Finite Group Databasebeta

← Group #10713389

Character table — Group #10713389

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12448888222344466688888812121212242424242424242422446666668888121212121212242424242424242424242424161616161616161648484848484848484848484848484848244488881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111
χ91111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ121111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ131111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111−i−iiiii−i−i
χ141111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii
χ151111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111ii−i−i−i−iii
χ161111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-2-1-11111-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222-1222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111-2-2-2-2-1-11111-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222-2-222-2-2222-2-222-2-22222222222220000-2-200000000-2-20000-2-2-2-20000000000002-22-20000000022-2-222-2-20000000000000000
χ22222222222-2-222-2-2222-2-222-2-22222222222220000-2-200000000-2-20000-2-2-2-2000000000000-22-2200000000-2-222-2-2220000000000000000
χ23222222222-2-2-12-2-2-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1000011−i3−i3i3i3000011−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i300002-22-2−i3−i3i3i3−i3−i3i3i3-1-111-1-1110000000000000000
χ24222222222-2-2-12-2-2-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1000011−i3−i3i3i3000011−i3−i3i3i31111−i3−i3−i3−i3i3i3i3i30000-22-22i3i3−i3−i3i3i3−i3−i311-1-111-1-10000000000000000
χ25222222222-2-2-12-2-2-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1000011i3i3−i3−i3000011i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i300002-22-2i3i3−i3−i3i3i3−i3−i3-1-111-1-1110000000000000000
χ26222222222-2-2-12-2-2-1-1-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1000011i3i3−i3−i3000011i3i3−i3−i31111i3i3i3i3−i3−i3−i3−i30000-22-22−i3−i3i3i3−i3−i3i3i311-1-111-1-10000000000000000
χ2722222222-22-22-22-2-2-22-2-2-2-222-2-2222222-2-2-2-200002-2000000002-2000022-2-2000000000000000000000000000000000000000000002-22-2
χ2822222222-22-22-22-2-2-22-2-2-2-222-2-2222222-2-2-2-200002-2000000002-2000022-2-200000000000000000000000000000000000000000000-22-22
χ2922222222-2-222-2-22-2-2222-2-2-2-2-2-2222222-2-2-2-20000-2200000000-220000-2-22200000000000000000000000000000000002-2002-200000000
χ3022222222-2-222-2-22-2-2222-2-2-2-2-2-2222222-2-2-2-20000-2200000000-220000-2-2220000000000000000000000000000000000-2200-2200000000
χ312222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-11111111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ322222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-1-1-1-1111111112222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ332222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-1-1-1-111111111-2-2-2-2-1-111112222-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ342222-2-2-2-2222-1222-1-1-1-2-2-2-2-2-2-1-1-1-111111111-2-2-2-2-1-111112222-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ352222-2-2-2-22-2-222-2-222222-2-2222222-2-2-2-2-2-2-2-20000-2-200000000-2-2000022220000000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ362222-2-2-2-22-2-222-2-222222-2-2222222-2-2-2-2-2-2-2-20000-2-200000000-2-200002222000000000000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ372222-2-2-2-22-2-2-12-2-2-1-1-122-2-222-1-1-1-111111111000011−i3−i3i3i3000011−i3−i3i3i3-1-1-1-1i3i3i3i3−i3−i3−i3−i300002i−2i−2i2i33−3−3−3−333−i−iiiii−i−i0000000000000000
χ382222-2-2-2-22-2-2-12-2-2-1-1-122-2-222-1-1-1-111111111000011−i3−i3i3i3000011−i3−i3i3i3-1-1-1-1i3i3i3i3−i3−i3−i3−i30000−2i2i2i−2i−3−33333−3−3ii−i−i−i−iii0000000000000000
χ392222-2-2-2-22-2-2-12-2-2-1-1-122-2-222-1-1-1-111111111000011i3i3−i3−i3000011i3i3−i3−i3-1-1-1-1−i3−i3−i3−i3i3i3i3i300002i−2i−2i2i−3−33333−3−3−i−iiiii−i−i0000000000000000
