Finite Group Databasebeta

← Group #10693613

Character table — Group #10693613

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order12224444223444444444444446661212121212121212121212124444446612121212121212121212121212121212121212121212888888882424242424242424242424242424242488888888888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ7111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1i−i
χ101111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-11−ii
χ111111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-11−ii
χ121111-1-1-1-1-1-111iiii−i−i−i−i11-1-11111-1-1-1-11111-1-1-1-11-1ii−i−i-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1-111111-1i−i
χ131111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-11-1−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-111111-1−ii
χ141111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-11-1−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-11i−i
χ151111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-11-1−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-11i−i
χ161111-1-1-1-1-1-111−i−i−i−iiiii11-1-11111-1-1-1-11111-1-1-1-11-1−i−iii-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii
χ1722222222222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ192222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ202222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ212222222222-1222222222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ222222222222-1222222222-2-2-2-22-1-1-1-1-1-1-111111111-2-2-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ232222222222-12-2-2-2-2-2-2-2-222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000000000000000
χ242222222222-12-2-2-2-2-2-2-2-222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000000000000000
χ252222222222-12-2-2-2-2-2-2-2-2-2-2-2-22-1-1-1-1-1-1-111111111-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−33300000000000000000000
χ262222222222-12-2-2-2-2-2-2-2-2-2-2-2-22-1-1-1-1-1-1-111111111-2-22222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−300000000000000000000
χ2722222222-2-22-2000000002222-2222222222222222-2-20000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-2000000000000
χ2822222222-2-22-2000000002222-2222222222222222-2-20000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-222000000000000
χ2922222222-2-22-200000000-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000-2-2-2-222220000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000
χ3022222222-2-22-200000000-2-2-2-2-22222222-2-2-2-2-2-2-2-2220000-2-2-2-22222000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000
χ312222-2-2-2-2222-20000000022-2-2-2222-2-2-2-22222-2-2-2-2-22000022-2-2-2-22200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ322222-2-2-2-2222-20000000022-2-2-2222-2-2-2-22222-2-2-2-2-22000022-2-2-2-2220000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ332222-2-2-2-2222-200000000-2-222-2222-2-2-2-2-2-2-2-222222-2000022-2-222-2-20000000000000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000
χ342222-2-2-2-2222-200000000-2-222-2222-2-2-2-2-2-2-2-222222-2000022-2-222-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000
χ352222-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2-2222222-2-2-2-2-2-2-2-22222-22−2i−2i2i2i-2-222-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000000000000000
χ362222-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2-2222222-2-2-2-2-2-2-2-22222-222i2i−2i−2i-2-222-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000000000000000
χ372222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i22-2-22-1-1-11111-1-1-1-111112-22i2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i22-2-2−i−i−i−iiiii-1-1-1-1111100000000000000000000
χ382222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i22-2-22-1-1-11111-1-1-1-111112-22i2i−2i−2i11-1-1-1-111−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2i-2-222iiii−i−i−i−i1111-1-1-1-100000000000000000000
χ392222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i-2-2222-1-1-111111111-1-1-1-1-22−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−300000000000000000000
χ402222-2-2-2-2-2-2-122i2i2i2i−2i−2i−2i−2i-2-2222-1-1-111111111-1-1-1-1-22−2i−2i2i2i11-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−33300000000000000000000
χ412222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i22-2-22-1-1-11111-1-1-1-111112-2−2i−2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i-2-222−i−i−i−iiiii1111-1-1-1-100000000000000000000
χ422222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i22-2-22-1-1-11111-1-1-1-111112-2−2i−2i2i2i11-1-1-1-111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2i22-2-2iiii−i−i−i−i-1-1-1-1111100000000000000000000
χ432222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i-2-2222-1-1-111111111-1-1-1-1-222i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−33300000000000000000000
χ442222-2-2-2-2-2-2-12−2i−2i−2i−2i2i2i2i2i-2-2222-1-1-111111111-1-1-1-1-222i2i−2i−2i11-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−300000000000000000000
χ4522-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-2-22i2i−2i−2i22-2-22i2i−2i−2i001+i−1−i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132−22−2−i2i2−i2i20000
χ4622-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i2-22i−2i02-2-22i2i−2i−2i22-2-22i2i−2i−2i001+i−1−i1−i−1+i000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−22−22i2−i2i2−i20000
χ4722-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i02-2-22i2i−2i−2i-2-222−2i−2i2i2i00−1−i1+i−1+i1−i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300−i2i2i2−i2−222−20000
χ4822-2-22i−2i2i−2i00201+i1+i−1−i−1−i1−i1−i−1+i−1+i-22−2i2i02-2-22i2i−2i−2i-2-222−2i−2i2i2i00−1−i1+i−1+i1−i000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300i2−i2−i2i22−2−220000
χ4922-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-2-22i2i−2i−2i22-2-22i2i−2i−2i00−1−i1+i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−22−22i2−i2i2−i20000
χ5022-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i2-22i−2i02-2-22i2i−2i−2i22-2-22i2i−2i−2i00−1−i1+i−1+i1−i00000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132−22−2−i2i2−i2i20000
χ5122-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i02-2-22i2i−2i−2i-2-222−2i−2i2i2i001+i−1−i1−i−1+i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ2300i2−i2−i2i22−2−220000
χ5222-2-22i−2i2i−2i0020−1−i−1−i1+i1+i−1+i−1+i1−i1−i-22−2i2i02-2-22i2i−2i−2i-2-222−2i−2i2i2i001+i−1−i1−i−1+i00000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−i2i2i2−i2−222−20000
χ5322-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-2-2−2i−2i2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232−22−2i2−i2i2−i20000
χ5422-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i2-2−2i2i02-2-2−2i−2i2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−22−22−i2i2−i2i20000
χ5522-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i02-2-2−2i−2i2i2i-2-2222i2i−2i−2i00−1+i1−i−1−i1+i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300i2−i2−i2i2−222−20000
χ5622-2-2−2i2i−2i2i00201−i1−i−1+i−1+i1+i1+i−1−i−1−i-222i−2i02-2-2−2i−2i2i2i-2-2222i2i−2i−2i00−1+i1−i−1−i1+i000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−i2i2i2−i22−2−220000
χ5722-2-2−2i2i−2i2i0020−1+i−1+i1−i1−i−1−i−1−i1+i1+i2-2−2i2i02-2-2−2i−2i2i2i22-2-2−2i−2i2i2i00−1+i1−i−1−i1+i00000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00000000000000000000000000−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−22−22−i2i2−i2i20000
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χ1114-4-4444-4-4-44-24000000000000-42-22-22-22−2323−2323−2323−23230000002-22-223−2323−23000000000000000000000000000000000000000000000000000000000000
χ1124-4-44-4-4444-444000000000000-4-44-4-44-44000000000000004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-4-4444-4-24000000000000-42-222-22-223−2323−23−2323−2323000000-222-2−232323−23000000000000000000000000000000000000000000000000000000000000
χ1144-4-44-4-4444-4-24000000000000-42-222-22-2−2323−232323−2323−23000000-222-223−23−2323000000000000000000000000000000000000000000000000000000000000

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