Finite Group Databasebeta

← Group #10690380

Character table — Group #10690380

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order1222444422344666121212124444668888121224242424242424242244666688888812121212121212122424242424242424242424242244888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i1-11-111-1-1i−iii−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i1-11-111-1-1i−iii−i−i11-1-111-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i-11-11-1-111i−i−i−iii11-1-1-1-111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-11-11-111ii−i−i-1-1iiii−i−i−i−i-11-11-1-111i−i−i−iii11-1-1-1-111ii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ131111-1-1-1-1111-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii1-11-111-1-1−ii−i−iii11-1-111-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ141111-1-1-1-1111-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii1-11-111-1-1−ii−i−iii11-1-111-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ151111-1-1-1-1111-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii-11-11-1-111−iiii−i−i11-1-1-1-111−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ161111-1-1-1-1111-1-1111-1-1-1-11-11-111−i−iii-1-1−i−i−i−iiiii-11-11-1-111−iiii−i−i11-1-1-1-111−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222222222222-2-2-2-2222222222222222200000000-2-20000-2-2-2-20000-2-2-2-2000000000000000000000000
χ1822222222222222222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-200000000220000-2-2-2-200002222000000000000000000000000
χ192222222222-122-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2111122-2-2-2-2-1-1-1-11111-1-1-1-1111111110000000000000000
χ212222222222-122-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-1111111112222-1-1-1-1-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111110000000000000000
χ222222222222-122-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-111111111-2-2-2-21111-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000−i3i3−i3i3-2-200001111−i3i3−i3i31111−i3−i3i3i3−i3−i3i3i30000000000000000
χ242222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-1-1-1-10000i3−i3i3−i3-2-200001111i3−i3i3−i31111i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111110000−i3i3−i3i32200001111−i3i3−i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-1111111110000i3−i3i3−i32200001111i3−i3i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-22-2-222222222-2-22-2-20000-2-20000000000000000002-22-22-22-2000000002-22-22-22-20000000000000000
χ2822222222-2-22-2-222222222-2-22-2-20000-2-2000000000000000000-22-222-22-200000000-22-22-22-220000000000000000
χ2922222222-2-22-2-22222222-222-2-2-20000-2-2000000002-2-2222-2-2000000-22-22-2-2220000000000000000000000000000
χ3022222222-2-22-2-22222222-222-2-2-20000-2-200000000-222-2-2-222000000-22-2222-2-20000000000000000000000000000
χ3122222222-2-2-1-2-2-1-1-1-1-1-1-12-2-2211000011−i3−i3i3i3−i3−i3i3i30000−i3i3i3−i3002-22-2-11-11i3−i3−i3i3−i3i3−i3i3-11-11-11-110000000000000000
χ3222222222-2-2-1-2-2-1-1-1-1-1-1-12-2-2211000011−i3−i3i3i3−i3−i3i3i30000i3−i3−i3i300-22-22-11-11−i3i3i3−i3−i3i3−i3i31-11-11-11-10000000000000000
χ3322222222-2-2-1-2-2-1-1-1-1-1-1-12-2-2211000011i3i3−i3−i3i3i3−i3−i30000−i3i3i3−i300-22-22-11-11i3−i3−i3i3i3−i3i3−i31-11-11-11-10000000000000000
χ3422222222-2-2-1-2-2-1-1-1-1-1-1-12-2-2211000011i3i3−i3−i3i3i3−i3−i30000i3−i3−i3i3002-22-2-11-11−i3i3i3−i3i3−i3i3−i3-11-11-11-110000000000000000
