Finite Group Databasebeta

← Group #10701897

Character table — Group #10701897

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order1222222222222222344444444666666666666666444444441212121212121212121212121212121212121212121212124444444412121212121212121212121212121212888888888888888822222222
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1
χ1011111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111
χ1111111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111
χ1211111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1
χ1311111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111
χ1411111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1
χ1511111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1
χ1611111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-211111111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-222111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222-2-2-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2222-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222-2-2-2-2-2-2222-2-22-2-2-2-222222222-2-2-2-2-2-2222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ2922222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-1111111-1-1-1112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ3022222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-1111111-1-1-1112222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ3122222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-1111111-1-1-111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ3222222-2-2-2-2-2-2222-2-2-12222-2-2-2-2-1-1-1-1111111-1-1-111-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ3322222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-1111111-1-1-11122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−333000000000000000000000000
χ3422222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-1111111-1-1-11122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−3000000000000000000000000
χ3522222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-1111111-1-1-111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−3000000000000000000000000
χ3622222-2-2-2-2-2-2222-2-2-1-2-2-2-22222-1-1-1-1111111-1-1-111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−333000000000000000000000000
χ37222-2-22222-2-22-2-2-2-220000000022-2-22222-2-22-2-2-2-2002-2002-200000000000022-2-2000022-2-2000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ38222-2-22222-2-22-2-2-2-220000000022-2-22222-2-22-2-2-2-2002-2002-200000000000022-2-2000022-2-2000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ39222-2-22222-2-22-2-2-2-220000000022-2-22222-2-22-2-2-2-200-2200-22000000000000-2-2220000-2-222000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ40222-2-22222-2-22-2-2-2-220000000022-2-22222-2-22-2-2-2-200-2200-22000000000000-2-2220000-2-222000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ41222-2-2-2-2-2-2222-2-22220000000022-2-2-2-2-2-2222-2-222002-200-2200000000000022-2-20000-2-22200000000000000000000000022−2−2−2−22222−2−2−2−22200000000
χ42222-2-2-2-2-2-2222-2-22220000000022-2-2-2-2-2-2222-2-222002-200-2200000000000022-2-20000-2-222000000000000000000000000−2−22222−2−2−2−22222−2−200000000
χ43222-2-2-2-2-2-2222-2-22220000000022-2-2-2-2-2-2222-2-22200-22002-2000000000000-2-222000022-2-200000000000000000000000022−2−2−2−222−2−22222−2−200000000
χ44222-2-2-2-2-2-2222-2-22220000000022-2-2-2-2-2-2222-2-22200-22002-2000000000000-2-222000022-2-2000000000000000000000000−2−22222−2−222−2−2−2−22200000000
χ4522-22-222-2-222-22-2-2-22000000002-22-222-2-222-22-2-2-22-2002-2000000000022-2-2000022-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ4622-22-222-2-222-22-2-2-22000000002-22-222-2-222-22-2-2-22-2002-2000000000022-2-2000022-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ4722-22-222-2-222-22-2-2-22000000002-22-222-2-222-22-2-2-2-2200-220000000000-2-2220000-2-2220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ4822-22-222-2-222-22-2-2-22000000002-22-222-2-222-22-2-2-2-2200-220000000000-2-2220000-2-2220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4922-22-2-2-222-2-2-22-2222000000002-22-2-2-222-2-2-22-2222-200-22000000000022-2-20000-2-22200000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ5022-22-2-2-222-2-2-22-2222000000002-22-2-2-222-2-2-22-2222-200-22000000000022-2-20000-2-2220000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ5122-22-2-2-222-2-2-22-2222000000002-22-2-2-222-2-2-22-222-22002-20000000000-2-222000022-2-200000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ5222-22-2-2-222-2-2-22-2222000000002-22-2-2-222-2-2-22-222-22002-20000000000-2-222000022-2-20000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ5322-2-2222-2-2-2-2-2-2222222-2-22-22-22-2-2222-2-2-2-2-2-22220000000022-2-222-2-20000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ5422-2-2222-2-2-2-2-2-2222222-2-22-22-22-2-2222-2-2-2-2-2-22220000000022-2-222-2-2000000000000000000000000000000000000000000000000-222-2-222-200000000
