Finite Group Databasebeta

← Group #10713732

Character table — Group #10713732

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order124422234446668888888812121212661212242424242424242444444488888812121212121212121212121224242424242424242424242416161616161616161616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ911111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ1211111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ1311111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-111111111-1-1-1-1111111110000000000000000
χ192222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-222-2-21111-1-1-1-111111111-1-1-1-111110000000000000000
χ202222222-1222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-2-22211111111-1-1-1-111111111-1-1-1-10000000000000000
χ212222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000000000000000
χ222222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-222-2-222-2-2221111-1-1-1-11111-1-1-1-11111-1-1-1-10000000000000000
χ242222222-1222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2-2-2222222-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ2522222-2-222-2-22-2-22222-2-2-2-222-2-22-22-22222-2-2-2-200000000000000000000000000000000000000002-22-200000000
χ2622222-2-222-2-22-2-22222-2-2-2-222-2-22-22-22222-2-2-2-20000000000000000000000000000000000000000-22-2200000000
χ2722222-2-222-2-22-2-2-2-2-2-2222222-2-22-22-2-2-2-2-2222200000000000000000000000000000000000000002i−2i−2i2i00000000
χ2822222-2-222-2-22-2-2-2-2-2-2222222-2-22-22-2-2-2-2-222220000000000000000000000000000000000000000−2i2i2i−2i00000000
χ292222-22-22-22-22-2-222-2-222-2-222-2-2-22-2222-2-222-2-20000000000000000000000000000000000002-22-2000000000000
χ302222-22-22-22-22-2-222-2-222-2-222-2-2-22-2222-2-222-2-2000000000000000000000000000000000000-22-22000000000000
χ312222-22-22-22-22-2-2-2-222-2-22222-2-2-22-22-2-222-2-2220000000000000000000000000000000000002i−2i−2i2i000000000000
χ322222-22-22-22-22-2-2-2-222-2-22222-2-2-22-22-2-222-2-222000000000000000000000000000000000000−2i2i2i−2i000000000000
χ332222-2-222-2-2222222-2-2-2-2222222-2-2-2-222-2-2-2-2222-200002-2000022-2-20000000022-2-2000000000000000000000000
χ342222-2-222-2-2222222-2-2-2-2222222-2-2-2-222-2-2-2-222-220000-220000-2-22200000000-2-222000000000000000000000000
χ352222-2-222-2-22222-2-22222-2-22222-2-2-2-2-2-22222-2-22-20000-22000022-2-200000000-2-222000000000000000000000000
χ362222-2-222-2-22222-2-22222-2-22222-2-2-2-2-2-22222-2-2-2200002-20000-2-2220000000022-2-2000000000000000000000000
χ372222-2-22-1-2-22-1-1-122-2-2-2-222-1-1-1-11111-1-11111-1-12-200002-20000-1-111−i3−i3i3i3−i3−i3i3i3-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ382222-2-22-1-2-22-1-1-122-2-2-2-222-1-1-1-11111-1-11111-1-12-200002-20000-1-111i3i3−i3−i3i3i3−i3−i3-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ392222-2-22-1-2-22-1-1-122-2-2-2-222-1-1-1-11111-1-11111-1-1-220000-22000011-1-1−i3−i3i3i3i3i3−i3−i311-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ402222-2-22-1-2-22-1-1-122-2-2-2-222-1-1-1-11111-1-11111-1-1-220000-22000011-1-1i3i3−i3−i3−i3−i3i3i311-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ412222