Finite Group Databasebeta

← Group #10728738

Character table — Group #10728738

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222222222223444444446666666666666664444444412121212121212121212121212121212121212121212121222224444666666661212121212121212222244444444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1411111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ172222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ212222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ25222222-2-22-2-2-2-22-2-222222-2-2-2-222222-2-2-2-2-2-22-2-22000000002222-2-2-2-20000000000000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ26222222-2-22-2-2-2-22-2-222222-2-2-2-222222-2-2-2-2-2-22-2-22000000002222-2-2-2-2000000000000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ27222222-2-22-2-2-2-22-2-22-2-2-2-2222222222-2-2-2-2-2-22-2-2200000000-2-2-2-222220000000000000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ28222222-2-22-2-2-2-22-2-22-2-2-2-2222222222-2-2-2-2-2-22-2-2200000000-2-2-2-22222000000000000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ292222-2-22-2-222-2-2-22-222i2i−2i−2i2i2i−2i−2i222-2-2222-2-2-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000002-2002i−2i000022-2-200002i2i−2i−2i000000000000000000000000
χ302222-2-22-2-222-2-2-22-222i2i−2i−2i2i2i−2i−2i222-2-2222-2-2-2-22-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000-2200−2i2i0000-2-2220000−2i−2i2i2i000000000000000000000000
χ312222-2-22-2-222-2-2-22-22−2i−2i2i2i−2i−2i2i2i222-2-2222-2-2-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000002-200−2i2i000022-2-20000−2i−2i2i2i000000000000000000000000
χ322222-2-22-2-222-2-2-22-22−2i−2i2i2i−2i−2i2i2i222-2-2222-2-2-2-22-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000-22002i−2i0000-2-22200002i2i−2i−2i000000000000000000000000
χ332222-2-22-2-222-2-2-22-2-12i2i−2i−2i2i2i−2i−2i-1-1-111-1-1-11111-11100000000−i−iii−i−iii−i3−i3−i3−i3i3i3i3i33333−3−3−3−3002-2002i−2i−i3−i3i3i3-1-11133−3−3−i−iii000000000000000000000000
χ342222-2-22-2-222-2-2-22-2-12i2i−2i−2i2i2i−2i−2i-1-1-111-1-1-11111-11100000000−i−iii−i−iii−i3−i3−i3−i3i3i3i3i33333−3−3−3−300-2200−2i2ii3i3−i3−i311-1-1−3−333ii−i−i000000000000000000000000
χ352222-2-22-2-222-2-2-22-2-12i2i−2i−2i2i2i−2i−2i-1-1-111-1-1-11111-11100000000−i−iii−i−iiii3i3i3i3−i3−i3−i3−i3−3−3−3−33333002-2002i−2ii3i3−i3−i3-1-111−3−333−i−iii000000000000000000000000
χ362222-2-22-2-222-2-2-22-2-12i2i−2i−2i2i2i−2i−2i-1-1-111-1-1-11111-11100000000−i−iii−i−iiii3i3i3i3−i3−i3−i3−i3−3−3−3−3333300-2200−2i2i−i3−i3i3i311-1-133−3−3ii−i−i000000000000000000000000
χ372222-2-22-2-222-2-2-22-2-1−2i−2i2i2i−2i−2i2i2i-1-1-111-1-1-11111-11100000000ii−i−iii−i−i−i3−i3−i3−i3i3i3i3i3−3−3−3−33333002-200−2i2i−i3−i3i3i3-1-111−3−333ii−i−i000000000000000000000000
χ382222-2-22-2-222-2-2-22-2-1−2i−2i2i2i−2i−2i2i2i-1-1-111-1-1-11111-11100000000ii−i−iii−i−i−i3−i3−i3−i3i3i3i3i3−3−3−3−3333300-22002i−2ii3i3−i3−i311-1-133−3−3−i−iii000000000000000000000000
χ392222-2-22-2-222-2-2-22-2-1−2i−2i2i2i−2i−2i2i2i-1-1-111-1-1-11111-11100000000ii−i−iii−i−ii3i3i3i3−i3−i3−i3−i33333−3−3−3−3002-200−2i2ii3i3−i3−i3-1-11133−3−3ii−i−i000000000000000000000000