χ5522-2-2222-2-2-2-2-2-22222-2-222-22-222-2-2222-2-2-2-2-2-222200000000-2-222-2-22200000000000000000000000000000000000000002-2-222-2-220000000000000000
χ5622-2-2222-2-2-2-2-2-22222-2-222-22-222-2-2222-2-2-2-2-2-222200000000-2-222-2-2220000000000000000000000000000000000000000-222-2-222-20000000000000000
χ5722-2-22-2-22222-2-22-2-2222-2-2-22-222-2-22-2-22222-2-22-2-20000000022-2-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ5822-2-22-2-22222-2-22-2-2222-2-2-22-222-2-22-2-22222-2-22-2-20000000022-2-2-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ5922-2-22-2-22222-2-22-2-22-2-2222-22-22-2-22-2-22222-2-22-2-200000000-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ6022-2-22-2-22222-2-22-2-22-2-2222-22-22-2-22-2-22222-2-22-2-200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ612-222-22-22-22-2-2-222-222-22-222-2-2-222-22-22-22-2-2-222-2000000002-22-22-22-2000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ622-222-22-22-22-2-2-222-222-22-222-2-2-222-22-22-22-2-2-222-2000000002-22-22-22-200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ632-222-22-22-22-2-2-222-22-22-22-2-222-222-22-22-22-2-2-222-200000000-22-22-22-2200000000000000002-22-200002-22-22-22-200000000000000000000000000000000
χ642-222-22-22-22-2-2-222-22-22-22-2-222-222-22-22-22-2-2-222-200000000-22-22-22-220000000000000000-22-220000-22-22-22-2200000000000000000000000000000000
χ652-222-22-22-22-2-2-222-2-12-22-222-2-21-1-11-11-11-1111-1-1100000000-11-11-11-113−33−33−33−33−33−33−33−300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii000000000000000000000000
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χ672-222-22-22-22-2-2-222-2-12-22-222-2-21-1-11-11-11-1111-1-1100000000-11-11-11-11−33−33−33−33−33−33−33−3300002i−2i2i−2ii3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii000000000000000000000000
χ682-222-22-22-22-2-2-222-2-12-22-222-2-21-1-11-11-11-1111-1-1100000000-11-11-11-11−33−33−33−33−33−33−33−330000−2i2i−2i2i−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i000000000000000000000000
χ692-222-22-22-22-2-2-222-2-1-22-22-2-2221-1-11-11-11-1111-1-11000000001-11-11-11-13−33−3−33−333−33−3−33−332-22-20000-11-11-11-113−3−333−3−33000000000000000000000000
χ702-222-22-22-22-2-2-222-2-1-22-22-2-2221-1-11-11-11-1111-1-11000000001-11-11-11-13−33−3−33−333−33−3−33−33-22-2200001-11-11-11-1−333−3−333−3000000000000000000000000
χ712-222-22-22-22-2-2-222-2-1-22-22-2-2221-1-11-11-11-1111-1-11000000001-11-11-11-1−33−333−33−3−33−333−33−32-22-20000-11-11-11-11−333−3−333−3000000000000000000000000
χ722-222-22-22-22-2-2-222-2-1-22-22-2-2221-1-11-11-11-1111-1-11000000001-11-11-11-1−33−333−33−3−33−333−33−3-22-2200001-11-11-11-13−3−333−3−33000000000000000000000000
χ732-222-2-22-22-22-2-22-2222-22-2-2-222-222-2-22-22-22-2-22-22000000002-22-2-22-22000000000000000000002-2-22000000002-22-2-22-22000000000000000000000000
χ742-222-2-22-22-22-2-22-2222-22-2-2-222-222-2-22-22-22-2-22-22000000002-22-2-22-2200000000000000000000-222-200000000-22-222-22-2000000000000000000000000
χ752-222-2-22-22-22-2-22-222-22-2222-2-2-222-2-22-22-22-2-22-2200000000-22-222-22-200000000000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ762-222-2-22-22-22-2-22-222-22-2222-2-2-222-2-22-22-22-2-22-2200000000-22-222-22-20000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ772-222-2-22-22-22-2-22-22-12-22-2-2-2221-1-111-11-11-111-11-100000000-11-111-11-13−33−33−33−3−33−33−33−3300002-2-22−333−33−3−33-11-111-11-1000000000000000000000000
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χ912-2-2-2-2-222-22-2222-222-222-22-2-22-2-2-2-2-222-22-2222-2200000000-222-22-2-220000000000000000000000000000000000000000000000000000000000002-2-22
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χ1154-4-444-444-4-444-4-44-4-20000000022-2-22-2-222-2-222-22000000000000000023−23−23230000−232323−230000000000000000000000000000000000000000000000000000
χ1164-4-444-444-4-444-4-44-4-20000000022-2-22-2-222-2-222-220000000000000000−232323−23000023−23−23230000000000000000000000000000000000000000000000000000
χ1174-4-4-4-44-4-44-444444-4-24-4-444-4-442222-222-22-2-2-2-2-2200000000-222-2-222-20000000000000000000000000000000000000000000000000000000000000000
χ1184-4-4-4-44-4-44-444444-4-2-444-4-444-42222-222-22-2-2-2-2-22000000002-2-222-2-220000000000000000000000000000000000000000000000000000000000000000
χ1194-4-4-4-4-444-44-4444-44-24-4-44-444-422222-2-22-22-2-2-22-200000000-222-22-2-220000000000000000000000000000000000000000000000000000000000000000
χ1204-4-4-4-4-444-44-4444-44-2-444-44-4-4422222-2-22-22-2-2-22-2000000002-2-22-222-20000000000000000000000000000000000000000000000000000000000000000

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