Finite Group Databasebeta

← Group #10772491

Character table — Group #10772491

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222222222222222222444444444444444444444444444444444444448888888888888888888888242424242424242448484848
order12222234444444466666661212121212121212224444888888881212121212121212242424242424242424242424242424242466668888121212122424242424242424244444442488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-11-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ6111111111111111111111111111111-1-11-1-1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1
χ7111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-11-1-111-1-1
χ8111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-111-1-111
χ91111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-111-111-1-1-11-11-1
χ101111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-11111-1-1-111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-11111-1-1-1-1-1-11-1-1111-11-11
χ111111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-11111-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-1111111-111-1-1-1-11-11
χ121111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-11111-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-11111-11-1
χ131111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-111-1-1-11111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-111-111-1
χ141111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-111-1-1-11111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111-1-1-1-11111-1-11111-1-11-1-11
χ151111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-11
χ161111-1-11-1-11-1-1111-1-1-1-111111-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-111-1
χ17222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200-200200000000-2-222-2-222000000000000000000000000000000000000000002-202-20000
χ18222222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200-200200000000-2-222-2-22200000000000000000000000000000000000000000-220-220000
χ192222222-2-22222-2-222222222222222200-200-200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000002-2200-2000000
χ202222222-2-22222-2-222222222222222200-200-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000-22-2002000000
χ212222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2222-2-2-20000000022-2-222-2-200000000000000002-222220000-2-2-2-200000000000000000000
χ222222222-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2222-20000000022-2-222-2-20000000000000000-22-2-2-2-20000222200000000000000000000
χ23222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000
χ25222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-2222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2-2111111111111000000000000
χ26222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2111122221111-1-1-1-1-1-1-1-1000000000000
χ27222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111222-2-2-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−32-2-1-1-1-10000111133−3−333−3−3000000000000
χ28222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111222-2-2-200000000-1-111-1-111−3−3−3−33333−3−3−3−333332-2-1-1-1-100001111−3−333−3−333000000000000
χ29222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2222-200000000-1-111-1-1113333−3−3−3−33333−3−3−3−3-2211110000-1-1-1-1−3−333−3−333000000000000
χ30222222-1-2-2-2-2-2-222-1-1-1-1-1-1-111111111-2-2222-200000000-1-111-1-111−3−3−3−33333−3−3−3−33333-2211110000-1-1-1-133−3−333−3−3000000000000
χ312222-2-22222-2-22-2-2-2-2-2-222222-2-2-2-22200200-200000000-2-22222-2-2000000000000000000000000000000000000002-2-2002000000
χ322222-2-22222-2-22-2-2-2-2-2-222222-2-2-2-22200200-200000000-2-22222-2-200000000000000000000000000000000000000-22200-2000000
χ332222-2-2222-222-222-2-2-2-2222-2-22222-2-222-222-2000000002222-2-2-2-20000000000000000-2-222-2-20000-2-22200000000000000000000
χ342222-2-2222-222-222-2-2-2-2222-2-22222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000022-2-222000022-2-200000000000000000000
χ352222-2-22-2-2-222-2-2-2-2-2-2-2222-2-22222-2-200200200000000-2-2-2-22222000000000000000000000000000000000000000002-20-220000
χ362222-2-22-2-2-222-2-2-2-2-2-2-2222-2-22222-2-200200200000000-2-2-2-2222200000000000000000000000000000000000000000-2202-20000
χ372222-2-2-122-222-2221111-1-1-111-1-1-1-11122-222-200000000-1-1-1-111113333−3−3−3−3−3−3−3−33333-2-2-1-111000011-1-133−3−3−3−333000000000000
χ382222-2-2-122-222-2221111-1-1-111-1-1-1-11122-222-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−3-2-2-1-111000011-1-1−3−33333−3−3000000000000
χ392222-2-2-122-222-2221111-1-1-111-1-1-1-111-2-2-2-2-2-200000000-1-1-1-111113333−3−3−3−3−3−3−3−333332211-1-10000-1-111−3−33333−3−3000000000000
