Finite Group Databasebeta

← Group #10690513

Character table — Group #10690513

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order122244443444444446661212121224888888881212121212121212242424242424242424242424242424244444688881212121212121212122424242424242424888888888888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ91111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1i−ii−i11111-1-1-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1
χ101111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1i−ii−i11111-1-1-1-1ii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11
χ111111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1i−i−ii1-1-1-1-11111ii−i−i−i−iii1111-1-1-1-1ii−i−i−i−iii-11
χ121111-1-1-1-111111-1-1-1-1111-1-1-1-1-11ii−i−i−i−iii1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-111-1i−i−ii1-1-1-1-11111ii−i−i−i−iii-1-1-1-11111−i−iiiii−i−i1-1
χ131111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1−iii−i1-1-1-1-11111−i−iiiii−i−i1111-1-1-1-1−i−iiiii−i−i-11
χ141111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iiiii−i−i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-111-1−iii−i1-1-1-1-11111−i−iiiii−i−i-1-1-1-11111ii−i−i−i−iii1-1
χ151111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1−ii−ii11111-1-1-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1
χ161111-1-1-1-111111-1-1-1-1111-1-1-1-1-11−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1−ii−ii11111-1-1-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ1722222222222-2-222-2-22222222-2-20000222222-2-222-2-200000000222222220000-200-2-2-2000000000000-2-2-2-2000000000000000000
χ1822222222222-2-222-2-22222222-2-20000-2-2-2-222-2-222-2-200000000-2-2-2-2-2-2-2-20000-20022-20000000000002222000000000000000000
χ19222222222-2-222-2-2222222222-2-222220000-2-222-2-22222222222000000000000-2-2-200-200000000-2-2-2-20000000000000000000000
χ20222222222-2-222-2-2222222222-2-2-2-2-2-20000-2-222-2-222-2-2-2-2-2-2-2-2000000000000-22200-20000000022220000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000000000002-22-220000222-2-222-2-200000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000000000-22-22200002-2-222-2-22200000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-122-2-2-111111111-1-1-1-11111000000000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-2-2-2-1-2-222-1111111111111-1-1-1-1000000000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-1-2-2-2-2-1-1-1-1-1-1-1-1-111111111000000000000000000
χ2722222222-122-2-222-2-2-1-1-1-1-1-1-1-2-200002222-1-111-1-111−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-10000100-2-21−i3i3−i3i3−i3i3−i3i3−i3i3−i3i31111000000000000000000
χ2822222222-122-2-222-2-2-1-1-1-1-1-1-1-2-200002222-1-111-1-111i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-10000100-2-21i3−i3i3−i3i3−i3i3−i3i3−i3i3−i31111000000000000000000
χ2922222222-122-2-222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-111-1-111−i3−i3i3i3−i3−i3i3i3111111110000100221i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3-1-1-1-1000000000000000000
χ3022222222-122-2-222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-111-1-111i3i3−i3−i3i3i3−i3−i3111111110000100221−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3-1-1-1-1000000000000000000
χ3122222222-1-2-222-2-222-1-1-1-1-1-1-1-2-22222000011-1-111-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i300001-2-2001−i3i3i3−i3−i3i3i3−i31111−i3i3−i3i3000000000000000000
χ3222222222-1-2-222-2-222-1-1-1-1-1-1-1-2-22222000011-1-111-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i300001-2-2001i3−i3−i3i3i3−i3−i3i31111i3−i3i3−i3000000000000000000
χ3322222222-1-2-222-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2000011-1-111-1-111111111−i3−i3i3i3−i3−i3i3i30000122001i3−i3−i3i3i3−i3−i3i3-1-1-1-1−i3i3−i3i3000000000000000000
χ3422222222-1-2-222-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2000011-1-111-1-111111111i3i3−i3−i3i3i3−i3−i30000122001−i3i3i3−i3−i3i3i3−i3-1-1-1-1i3−i3i3−i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i32-22-2-10000-1-1-111-1-111i3−i3i3−i3i3−i3i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3-22-22-10000-111-1-111-1-1i3−i3i3−i3−i3i3−i3i3000000000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3-22-22-10000-111-1-111-1-1−i3i3−i3i3i3−i3i3−i3000000000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i32-22-2-10000-1-1-111-1-111−i3i3−i3i3−i3i3−i3i3000000000000000000
χ392222-2-2-2-2222-2-2-2-222222-2-2-2-22-200002i2i−2i−2i22-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i0000200−2i2i-2000000000000−2i−2i2i2i000000000000000000
χ402222-2-2-2-2222-2-2-2-222222-2-2-2-22-20000−2i−2i2i2i22-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i00002002i−2i-20000000000002i2i−2i−2i000000000000000000
