Finite Group Databasebeta

← Group #10836671

Character table — Group #10836671

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order122222344444466612121212444444466888812121212121212121212121212122424242424242424246688888812121212242424242424242424242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-111111111111-1-111-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-11-1
χ101111111-1-111111111111-1-111-1111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-11-11
χ111111111-1-111111111111-1-111-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11-11
χ121111111-1-111111111111-1-111-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-1111-11-1
χ131111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ141111111-1-111111111111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ151111111-1-111111111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111-1-111111111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ17222222222-2-2-2-2222-2-2-2-2-2-200200220000-2-222-2-200000000000000000000002i−2i2i−2i2-20000002i2i−2i−2i2i2i−2i−2i000000000000
χ18222222222-2-2-2-2222-2-2-2-2-2-200200220000-2-222-2-20000000000000000000000−2i2i−2i2i2-2000000−2i−2i2i2i−2i−2i2i2i000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-22200-200220000-2-2-2-22200000000000000000000002i−2i−2i2i-220000002i2i−2i−2i−2i−2i2i2i000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-22200-200220000-2-2-2-2220000000000000000000000−2i2i2i−2i-22000000−2i−2i2i2i2i2i−2i−2i000000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-1-1-2-2-2-2-2-2-1-1-1-1111111111111000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-12222-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-21122-2-2-2-2-1-111-1-1-1-111111111000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-2-2-2-2-1-1-1-1-1-11111111111111111-2-211-2-22222-1-1111111-1-1-1-1-1-1-1-1000000000000
χ25222222-122-2-2-2-2-1-1-11111-2-200200-1-1000011-1-111−i3−i3−i3−i3i3i3i3i333−3−333−3−300−i3i3002i−2i2i−2i-11−i3i33−33−3−i−iii−i−iii000000000000
χ26222222-122-2-2-2-2-1-1-11111-2-200200-1-1000011-1-111−i3−i3−i3−i3i3i3i3i3−3−333−3−33300−i3i300−2i2i−2i2i-11−i3i3−33−33ii−i−iii−i−i000000000000
χ27222222-122-2-2-2-2-1-1-11111-2-200200-1-1000011-1-111i3i3i3i3−i3−i3−i3−i333−3−333−3−300i3−i300−2i2i−2i2i-11i3−i33−33−3ii−i−iii−i−i000000000000
χ28222222-122-2-2-2-2-1-1-11111-2-200200-1-1000011-1-111i3i3i3i3−i3−i3−i3−i3−3−333−3−33300i3−i3002i−2i2i−2i-11i3−i3−33−33−i−iii−i−iii000000000000
χ29222222-1-2-22222-1-1-1-1-1-1-1-2-222-222-1-122-2-2-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2-2112-222-2-21111-1-111-1-1-1-11111000000000000
χ30222222-1-2-22222-1-1-1-1-1-1-1-2-222-222-1-1-2-222-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-2-211-22-2-222111111-1-11111-1-1-1-1000000000000
χ31222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-122-2-2-1-1111111111111-1-1-1-1111122-1-12-2-2-22211-1-1-1-1111111-1-1-1-1000000000000
χ32222222-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-1-2-222-1-11111111111111111-1-1-1-122-1-1-2222-2-211-1-111-1-1-1-1-1-11111000000000000
χ33222222-1-2-2-2-2-2-2-1-1-111112200-200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i333−3−3−3−33300i3−i3002i−2i−2i2i1-1i3−i33−3−33−i−iiiii−i−i000000000000
χ34222222-1-2-2-2-2-2-2-1-1-111112200-200-1-100001111-1-1−i3−i3−i3−i3i3i3i3i3−3−33333−3−300i3−i300−2i2i2i−2i1-1i3−i3−333−3ii−i−i−i−iii000000000000
χ35222222-1-2-2-2-2-2-2-1-1-111112200-200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i333−3−3−3−33300−i3i300−2i2i2i−2i1-1−i3i33−3−33ii−i−i−i−iii000000000000