χ3522222222-2-2-1-2-2-1-1-1-1-1-1-1-222-211000011−i3−i3i3i3−i3−i3i3i32-2-22-1-1110000001-11-111-1-1i3−i3i3−i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ3622222222-2-2-1-2-2-1-1-1-1-1-1-1-222-211000011−i3−i3i3i3−i3−i3i3i3-222-211-1-10000001-11-1-1-111i3−i3i3−i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ3722222222-2-2-1-2-2-1-1-1-1-1-1-1-222-211000011i3i3−i3−i3i3i3−i3−i32-2-22-1-1110000001-11-111-1-1−i3i3−i3i3i3−i3−i3i3i3−i3−i3i30000000000000000
χ3822222222-2-2-1-2-2-1-1-1-1-1-1-1-222-211000011i3i3−i3−i3i3i3−i3−i3-222-211-1-10000001-11-1-1-111−i3i3−i3i3−i3i3i3−i3−i3i3i3−i30000000000000000
χ392222-2-2-2-2222-2-2222-2-2-2-2-22-22222i2i−2i−2i-2-22i2i2i2i−2i−2i−2i−2i00000000−2i2i0000-2-2220000−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2222-2-2222-2-2-2-2-22-2222−2i−2i2i2i-2-2−2i−2i−2i−2i2i2i2i2i000000002i−2i0000-2-22200002i2i−2i−2i000000000000000000000000
χ412222-2-2-2-222-1-2-2-1-1-111112-22-2-1-12i2i−2i−2i11−i−i−i−iiiii2-22-2-1-1112i−2i2i2i−2i−2i-1-111-1-111−i−iii−i−i−i−iiiii0000000000000000
χ422222-2-2-2-222-1-2-2-1-1-111112-22-2-1-12i2i−2i−2i11−i−i−i−iiiii-22-2211-1-12i−2i−2i−2i2i2i-1-11111-1-1−i−iiiiiii−i−i−i−i0000000000000000
χ432222-2-2-2-222-1-2-2-1-1-111112-22-2-1-1−2i−2i2i2i11iiii−i−i−i−i2-22-2-1-111−2i2i−2i−2i2i2i-1-111-1-111ii−i−iiiii−i−i−i−i0000000000000000
χ442222-2-2-2-222-1-2-2-1-1-111112-22-2-1-1−2i−2i2i2i11iiii−i−i−i−i-22-2211-1-1−2i2i2i2i−2i−2i-1-11111-1-1ii−i−i−i−i−i−iiiii0000000000000000
χ452222-2-2-2-222-1-2-2-1-1-11111-22-22-1-12i2i−2i−2i11−i−i−i−iiiii0000−i3i3i3−i3−2i2i000011-1-1−i3i3i3−i3ii−i−i33−3−3−3−3330000000000000000
χ462222-2-2-2-222-1-2-2-1-1-11111-22-22-1-12i2i−2i−2i11−i−i−i−iiiii0000i3−i3−i3i3−2i2i000011-1-1i3−i3−i3i3ii−i−i−3−33333−3−30000000000000000
χ472222-2-2-2-222-1-2-2-1-1-11111-22-22-1-1−2i−2i2i2i11iiii−i−i−i−i0000−i3i3i3−i32i−2i000011-1-1−i3i3i3−i3−i−iii−3−33333−3−30000000000000000
χ482222-2-2-2-222-1-2-2-1-1-11111-22-22-1-1−2i−2i2i2i11iiii−i−i−i−i0000i3−i3−i3i32i−2i000011-1-1i3−i3−i3i3−i−iii33−3−3−3−3330000000000000000
χ492222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-20000220000000000000000002i−2i−2i2i2-2-22000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ502222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-2000022000000000000000000−2i2i2i−2i2-2-2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ512222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-20000220000000022-2-22222000000-222-2-2-2-2-20000000000000000000000000000
χ522222-2-2-2-2-2-2222222-2-2-2-2-2-222-2-200002200000000-2-222-2-2-2-2000000-222-222220000000000000000000000000000
χ532222-2-2-2-2-2-2-122-1-1-1111122-2-2110000-1-133−3−3−3−3330000−i3i3−i3i3002i−2i−2i2i-111-1i3−i3i3−i33−3−33−ii−iii−ii−i0000000000000000
χ542222-2-2-2-2-2-2-122-1-1-1111122-2-2110000-1-133−3−3−3−3330000i3−i3i3−i300−2i2i2i−2i-111-1−i3i3−i3i33−3−33i−ii−i−ii−ii0000000000000000
χ552222-2-2-2-2-2-2-122-1-1-1111122-2-2110000-1-1−3−33333−3−30000−i3i3−i3i300−2i2i2i−2i-111-1i3−i3i3−i3−333−3i−ii−i−ii−ii0000000000000000
χ562222-2-2-2-2-2-2-122-1-1-1111122-2-2110000-1-1−3−33333−3−30000i3−i3i3−i3002i−2i−2i2i-111-1−i3i3−i3i3−333−3−ii−iii−ii−i0000000000000000
χ572222-2-2-2-2-2-2-122-1-1-11111-2-222110000-1-133−3−3−3−33322-2-2-1-1-1-10000001-1-111111−333−33−3−33−333−30000000000000000
χ582222-2-2-2-2-2-2-122-1-1-11111-2-222110000-1-133−3−3−3−333-2-22211110000001-1-11-1-1-1-1−333−3−333−33−3−330000000000000000