-2-22-1-2-22-1-1-1-2-22222-2-2-1-1-1-1111111-1-1-1-1112-20000-220000-1-111−i3−i3i3i3−i3−i3i3i311-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ422222-2-22-1-2-22-1-1-1-2-22222-2-2-1-1-1-1111111-1-1-1-1112-20000-220000-1-111i3i3−i3−i3i3i3−i3−i311-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ432222-2-22-1-2-22-1-1-1-2-22222-2-2-1-1-1-1111111-1-1-1-111-2200002-2000011-1-1−i3−i3i3i3i3i3−i3−i3-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-22-1-2-22-1-1-1-2-22222-2-2-1-1-1-1111111-1-1-1-111-2200002-2000011-1-1i3i3−i3−i3−i3−i3i3i3-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ4522-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i00002-200002i−2i000000002-22-2000000002i−2i2i−2i0000000000000000
χ4622-2-22222-2-2-22222i−2i2i−2i2i−2i2i−2i-2-2-2-222-2-22i−2i2i−2i2i−2i2i−2i0000-220000−2i2i00000000-22-2200000000−2i2i−2i2i0000000000000000
χ4722-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i00002-20000−2i2i000000002-22-200000000−2i2i−2i2i0000000000000000
χ4822-2-22222-2-2-2222−2i2i−2i2i−2i2i−2i2i-2-2-2-222-2-2−2i2i−2i2i−2i2i−2i2i0000-2200002i−2i00000000-22-22000000002i−2i2i−2i0000000000000000
χ4922-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii00002-200002i−2i−i3i3−i3i3−i3i3−i3i3-11-113−33−33−33−3−ii−ii0000000000000000
χ5022-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii00002-200002i−2ii3−i3i3−i3i3−i3i3−i3-11-11−33−33−33−33−ii−ii0000000000000000
χ5122-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii0000-220000−2i2i−i3i3−i3i3i3−i3i3−i31-11-13−33−3−33−33i−ii−i0000000000000000
χ5222-2-2222-1-2-2-2-1-1-12i−2i2i−2i2i−2i2i−2i1111-1-111−ii−ii−ii−ii0000-220000−2i2ii3−i3i3−i3−i3i3−i3i31-11-1−33−333−33−3i−ii−i0000000000000000
χ5322-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i00002-20000−2i2i−i3i3−i3i3−i3i3−i3i3-11-11−33−33−33−33i−ii−i0000000000000000
χ5422-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i00002-20000−2i2ii3−i3i3−i3i3−i3i3−i3-11-113−33−33−33−3i−ii−i0000000000000000
χ5522-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i0000-2200002i−2i−i3i3−i3i3i3−i3i3−i31-11-1−33−333−33−3−ii−ii0000000000000000
χ5622-2-2222-1-2-2-2-1-1-1−2i2i−2i2i−2i2i−2i2i1111-1-111i−ii−ii−ii−i0000-2200002i−2ii3−i3i3−i3−i3i3−i3i31-11-13−33−3−33−33−ii−ii0000000000000000
χ5722-2-22-2-22-2222-2-22i−2i2i−2i−2i2i−2i2i-2-2222-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ5822-2-22-2-22-2222-2-22i−2i2i−2i−2i2i−2i2i-2-2222-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ5922-2-22-2-22-2222-2-2−2i2i−2i2i2i−2i2i−2i-2-2222-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ6022-2-22-2-22-2222-2-2−2i2i−2i2i2i−2i2i−2i-2-2222-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ6122-2-2-22-222-222-2-22i−2i−2i2i2i−2i−2i2i-2-222-222-22i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ6222-2-2-22-222-222-2-22i−2i−2i2i2i−2i−2i2i-2-222-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ6322-2-2-22-222-222-2-2−2i2i2i−2i−2i2i2i−2i-2-222-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ6422-2-2-22-222-222-2-2−2i2i2i−2i−2i2i2i−2i-2-222-222-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ6522-2-2-2-22222-22222i−2i−2i2i−2i2i2i−2i-2-2-2-2-2-2222i−2i−2i2i−2i2i2i−2i002-200002i−2i0000002-2-22000000002i−2i−2i2i00000000000000000000