χ36222222-1-2-2-2-2-2-2-1-1-111112200-200-1-100001111-1-1i3i3i3i3−i3−i3−i3−i3−3−33333−3−300−i3i3002i−2i−2i2i1-1−i3i3−333−3−i−iiiii−i−i000000000000
χ372222-2-222222-2-222222222-200-200-2-22222-2-2222200000000222222220000-2-20000-2-200-2-2-2-200000000000000000000
χ382222-2-222222-2-222222222-200-200-2-2-2-2-2-2-2-2222200000000-2-2-2-2-2-2-2-20000220000-2-200222200000000000000000000
χ392222-2-2222-2-222222-2-2-2-2-2222-2-2-2-2-200002222-2-222-2-222-2-200000000-22-2-2000000-2222000000000000000000000000
χ402222-2-2222-2-222222-2-2-2-2-22-2-2-222-2-200002222-2-2-2-222-2-222000000002-222000000-22-2-2000000000000000000000000
χ412222-2-22-2-222-2-22222222-2200200-2-222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000-2200002200-2-22200000000000000000000
χ422222-2-22-2-222-2-22222222-2200200-2-2-2-222-2-2-2-2-2-200000000-2-2-2-2222200002-20000220022-2-200000000000000000000
χ432222-2-22-2-2-2-222222-2-2-2-22-2222-2-2-2-2000022-2-22222-2-222-2-2000000002-2220000002-2-2-2000000000000000000000000
χ442222-2-22-2-2-2-222222-2-2-2-22-2-2-2222-2-2000022-2-222-2-222-2-22200000000-22-2-20000002-222000000000000000000000000
χ452222-2-2-12222-2-2-1-1-1-1-1-1-12-200-20011222211-1-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1-1-1-1-100i3−i3-2-2000011−i3i31111−i3i3−i3i3−i3i3−i3i3000000000000
χ462222-2-2-12222-2-2-1-1-1-1-1-1-12-200-20011222211-1-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1-1-1-1-100−i3i3-2-2000011i3−i31111i3−i3i3−i3i3−i3i3−i3000000000000
χ472222-2-2-12222-2-2-1-1-1-1-1-1-12-200-20011-2-2-2-211-1-1-1-1−i3−i3i3i3i3i3−i3−i31111111100i3−i322000011−i3i3-1-1-1-1i3−i3i3−i3i3−i3i3−i3000000000000
χ482222-2-2-12222-2-2-1-1-1-1-1-1-12-200-20011-2-2-2-211-1-1-1-1i3i3−i3−i3−i3−i3i3i31111111100−i3i322000011i3−i3-1-1-1-1−i3i3−i3i3−i3i3−i3i3000000000000
χ492222-2-2-122-2-222-1-1-11111-2222-2-2-2110000-1-1-1-111-1-111-1-11133−3−333−3−3-22110000001-1-1-1−33−333−3−333−3−33000000000000
χ502222-2-2-122-2-222-1-1-11111-2222-2-2-2110000-1-1-1-111-1-111-1-111−3−333−3−333-22110000001-1-1-13−33−3−333−3−333−3000000000000
χ512222-2-2-122-2-222-1-1-11111-22-2-2-222110000-1-1-1-11111-1-111-1-133−3−333−3−32-2-1-10000001-111−33−33−333−3−333−3000000000000
χ522222-2-2-122-2-222-1-1-11111-22-2-2-222110000-1-1-1-11111-1-111-1-1−3−333−3−3332-2-1-10000001-1113−33−33−3−333−3−33000000000000
χ532222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-22002001122-2-2111111−i3−i3i3i3i3i3−i3−i3-1-1-1-1111100−i3i3-220000-1-1i3−i311-1-1−i3i3−i3i3i3−i3i3−i3000000000000
χ542222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-22002001122-2-2111111i3i3−i3−i3−i3−i3i3i3-1-1-1-1111100i3−i3-220000-1-1−i3i311-1-1i3−i3i3−i3−i3i3−i3i3000000000000
χ552222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-220020011-2-222111111−i3−i3i3i3i3i3−i3−i31111-1-1-1-100−i3i32-20000-1-1i3−i3-1-111i3−i3i3−i3−i3i3−i3i3000000000000
χ562222-2-2-1-2-222-2-2-1-1-1-1-1-1-1-220020011-2-222111111i3i3−i3−i3−i3−i3i3i31111-1-1-1-100i3−i32-20000-1-1−i3i3-1-111−i3i3−i3i3i3−i3i3−i3000000000000
χ572222-2-2-1-2-2-2-222-1-1-111112-2222-2-2110000-1-111-1-1-1-111-1-11133−3−3−3−3332-2-1-1000000-1111−333−33−3−33−333−3000000000000
χ582222-2-2-1-2-2-2-222-1-1-111112-2222-2-2110000-1-111-1-1-1-111-1-111−3−33333−3−32-2-1-1000000-11113−3−33−333−33−3−33000000000000
χ592222-2-2-1-2-2-2-222-1-1-111112-2-2-2222110000-1-111-1-111-1-111-1-133−3−3−3−333-2211000000-11-1-1−333−3−333−33−3−33000000000000
χ602222-2-2-1-2-2-2-222-1-1-111112-2-2-2222110000-1-111-1-111-1-111-1-1−3−33333−3−3-2211000000-11-1-13−3−333−3−33−333−3000000000000
χ6122-2-22-22002-2-222-2-222-2-2002i−2i02i−2i2-200002-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000002i−2i002-20000
