22222-2-200-222-20000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ814-4-44-4-444-44-2-400004-22222-2-2002-2-220000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ824-4-44-4-444-44-2-400004-22222-2-2002-2-2200000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ8388-8-88i−8i8i−8i00-40000004-44−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ8488-8-8−8i8i−8i8i00-40000004-444i−4i4i−4i000000000000000000000000000000000000000000000000000000000000

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