χ402222-2-2-2-22-2-2-12-2-2-1-1-122-2-222-1-1-1-111111111000011i3i3−i3−i3000011i3i3−i3−i3-1-1-1-1−i3−i3−i3−i3i3i3i3i30000−2i2i2i−2i33−3−3−3−333ii−i−i−i−iii0000000000000000
χ412222-2-2-2-2-22-22-22-2-2-222222-2-2-2-222-2-2-2-2222200002-2000000002-20000-2-222000000000000000000000000000000000000000000002i−2i−2i2i
χ422222-2-2-2-2-22-22-22-2-2-222222-2-2-2-222-2-2-2-2222200002-2000000002-20000-2-22200000000000000000000000000000000000000000000−2i2i2i−2i
χ432222-2-2-2-2-2-222-2-22-2-22-2-22222-2-222-2-2-2-222220000-2200000000-22000022-2-200000000000000000000000000000000002-200-2200000000
χ442222-2-2-2-2-2-222-2-22-2-22-2-22222-2-222-2-2-2-222220000-2200000000-22000022-2-20000000000000000000000000000000000-22002-200000000
χ4522-2-22i2i−2i−2i2222-2-2-22222i−2i2i−2i2i−2i-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22222222i2i−2i−2i-2-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4622-2-22i2i−2i−2i2222-2-2-22222i−2i2i−2i2i−2i-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-22222-2-2-2-2−2i−2i2i2i-2-222222i−2i2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ4722-2-22i2i−2i−2i222-1-2-2-2-1-1-12i−2i2i−2i2i−2i1111−i−iii−i−iii22-2-2-1-1-1-1-1-12i2i−2i−2i111111−ii−ii−i−iii−i−iii00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ4822-2-22i2i−2i−2i222-1-2-2-2-1-1-12i−2i2i−2i2i−2i1111−i−iii−i−iii22-2-2-1-1-1-1-1-12i2i−2i−2i111111−ii−ii−i−iii−i−iii00000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ4922-2-22i2i−2i−2i222-1-2-2-2-1-1-12i−2i2i−2i2i−2i1111−i−iii−i−iii-2-222-1-11111−2i−2i2i2i11-1-1-1-1−ii−iiii−i−iii−i−i00000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ5022-2-22i2i−2i−2i222-1-2-2-2-1-1-12i−2i2i−2i2i−2i1111−i−iii−i−iii-2-222-1-11111−2i−2i2i2i11-1-1-1-1−ii−iiii−i−iii−i−i00000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ5122-2-22i2i−2i−2i2-2-22-222222−2i2i2i−2i−2i2i-2-2-2-22i2i−2i−2i2i2i−2i−2i0000-2-200000000220000−2i2i−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000
χ5222-2-22i2i−2i−2i2-2-22-222222−2i2i2i−2i−2i2i-2-2-2-22i2i−2i−2i2i2i−2i−2i0000-2-200000000220000−2i2i−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000
χ5322-2-22i2i−2i−2i2-2-2-1-222-1-1-1−2i2i2i−2i−2i2i1111−i−iii−i−iii000011−i3−i3i3i30000-1-1i3i3−i3−i3i−ii−i33−3−3−3−3332ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ5422-2-22i2i−2i−2i2-2-2-1-222-1-1-1−2i2i2i−2i−2i2i1111−i−iii−i−iii000011−i3−i3i3i30000-1-1i3i3−i3−i3i−ii−i33−3−3−3−333−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ5522-2-22i2i−2i−2i2-2-2-1-222-1-1-1−2i2i2i−2i−2i2i1111−i−iii−i−iii000011i3i3−i3−i30000-1-1−i3−i3i3i3i−ii−i−3−33333−3−32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000000000
χ5622-2-22i2i−2i−2i2-2-2-1-222-1-1-1−2i2i2i−2i−2i2i1111−i−iii−i−iii000011i3i3−i3−i30000-1-1−i3−i3i3i3i−ii−i−3−33333−3−3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000000000
χ5722-2-22i2i−2i−2i-22-222-22-2-22−2i2i−2i2i2i−2i22-2-22i2i−2i−2i−2i−2i2i2i00002-200000000-2200002i−2i−2i2i0000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ5822-2-22i2i−2i−2i-22-222-22-2-22−2i2i−2i2i2i−2i22-2-22i2i−2i−2i−2i−2i2i2i00002-200000000-2200002i−2i−2i2i00000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ5922-2-22i2i−2i−2i-2-22222-2-2-222i−2i−2i2i−2i2i22-2-22i2i−2i−2i−2i−2i2i2i0000-22000000002-20000−2i2i2i−2i000000000000000000000000000000002-2002i−2i0000000000
χ6022-2-22i2i−2i−2i-2-22222-2-2-222i−2i−2i2i−2i2i22-2-22i2i−2i−2i−2i−2i2i2i0000-22000000002-20000−2i2i2i−2i00000000000000000000000000000000-2200−2i2i0000000000
χ6122-2-2−2i−2i2i2i2222-2-2-2222−2i2i−2i2i−2i2i-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2222222−2i−2i2i2i-2-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6222-2-2−2i−2i2i2i2222-2-2-2222−2i2i−2i2i−2i2i-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-22222-2-2-2-22i2i−2i−2i-2-22222−2i2i−2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.