χ6222-2-22-22002-2-222-2-222-2-2002i−2i02i−2i2-200002-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000−2i2i00-220000
χ6322-2-22-22002-2-222-2-222-2-200−2i2i0−2i2i2-200002-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000002i−2i00-220000
χ6422-2-22-22002-2-222-2-222-2-200−2i2i0−2i2i2-200002-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000−2i2i002-20000
χ6522-2-2-22200-22-222-2-2-2-222002i−2i0−2i2i-2200002-200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000002-2002i−2i000000
χ6622-2-2-22200-22-222-2-2-2-222002i−2i0−2i2i-2200002-200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000-2200−2i2i000000
χ6722-2-2-22200-22-222-2-2-2-22200−2i2i02i−2i-2200002-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000002-200−2i2i000000
χ6822-2-2-22200-22-222-2-2-2-22200−2i2i02i−2i-2200002-20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000-22002i−2i000000
χ6944-4-44-4400-444-44-4-4-4-44400000004-40000-440000000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-2004-4-44-222-2-222004i−4i04i−4i-220000-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7144-4-44-4-2004-4-44-222-2-22200−4i4i0−4i4i-220000-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7244-4-44-4-200-444-4-22222-2-20000000-2200002-2000023−2323−23−2323−23230000000000000000000000000000000000000000000000
χ7344-4-44-4-200-444-4-22222-2-20000000-2200002-20000−2323−232323−2323−230000000000000000000000000000000000000000000000
χ7444-4-4-444004-44-44-4-444-4-40000000-440000-440000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-2004-44-4-222-2-22200000002-200002-2000023−23−2323−232323−230000000000000000000000000000000000000000000000
χ7644-4-4-44-2004-44-4-222-2-22200000002-200002-20000−232323−2323−23−23230000000000000000000000000000000000000000000000
χ7744-4-4-44-200-44-44-22222-2-2004i−4i0−4i4i2-20000-220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-200-44-44-22222-2-200−4i4i04i−4i2-20000-2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000
χ794-4-440044-40000-44-40000000000000−2i22i2−2i22i2004-40000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000
χ804-4-440044-40000-44-400000000000002i2−2i22i2−2i2004-400000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000
χ814-4-44004-440000-44-40000000000000−2i22i22i2−2i200-440000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ824-4-44004-440000-44-400000000000002i2−2i2−2i22i200-4400000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ834-4-4400-24-400002-2223−2323−23000000000−2i22i2−2i22i200-2223−23000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000
χ844-4-4400-24-400002-2223−2323−230000000002i2−2i22i2−2i200-2223−2300000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ854-4-4400-24-400002-22−2323−2323000000000−2i22i2−2i22i200-22−2323000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ864-4-4400-24-400002-22−2323−23230000000002i2−2i22i2−2i200-22−232300000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ874-4-4400-2-4400002-2223−2323−23000000000−2i22i22i2−2i2002-2−2323000000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ884-4-4400-2-4400002-2223−2323−230000000002i2−2i2−2i22i2002-2−232300000000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000
χ894-4-4400-2-4400002-22−2323−2323000000000−2i22i22i2−2i2002-223−23000000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ904-4-4400-2-4400002-22−2323−23230000000002i2−2i2−2i22i2002-223−2300000000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ918-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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