χ6622-2-2-2-22222-22222i−2i−2i2i−2i2i2i−2i-2-2-2-2-2-2222i−2i−2i2i−2i2i2i−2i00-220000−2i2i000000-222-200000000−2i2i2i−2i00000000000000000000
χ6722-2-2-2-22222-2222−2i2i2i−2i2i−2i−2i2i-2-2-2-2-2-222−2i2i2i−2i2i−2i−2i2i002-20000−2i2i0000002-2-2200000000−2i2i2i−2i00000000000000000000
χ6822-2-2-2-22222-2222−2i2i2i−2i2i−2i−2i2i-2-2-2-2-2-222−2i2i2i−2i2i−2i−2i2i00-2200002i−2i000000-222-2000000002i−2i−2i2i00000000000000000000
χ6922-2-2-2-22-122-2-1-1-12i−2i−2i2i−2i2i2i−2i111111-1-1−iii−ii−i−ii002-200002i−2i00−i3i3i3−i3-111-1−i3i3i3−i33−3−33−iii−i3−3−330000000000000000
χ7022-2-2-2-22-122-2-1-1-12i−2i−2i2i−2i2i2i−2i111111-1-1−iii−ii−i−ii002-200002i−2i00i3−i3−i3i3-111-1i3−i3−i3i3−333−3−iii−i−333−30000000000000000
χ7122-2-2-2-22-122-2-1-1-12i−2i−2i2i−2i2i2i−2i111111-1-1−iii−ii−i−ii00-220000−2i2i00−i3i3i3−i31-1-11i3−i3−i3i33−3−33i−i−ii−333−30000000000000000
χ7222-2-2-2-22-122-2-1-1-12i−2i−2i2i−2i2i2i−2i111111-1-1−iii−ii−i−ii00-220000−2i2i00i3−i3−i3i31-1-11−i3i3i3−i3−333−3i−i−ii3−3−330000000000000000
χ7322-2-2-2-22-122-2-1-1-1−2i2i2i−2i2i−2i−2i2i111111-1-1i−i−ii−iii−i002-20000−2i2i00−i3i3i3−i3-111-1−i3i3i3−i3−333−3i−i−ii−333−30000000000000000
χ7422-2-2-2-22-122-2-1-1-1−2i2i2i−2i2i−2i−2i2i111111-1-1i−i−ii−iii−i002-20000−2i2i00i3−i3−i3i3-111-1i3−i3−i3i33−3−33i−i−ii3−3−330000000000000000
χ7522-2-2-2-22-122-2-1-1-1−2i2i2i−2i2i−2i−2i2i111111-1-1i−i−ii−iii−i00-2200002i−2i00−i3i3i3−i31-1-11i3−i3−i3i3−333−3−iii−i3−3−330000000000000000
χ7622-2-2-2-22-122-2-1-1-1−2i2i2i−2i2i−2i−2i2i111111-1-1i−i−ii−iii−i00-2200002i−2i00i3−i3−i3i31-1-11−i3i3i3−i33−3−33−iii−i−333−30000000000000000
χ7744444-4-4-24-4-4-2224444-4-4-4-4-2-222-22-22-2-2-2-222220000000000000000000000000000000000000000000000000000
χ7844444-4-4-24-4-4-222-4-4-4-44444-2-222-22-222222-2-2-2-20000000000000000000000000000000000000000000000000000
χ794444-44-4-2-44-4-22244-4-444-4-4-2-2222-22-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ804444-44-4-2-44-4-222-4-444-4-444-2-2222-22-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ8144-4-44-4-4-2-444-2224i−4i4i−4i−4i4i−4i4i22-2-2-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8244-4-44-4-4-2-444-222−4i4i−4i4i4i−4i4i−4i22-2-2-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-44-4-24-44-2224i−4i−4i4i4i−4i−4i4i22-2-22-2-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8444-4-4-44-4-24-44-222−4i4i4i−4i−4i4i4i−4i22-2-22-2-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ858-88i−8i0008000-800000000008i−8i000000000000000000000000000000000000000000000000000000000000000000
χ868-88i−8i000-40004−4i34i300000000−4i4i43−430000000000000000000000000000000000000000000000000000000000000000
χ878-88i−8i000-400044i3−4i300000000−4i4i−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8−8i8i0008000-80000000000−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ898-8−8i8i000-40004−4i34i3000000004i−4i−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8−8i8i000-400044i3−4i3000000004i−4i43−430000000000000000000000000000000000000000000000000000000000000000

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