χ402222-2-2-122-222-2221111-1-1-111-1-1-1-111-2-2-2-2-2-200000000-1-1-1-11111−3−3−3−333333333−3−3−3−32211-1-10000-1-11133−3−3−3−333000000000000
χ412222-2-2-1-2-22-2-22221111-1-1-1-1-11111-1-122-2-2-222222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111-22-1-11122-2-2-1-111-1-1-1-11111000000000000
χ422222-2-2-1-2-22-2-22221111-1-1-1-1-11111-1-122-2-2-22-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1-22-1-111-2-222-1-1111111-1-1-1-1000000000000
χ432222-2-2-1-2-22-2-22221111-1-1-1-1-11111-1-1-2-2-22222222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112-211-1-1-2-22211-1-11111-1-1-1-1000000000000
χ442222-2-2-1-2-22-2-22221111-1-1-1-1-11111-1-1-2-2-2222-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-12-211-1-122-2-211-1-1-1-1-1-11111000000000000
χ4522-2-20022i−2i02i−2i02-200002-2-2002i2i−2i−2i002-202i−2i022−2−2−i2−i2i2i22-22i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2002-2002−2−i2i2002i−2i2−22−2−i2i2−i2i2000000000000
χ4622-2-20022i−2i02i−2i02-200002-2-2002i2i−2i−2i002-202i−2i0−2−222i2i2−i2−i22-22i−2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i2002-200−22i2−i2002i−2i−22−22i2−i2i2−i2000000000000
χ4722-2-20022i−2i02i−2i02-200002-2-2002i2i−2i−2i00-220−2i2i022−2−2−i2−i2i2i22-22i−2i000022−2−222−2−2−i2−i2i2i2−i2−i2i2i200-2200−22i2−i200−2i2i−22−22i2−i2i2−i2000000000000
χ4822-2-20022i−2i02i−2i02-200002-2-2002i2i−2i−2i00-220−2i2i0−2−222i2i2−i2−i22-22i−2i0000−2−222−2−222i2i2−i2−i2i2i2−i2−i200-22002−2−i2i200−2i2i2−22−2−i2i2−i2i2000000000000
χ4922-2-2002−2i2i0−2i2i02-200002-2-200−2i−2i2i2i002-20−2i2i022−2−2i2i2−i2−i22-2−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2002-2002−2i2−i200−2i2i2−22−2i2−i2i2−i2000000000000
χ5022-2-2002−2i2i0−2i2i02-200002-2-200−2i−2i2i2i002-20−2i2i0−2−222−i2−i2i2i22-2−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i2002-200−22−i2i200−2i2i−22−22−i2i2−i2i2000000000000
χ5122-2-2002−2i2i0−2i2i02-200002-2-200−2i−2i2i2i00-2202i−2i022−2−2i2i2−i2−i22-2−2i2i000022−2−222−2−2i2i2−i2−i2i2i2−i2−i200-2200−22−i2i2002i−2i−22−22−i2i2−i2i2000000000000
χ5222-2-2002−2i2i0−2i2i02-200002-2-200−2i−2i2i2i00-2202i−2i0−2−222−i2−i2i2i22-2−2i2i0000−2−222−2−222−i2−i2i2i2−i2−i2i2i200-22002−2i2−i2002i−2i2−22−2i2−i2i2−i2000000000000
χ5322-2-200-12i−2i02i−2i02-2−i3−i3i3i3-1113−3−i−iii3−32-202i−2i022−2−2−i2−i2i2i2-11−ii−i3i33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300-11−i3i32−2−i2i23−3−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5422-2-200-12i−2i02i−2i02-2−i3−i3i3i3-1113−3−i−iii3−32-202i−2i0−2−222i2i2−i2−i2-11−ii−i3i33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300-11−i3i3−22i2−i23−3−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5522-2-200-12i−2i02i−2i02-2−i3−i3i3i3-1113−3−i−iii3−3-220−2i2i022−2−2−i2−i2i2i2-11−ii−i3i33−3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23001-1i3−i3−22i2−i2−33i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23000000000000
χ5622-2-200-12i−2i02i−2i02-2−i3−i3i3i3-1113−3−i−iii3−3-220−2i2i0−2−222i2i2−i2−i2-11−ii−i3i33−3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23001-1i3−i32−2−i2i2−33i−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23000000000000
χ5722-2-200-12i−2i02i−2i02-2i3i3−i3−i3-111−33−i−iii−332-202i−2i022−2−2−i2−i2i2i2-11−iii3−i3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-11i3−i32−2−i2i2−33−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ5822-2-200-12i−2i02i−2i02-2i3i3−i3−i3-111−33−i−iii−332-202i−2i0−2−222i2i2−i2−i2-11−iii3−i3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-11i3−i3−22i2−i2−33−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ5922-2-200-12i−2i02i−2i02-2i3i3−i3−i3-111−33−i−iii−33-220−2i2i022−2−2−i2−i2i2i2-11−iii3−i3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7001-1−i3i3−22i2−i23−3i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ6022-2-200-12i−2i02i−2i02-2i3i3−i3−i3-111−33−i−iii−33-220−2i2i0−2−222i2i2−i2−i2-11−iii3−i3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-1−i3i32−2−i2i23−3i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ6122-2-200-1−2i2i0−2i2i02-2−i3−i3i3i3-111−33ii−i−i−332-20−2i2i022−2−2i2i2−i2−i2-11i−i−i3i3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700-11−i3i32−2i2−i2−33i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7000000000000
χ6222-2-200-1−2i2i0−2i2i02-2−i3−i3i3i3-111−33ii−i−i−332-20−2i2i0−2−222−i2−i2i2i2-11i−i−i3i3−33−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700-11−i3i3−22−i2i2−33i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
χ6322-2-200-1−2i2i0−2i2i02-2−i3−i3i3i3-111−33ii−i−i−33-2202i−2i022−2−2i2i2−i2−i2-11i−i−i3i3−33ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7001-1i3−i3−22−i2i23−3−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.