Finite Group Databasebeta

← Group #10690076

Character table — Group #10690076

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444488888888888888888888888812121212121212121212121216161616161624242424242424242424
order1222444422344444466612121212224444661212121212124466888812121212121212122424242424242424888888888888246612128888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-11-1-1111111111-1-1-1-1111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-11-1-1111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111-1-11-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1
χ91111-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-111-1-1111-11111-1-11-111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1i−iii−i−iii−i−i
χ101111-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-111-1-1111-11111-1-11-111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−ii−i−iii−i−iii
χ111111-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-111-1-1111-111-1-1111-111-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii-11-1-111i−iii−i−i−i−iii
χ121111-1-1-1-1-1-111111-1-1111-1-1-1-1111-1-1-1-1-111-1-1111-111-1-1111-111-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i-11-1-111−ii−i−iiiii−i−i
χ131111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1111-1-1-111-1-111-11-1-111-1-11-1-1-111111111-1-1-1-1ii−i−iiiii−i−i−i−i-11-1-111i−i−i−iii−i−iii
χ141111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1111-1-1-111-1-111-11-1-111-1-11-1-1-111111111-1-1-1-1−i−iii−i−i−i−iiiii-11-1-111−iiii−i−iii−i−i
χ151111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1111-1-1-111-1-111-11-1-1-1-1111-1-1-11111-1-1-1-11111ii−i−i−i−i−i−iiiii1-111-1-1i−i−i−iiiii−i−i
χ161111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1111-1-1-111-1-111-11-1-1-1-1111-1-1-11111-1-1-1-11111−i−iiiiiii−i−i−i−i1-111-1-1−iiii−i−i−i−iii
χ1722222222222-2-222-2-2222222222-222-222-2-2-2-222-2-2220000-2-2-2-2-2-222000000000000000000000000000000000000
χ1822222222222-2-222-2-22222222-2-2-2-2-2-222-2-2-2-22222-2-20000-2-22222-2-2000000000000000000000000000000000000
χ192222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ202222222222-1222222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000-2-211110000000000
χ212222222222-1222222-1-1-1-1-1-1-1-2-22-2-22-1-1-1-1-1-1-1-1-2-2112222-1-1111111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ222222222222-1222222-1-1-1-1-1-1-1-2-22-2-22-1-1-1-1-1-1-1-1-2-211-2-2-2-2-1-11111111111111100000000000022-1-1-1-10000000000
χ232222222222-1-2-222-2-2-1-1-1-1-1-1-122-222-2-1-11111-1-1-2-2-1-10000111111-1-1−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ242222222222-1-2-222-2-2-1-1-1-1-1-1-122-222-2-1-11111-1-1-2-2-1-10000111111-1-1i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ252222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12211000011-1-1-1-111−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ262222222222-1-2-222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111-1-12211000011-1-1-1-111i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ2722222222-2-2222-2-222222222200-200-2-2-22222-2-200000000-2-200000000000000222200000000000000-2-200000000
χ2822222222-2-2222-2-222222222200-200-2-2-22222-2-200000000-2-200000000000000-2-2-2-2000000000000002200000000
χ2922222222-2-22-2-2-2-2-2-22222222002002-2-2-2-2-2-2-2-2000000002200000000000000000000000000000000002-22-20000
χ3022222222-2-22-2-2-2-2-2-22222222002002-2-2-2-2-2-2-2-200000000220000000000000000000000000000000000-22-220000