χ592222-2-2-2-2-2-2-122-1-1-11111-2-222110000-1-1−3−33333−3−322-2-2-1-1-1-10000001-1-1111113−3−33−333−33−3−330000000000000000
χ602222-2-2-2-2-2-2-122-1-1-11111-2-222110000-1-1−3−33333−3−3-2-22211110000001-1-11-1-1-1-13−3−333−3−33−333−30000000000000000
χ612-2-2222-2-22-222-2-2-2222-2-200002-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000002−22−2−i2i2−i2i2
χ622-2-2222-2-22-222-2-2-2222-2-200002-22i−2i2i−2i2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000−22−22i2−i2i2−i2
χ632-2-2222-2-22-222-2-2-2222-2-200002-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000002−22−2i2−i2i2−i2
χ642-2-2222-2-22-222-2-2-2222-2-200002-2−2i2i−2i2i2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000−22−22−i2i2−i2i2
χ652-2-22-2-2222-22-22-2-22-2-22200002-22-2-22-222-22-2-22-220000000000000000000000000000000000000000002−2−22−222−2
χ662-2-22-2-2222-22-22-2-22-2-22200002-22-2-22-222-22-2-22-22000000000000000000000000000000000000000000−222−22−2−22
χ672-2-22-2-2222-22-22-2-22-2-22200002-2-222-2-22-22-222-22-20000000000000000000000000000000000000000002−2−222−2−22
χ682-2-22-2-2222-22-22-2-22-2-22200002-2-222-2-22-22-222-22-2000000000000000000000000000000000000000000−222−2−222−2
χ6944-4-44i−4i4i−4i004004-4-44i−4i4i−4i0000000000000000000000000000000000000000000000000000002-22i−2i000000000000
χ7044-4-44i−4i4i−4i004004-4-44i−4i4i−4i000000000000000000000000000000000000000000000000000000-22−2i2i000000000000
χ7144-4-4−4i4i−4i4i004004-4-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000002-2−2i2i000000000000
χ7244-4-4−4i4i−4i4i004004-4-4−4i4i−4i4i000000000000000000000000000000000000000000000000000000-222i−2i000000000000
χ734-44-44i−4i−4i4i00400-44-44i−4i−4i4i0000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000
χ744-44-44i−4i−4i4i00400-44-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000
χ754-44-4−4i4i4i−4i00400-44-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000
χ764-44-4−4i4i4i−4i00400-44-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000
χ774-4-4444-4-44-4-24-422-2-2-2220000-224i−4i4i−4i-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ784-4-4444-4-44-4-24-422-2-2-2220000-22−4i4i−4i4i-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ794-4-4444-4-4-444-44-4-4444-4-40000-440000-440000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-4-44-2-4422-2-2-22200002-200002-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-44-2-4422-2-2-22200002-200002-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ824-4-44-4-4444-4-2-4422-222-2-20000-224-4-442-2-22-222-22-200000000000000000000000000000000000000000000000000
χ834-4-44-4-4444-4-2-4422-222-2-20000-22-444-42-22-22-2-22-2200000000000000000000000000000000000000000000000000
χ844-4-44-4-444-4444-4-4-44-4-4440000-4400004-40000000000000000000000000000000000000000000000000000000000
χ854-4-44-4-444-44-24-422-222-2-200002-20000-22−2i32i32i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000000000
χ864-4-44-4-444-44-24-422-222-2-200002-20000-222i3−2i3−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000000000
χ8788-8-88i−8i8i−8i00-400-444−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8−8i8i−8i8i00-400-4444i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ898-88-88i−8i−8i8i00-4004-44−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8−8i8i8i−8i00-4004-444i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000000

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