χ402222-2-22-2-222-2-2-22-2-1−2i−2i2i2i−2i−2i2i2i-1-1-111-1-1-11111-11100000000ii−i−iii−i−ii3i3i3i3−i3−i3−i3−i33333−3−3−3−300-22002i−2i−i3−i3i3i311-1-1−3−333−i−iii000000000000000000000000
χ412222-2-2-22-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i222-2-2-2-2-2222-2-22-2000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000002-22i−2i0000
χ422222-2-2-22-2-2-222-2-2222i2i−2i−2i−2i−2i2i2i222-2-2-2-2-2222-2-22-2000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000-22−2i2i0000
χ432222-2-2-22-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i222-2-2-2-2-2222-2-22-200000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000002-2−2i2i0000
χ442222-2-2-22-2-2-222-2-222−2i−2i2i2i2i2i−2i−2i222-2-2-2-2-2222-2-22-200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000-222i−2i0000
χ4522-2-2222-2-2-2-222-22-222i−2i2i−2i2i−2i2i−2i2-2-2222-2-222-2-22-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000002-2002i−2i002-22-200002i−2i2i−2i0000000000000000000000000000
χ4622-2-2222-2-2-2-222-22-222i−2i2i−2i2i−2i2i−2i2-2-2222-2-222-2-22-2-2000000002i−2i2i−2i2i−2i2i−2i0000000000000000-2200−2i2i00-22-220000−2i2i−2i2i0000000000000000000000000000
χ4722-2-2222-2-2-2-222-22-22−2i2i−2i2i−2i2i−2i2i2-2-2222-2-222-2-22-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000002-200−2i2i002-22-20000−2i2i−2i2i0000000000000000000000000000
χ4822-2-2222-2-2-2-222-22-22−2i2i−2i2i−2i2i−2i2i2-2-2222-2-222-2-22-2-200000000−2i2i−2i2i−2i2i−2i2i0000000000000000-22002i−2i00-22-2200002i−2i2i−2i0000000000000000000000000000
χ4922-2-2222-2-2-2-222-22-2-12i−2i2i−2i2i−2i2i−2i-111-1-1-111-1-111-11100000000−ii−ii−ii−ii−i3−i3i3i3−i3−i3i3i333−3−333−3−32-2002i−2i00-11-11−i3i3−i3i3−ii−ii3−33−3000000000000000000000000
χ5022-2-2222-2-2-2-222-22-2-12i−2i2i−2i2i−2i2i−2i-111-1-1-111-1-111-11100000000−ii−ii−ii−ii−i3−i3i3i3−i3−i3i3i333−3−333−3−3-2200−2i2i001-11-1i3−i3i3−i3i−ii−i−33−33000000000000000000000000
χ5122-2-2222-2-2-2-222-22-2-12i−2i2i−2i2i−2i2i−2i-111-1-1-111-1-111-11100000000−ii−ii−ii−iii3i3−i3−i3i3i3−i3−i3−3−333−3−3332-2002i−2i00-11-11i3−i3i3−i3−ii−ii−33−33000000000000000000000000
χ5222-2-2222-2-2-2-222-22-2-12i−2i2i−2i2i−2i2i−2i-111-1-1-111-1-111-11100000000−ii−ii−ii−iii3i3−i3−i3i3i3−i3−i3−3−333−3−333-2200−2i2i001-11-1−i3i3−i3i3i−ii−i3−33−3000000000000000000000000
χ5322-2-2222-2-2-2-222-22-2-1−2i2i−2i2i−2i2i−2i2i-111-1-1-111-1-111-11100000000i−ii−ii−ii−i−i3−i3i3i3−i3−i3i3i3−3−333−3−3332-200−2i2i00-11-11−i3i3−i3i3i−ii−i−33−33000000000000000000000000
χ5422-2-2222-2-2-2-222-22-2-1−2i2i−2i2i−2i2i−2i2i-111-1-1-111-1-111-11100000000i−ii−ii−ii−i−i3−i3i3i3−i3−i3i3i3−3−333−3−333-22002i−2i001-11-1i3−i3i3−i3−ii−ii3−33−3000000000000000000000000
χ5522-2-2222-2-2-2-222-22-2-1−2i2i−2i2i−2i2i−2i2i-111-1-1-111-1-111-11100000000i−ii−ii−ii−ii3i3−i3−i3i3i3−i3−i333−3−333−3−32-200−2i2i00-11-11i3−i3i3−i3i−ii−i3−33−3000000000000000000000000
χ5622-2-2222-2-2-2-222-22-2-1−2i2i−2i2i−2i2i−2i2i-111-1-1-111-1-111-11100000000i−ii−ii−ii−ii3i3−i3−i3i3i3−i3−i333−3−333−3−3-22002i−2i001-11-1−i3i3−i3i3−ii−ii−33−33000000000000000000000000