χ312222-2-2-2-222222-2-2-2-2222-2-2-2-200-20022222-2-2-2-200000000-22000000000000002i2i−2i−2i00000000000000−2i2i00000000
χ322222-2-2-2-222222-2-2-2-2222-2-2-2-200-20022222-2-2-2-200000000-2200000000000000−2i−2i2i2i000000000000002i−2i00000000
χ332222-2-2-2-2222-2-2-2-222222-2-2-2-200200-222-2-222-2-2000000002-200000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-2222-2-2-2-222222-2-2-2-200200-222-2-222-2-2000000002-20000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-2-2-22-2-22222222-2-2-2-222-2-2-22-2-2-2-22222-22220000-22-2-222-2-2000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-22222222-2-2-2-2-2-2-2222-2-2-2-222222-2-2-20000-2222-2-222000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-12222-2-2-1-1-11111222-2-2-211-1-111-1-12-2-1-122-2-2-11-1-11111-1-1-1-111110000000000002-2-1-1110000000000
χ382222-2-2-2-2-2-2-12222-2-2-1-1-11111222-2-2-211-1-111-1-12-2-1-1-2-222-11-1-111111111-1-1-1-1000000000000-2211-1-10000000000
χ392222-2-2-2-2-2-2-12222-2-2-1-1-11111-2-2222-211-1-111-1-1-221122-2-2-1111-1-1-1-1-1-1-1-11111000000000000-2211-1-10000000000
χ402222-2-2-2-2-2-2-12222-2-2-1-1-11111-2-2222-211-1-111-1-1-2211-2-222-1111-1-1-1-11111-1-1-1-10000000000002-2-1-1110000000000
χ412222-2-2-2-2-2-2-1-2-22222-1-1-1111122-2-2-221111-1-1-1-1-22-1-100001-111-1-111−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i30000000000
χ422222-2-2-2-2-2-2-1-2-22222-1-1-1111122-2-2-221111-1-1-1-1-22-1-100001-111-1-111i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i30000000000
χ432222-2-2-2-2-2-2-1-2-22222-1-1-11111-2-2-22221111-1-1-1-12-21100001-1-1-111-1-1−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i30000000000
χ442222-2-2-2-2-2-2-1-2-22222-1-1-11111-2-2-22221111-1-1-1-12-21100001-1-1-111-1-1i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i30000000000
χ4522-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i0000002−2−i2i2000000002−22−2−i2i2−i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ4622-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i0000002−2−i2i2000000002−22−2−i2i2−i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ4722-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i000000−22i2−i200000000−22−22i2−i2i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000
χ4822-2-22i−2i2i−2i0022-2002i−2i2-2-22i2i−2i−2i000000002-22i−2i000000−22i2−i200000000−22−22i2−i2i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000
χ4922-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i0000002−2i2−i2000000002−22−2i2−i2i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ5022-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i0000002−2i2−i2000000002−22−2i2−i2i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ5122-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i000000−22−i2i200000000−22−22−i2i2−i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000
χ5222-2-2−2i2i−2i2i0022-200−2i2i2-2-2−2i−2i2i2i000000002-2−2i2i000000−22−i2i200000000−22−22−i2i2−i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000
χ532-2-2222-2-22-2200-2200-2-222-22-22-202-202-20000-22002-200000000002-2000000000000−i2i2−i2i2−i2i2−i2i2000000000000−i2i2−i2i2
χ542-2-2222-2-22-2200-2200-2-222-22-22-202-202-20000-22002-200000000002-2000000000000i2−i2i2−i2i2−i2i2−i2000000000000i2−i2i2−i2
χ552-2-2222-2-22-2200-2200-2-222-22-2-220-2202-20000-2200-220000000000-22000000000000−i2i2−i2i2−i2i2−i2i2000000000000i2−i2i2−i2