χ412222-2-2-2-22-2-22222-2-2222-2-2-2-22-22i2i−2i−2i0000-2-22222-2-22i2i2i2i−2i−2i−2i−2i0000000000002−2i2i00-200000000−2i−2i2i2i0000000000000000000000
χ422222-2-2-2-22-2-22222-2-2222-2-2-2-22-2−2i−2i2i2i0000-2-22222-2-2−2i−2i−2i−2i2i2i2i2i00000000000022i−2i00-2000000002i2i−2i−2i0000000000000000000000
χ432222-2-2-2-22-2-2-2-22222222-2-2-2-2-2200000000-2-2-2-2222200000000000000002-2-22-20000222-2-2-2-22200000000000000000000000000
χ442222-2-2-2-22-2-2-2-22222222-2-2-2-2-2200000000-2-2-2-222220000000000000000-222-2-200002-2-22222-2-200000000000000000000000000
χ452222-2-2-2-2-12222-2-2-2-2-1-1-11111-222i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii22-2-212i−2i2i−2i-1-1-1-1-11111−i−iii−i−iii000000000000000000
χ462222-2-2-2-2-12222-2-2-2-2-1-1-11111-222i2i−2i−2i−2i−2i2i2i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-2-22212i−2i−2i2i-11111-1-1-1-1−i−iiiii−i−i000000000000000000
χ472222-2-2-2-2-12222-2-2-2-2-1-1-11111-22−2i−2i2i2i2i2i−2i−2i-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-2-2221−2i2i2i−2i-11111-1-1-1-1ii−i−i−i−iii000000000000000000
χ482222-2-2-2-2-12222-2-2-2-2-1-1-11111-22−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i22-2-21−2i2i−2i2i-1-1-1-1-11111ii−i−iii−i−i000000000000000000
χ492222-2-2-2-2-122-2-2-2-222-1-1-111112-200002i2i−2i−2i-1-11111-1-133−3−3−3−333−i−i−i−iiiii0000-100−2i2i1−i3i3−i3i3i3−i3i3−i33−3−33ii−i−i000000000000000000
χ502222-2-2-2-2-122-2-2-2-222-1-1-111112-200002i2i−2i−2i-1-11111-1-1−3−33333−3−3−i−i−i−iiiii0000-100−2i2i1i3−i3i3−i3−i3i3−i3i3−333−3ii−i−i000000000000000000
χ512222-2-2-2-2-122-2-2-2-222-1-1-111112-20000−2i−2i2i2i-1-11111-1-133−3−3−3−333iiii−i−i−i−i0000-1002i−2i1i3−i3i3−i3−i3i3−i3i33−3−33−i−iii000000000000000000
χ522222-2-2-2-2-122-2-2-2-222-1-1-111112-20000−2i−2i2i2i-1-11111-1-1−3−33333−3−3iiii−i−i−i−i0000-1002i−2i1−i3i3−i3i3i3−i3i3−i3−333−3−i−iii000000000000000000
χ532222-2-2-2-2-1-2-22222-2-2-1-1-111112-22i2i−2i−2i000011-1-1-1-111−i−i−i−iiiii33−3−3−3−3330000-1−2i2i001−i3i3i3−i3i3−i3−i3i3ii−i−i3−3−33000000000000000000
χ542222-2-2-2-2-1-2-22222-2-2-1-1-111112-22i2i−2i−2i000011-1-1-1-111−i−i−i−iiiii−3−33333−3−30000-1−2i2i001i3−i3−i3i3−i3i3i3−i3ii−i−i−333−3000000000000000000
χ552222-2-2-2-2-1-2-22222-2-2-1-1-111112-2−2i−2i2i2i000011-1-1-1-111iiii−i−i−i−i33−3−3−3−3330000-12i−2i001i3−i3−i3i3−i3i3i3−i3−i−iii3−3−33000000000000000000
χ562222-2-2-2-2-1-2-22222-2-2-1-1-111112-2−2i−2i2i2i000011-1-1-1-111iiii−i−i−i−i−3−33333−3−30000-12i−2i001−i3i3i3−i3i3−i3−i3i3−i−iii−333−3000000000000000000
χ572222-2-2-2-2-1-2-2-2-22222-1-1-11111-22000000001111-1-1-1-133−3−3−3−33333−3−3−3−3332-2-2210000-1-1-11111-1-1−333−3−333−3000000000000000000
χ582222-2-2-2-2-1-2-2-2-22222-1-1-11111-22000000001111-1-1-1-133−3−3−3−333−3−33333−3−3-222-210000-111-1-1-1-111−333−33−3−33000000000000000000
χ592222-2-2-2-2-1-2-2-2-22222-1-1-11111-22000000001111-1-1-1-1−3−33333−3−333−3−3−3−333-222-210000-111-1-1-1-1113−3−33−333−3000000000000000000
χ602222-2-2-2-2-1-2-2-2-22222-1-1-11111-22000000001111-1-1-1-1−3−33333−3−3−3−33333−3−32-2-2210000-1-1-11111-1-13−3−333−3−33000000000000000000
χ6122-2-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002-2002i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000000022−2−2−i2−i2i2i21+i−1−i1−i−1+i000000
χ6222-2-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002-2002i−2i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000−2−222i2i2−i2−i2−1−i1+i−1+i1−i000000
χ6322-2-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002-2002i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000000022−2−2−i2−i2i2i2−1−i1+i−1+i1−i000000
χ6422-2-22i2i−2i−2i2002-2002i−2i-22-22i2i−2i−2i00−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002-2002i−2i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000−2−222i2i2−i2−i21+i−1−i1−i−1+i000000
χ6522-2-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002-200−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000000022−2−2i2i2−i2−i21−i−1+i1+i−1−i000000
χ6622-2-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i00−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002-200−2i2i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000−2−222−i2−i2i2i2−1+i1−i−1−i1+i000000
χ6722-2-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002-200−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000000022−2−2i2i2−i2−i2−1+i1−i−1−i1+i000000
χ6822-2-2−2i−2i2i2i2002-200−2i2i-22-2−2i−2i2i2i002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002-200−2i2i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000−2−222−i2−i2i2i21−i−1+i1+i−1−i000000
χ692-22-22i−2i2i−2i22-2002i−2i00-2-222i−2i2i−2i000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2002i−2i0000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000−i2i2−i2i22−22−200001+i−1−i1−i−1+i00
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.