χ5722-2-222-22-222-2-2-2-2222i−2i2i−2i−2i2i−2i2i2-2-222-222-2-22-2-22-2000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000002-22i−2i
χ5822-2-222-22-222-2-2-2-2222i−2i2i−2i−2i2i−2i2i2-2-222-222-2-22-2-22-2000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000000000-22−2i2i
χ5922-2-222-22-222-2-2-2-222−2i2i−2i2i2i−2i2i−2i2-2-222-222-2-22-2-22-200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000002-2−2i2i
χ6022-2-222-22-222-2-2-2-222−2i2i−2i2i2i−2i2i−2i2-2-222-222-2-22-2-22-200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000000000-222i−2i
χ6122-2-2-2-2222-2-2-2-222222-2-222-2-222-2-2-2-22-2-2-2-22222222-2-222-2-22-2-222-2-2222-2-2-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ6222-2-2-2-2222-2-2-2-222222-2-222-2-222-2-2-2-22-2-2-2-222222-2-222-2-2222-2-222-2-22-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ6322-2-2-2-2222-2-2-2-22222-222-2-222-22-2-2-2-22-2-2-2-22222222-2-2-2-222-222-2-222-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000000000
χ6422-2-2-2-2222-2-2-2-22222-222-2-222-22-2-2-2-22-2-2-2-222222-2-22222-2-2-222-2-222-2-2-22222-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ6522-2-2-2-2222-2-2-2-2222-12-2-222-2-22-11111-11111-1-1-1-1-122-2-222-2-2-111-1-111-1-1-11111-1-1-1-11111-1-100000000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000
χ6622-2-2-2-2222-2-2-2-2222-12-2-222-2-22-11111-11111-1-1-1-1-122-2-222-2-2-111-1-111-1-1-11111-1-1-1-11111-1-100000000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000
χ6722-2-2-2-2222-2-2-2-2222-12-2-222-2-22-11111-11111-1-1-1-1-1-2-222-2-222-111-1-111-111-1-1-1-11111-1-1-1-11100000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000
χ6822-2-2-2-2222-2-2-2-2222-12-2-222-2-22-11111-11111-1-1-1-1-1-2-222-2-222-111-1-111-111-1-1-1-11111-1-1-1-11100000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000
χ6922-2-2-2-2222-2-2-2-2222-1-222-2-222-2-11111-11111-1-1-1-1-122-2-2-2-2221-1-111-1-11-1-11111-1-111-1-1-1-11100000000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000
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χ7422-2-2-2-2-2-2222222-2-222-2-22-222-22-2-2-2-2-22222-22-2-22000000002-2-22-222-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ7522-2-2-2-2-2-2222222-2-22-222-22-2-222-2-2-2-2-22222-22-2-2200000000-222-22-2-22000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ7622-2-2-2-2-2-2222222-2-22-222-22-2-222-2-2-2-2-22222-22-2-2200000000-222-22-2-220000000000000000000000000000000000000000-2-22222-2-20000000000000000
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χ1114-4-444-44-44-444-4-4-44400000000-4-444-44-444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1144-4-444-4-4444-4-44-44-4400000000-4-444-4-44-4-444-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1184-4-44-4444-4-44-444-4-4-20000000022-22-2-22-22-2-2-22220000−4i4i4i−4i00000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000
χ1194-4-44-44-4-4-44-44-4444-20000000022-22-22-22-222-2-2-224-4-44000000000000-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ1204-4-44-44-4-4-44-44-4444-20000000022-22-22-22-222-2-2-22-444-40000000000002-2-22-222-200000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).