χ562-2-2222-2-22-2200-2200-2-222-22-2-220-2202-20000-2200-220000000000-22000000000000i2−i2i2−i2i2−i2i2−i2000000000000−i2i2−i2i2
χ572-2-22-2-222-22200-2200-2-22-22-222-20-220-220000-22002-20000000000-220000000000002−22−2−22−220000000000002−2−22
χ582-2-22-2-222-22200-2200-2-22-22-222-20-220-220000-22002-20000000000-22000000000000−22−222−22−2000000000000−222−2
χ592-2-22-2-222-22200-2200-2-22-22-22-2202-20-220000-2200-2200000000002-20000000000002−22−2−22−22000000000000−222−2
χ602-2-22-2-222-22200-2200-2-22-22-22-2202-20-220000-2200-2200000000002-2000000000000−22−222−22−20000000000002−2−22
χ6144444444-4-4-244-4-444-2-2-2-2-2-2-200-400-422-2-2-2-2220000000022000000000000000000000000000000000000000000
χ6244444444-4-4-2-4-4-4-4-4-4-2-2-2-2-2-2-20040042222222200000000-2-2000000000000000000000000000000000000000000
χ634444-4-4-4-444-244-4-4-4-4-2-2-2222200-4004-2-2-2-22222000000002-2000000000000000000000000000000000000000000
χ644444-4-4-4-444-2-4-4-4-444-2-2-2222200400-4-2-222-2-22200000000-22000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i004-4400−4i4i4-4-44i4i−4i−4i00000000-44−4i4i000000000000000000000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i00-24-4004i−4i-222−2i−2i2i2i00000000-22−2i2i00000022−22−2i22i200000000−22−22i2−i2i2−i20000000000000000000000000000
χ6744-4-44i−4i4i−4i00-24-4004i−4i-222−2i−2i2i2i00000000-22−2i2i000000−22222i2−2i2000000002−22−2−i2i2−i2i20000000000000000000000000000
χ6844-4-44i−4i4i−4i00-2-4400−4i4i-222−2i−2i2i2i000000002-22i−2i000000000000000000i6−i6−i6i66−6−660000000000000000000000000000
χ6944-4-44i−4i4i−4i00-2-4400−4i4i-222−2i−2i2i2i000000002-22i−2i000000000000000000−i6i6i6−i6−666−60000000000000000000000000000
χ7044-4-4−4i4i−4i4i004-44004i−4i4-4-4−4i−4i4i4i00000000-444i−4i000000000000000000000000000000000000000000000000000000
χ7144-4-4−4i4i−4i4i00-24-400−4i4i-2222i2i−2i−2i00000000-222i−2i00000022−222i2−2i200000000−22−22−i2i2−i2i20000000000000000000000000000
χ7244-4-4−4i4i−4i4i00-24-400−4i4i-2222i2i−2i−2i00000000-222i−2i000000−2222−2i22i2000000002−22−2i2−i2i2−i20000000000000000000000000000
χ7344-4-4−4i4i−4i4i00-2-44004i−4i-2222i2i−2i−2i000000002-2−2i2i000000000000000000i6−i6−i6i6−666−60000000000000000000000000000
χ7444-4-4−4i4i−4i4i00-2-44004i−4i-2222i2i−2i−2i000000002-2−2i2i000000000000000000−i6i6i6−i66−6−660000000000000000000000000000
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
χ794-4-4444-4-44-4-200-440022-2-22-224-404-40-2200002-200-220000000000-22000000000000000000000000000000000000
χ804-4-4444-4-44-4-200-440022-2-22-22-440-440-2200002-2002-200000000002-2000000000000000000000000000000000000
χ814-4-4444-4-4-444004-400-4-444-44-4000000-4400004-40000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-44-2004-40022-2-22-220000002-20000-22000000000023−2323−2300000000000000000000000000000000000000
χ834-4-4444-4-4-44-2004-40022-2-22-220000002-20000-220000000000−2323−232300000000000000000000000000000000000000
χ844-4-44-4-4444-44004-400-4-44-44-440000004-400004-40000000000000000000000000000000000000000000000000000
χ854-4-44-4-4444-4-2004-40022-22-22-2000000-220000-22000000000023−23−232300000000000000000000000000000000000000
χ864-4-44-4-4444-4-2004-40022-22-22-2000000-220000-220000000000−232323−2300000000000000000000000000000000000000
χ874-4-44-4-444-44-200-440022-22-22-24-40-4402-200002-200-2200000000002-2000000000000000000000000000000000000
χ884-4-44-4-444-44-200-440022-22-22-2-4404-402-200002-2002-20000000000-22000000000000000000000000000000000000
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.