Finite Group Databasebeta

← Group #10694000

Character table — Group #10694000

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order12222222444444443444444446666666121212121212121244444444121212121212121212121212121212121212121212121212224444446666121212121212121212121212888888888888888888888888
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
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222222-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-2222222222222222-2-222-2-222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
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
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ232222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-111111111111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ242222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-111111111111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ252222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-11111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000
χ262222222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-11111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ3122222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ3222222222-2-2-2-2-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-11111-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ3322222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ3422222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-2-1-2-2-2-22222-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ37222-2-22-2-22i2i2i−2i−2i−2i2i−2i20000000022-2-22-2-22i2i2i2i−2i−2i−2i−2i002i−2i002-200002i2i−2i−2i000022-2-2000000000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000
χ38222-2-22-2-22i2i2i−2i−2i−2i2i−2i20000000022-2-22-2-22i2i2i2i−2i−2i−2i−2i002i−2i002-200002i2i−2i−2i000022-2-200000000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000
χ39222-2-22-2-22i2i2i−2i−2i−2i2i−2i20000000022-2-22-2-22i2i2i2i−2i−2i−2i−2i00−2i2i00-220000−2i−2i2i2i0000-2-222000000000000000000000000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000
χ40222-2-22-2-22i2i2i−2i−2i−2i2i−2i20000000022-2-22-2-22i2i2i2i−2i−2i−2i−2i00−2i2i00-220000−2i−2i2i2i0000-2-22200000000000000000000000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000
χ41222-2-22-2-2−2i−2i−2i2i2i2i−2i2i20000000022-2-22-2-2−2i−2i−2i−2i2i2i2i2i002i−2i00-2200002i2i−2i−2i0000-2-222000000000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
χ42222-2-22-2-2−2i−2i−2i2i2i2i−2i2i20000000022-2-22-2-2−2i−2i−2i−2i2i2i2i2i002i−2i00-2200002i2i−2i−2i0000-2-22200000000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000
χ43222-2-22-2-2−2i−2i−2i2i2i2i−2i2i20000000022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00−2i2i002-20000−2i−2i2i2i000022-2-2000000000000000000000000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000
χ44222-2-22-2-2−2i−2i−2i2i2i2i−2i2i20000000022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00−2i2i002-20000−2i−2i2i2i000022-2-200000000000000000000000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000
χ4522-22-2-22-22i2i−2i2i−2i−2i−2i2i222-2-22i2i−2i−2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000000022-2-22i2i−2i−2i00002-22i−2i000000002-22-22i−2i2i−2i000000000000000000000000
χ4622-22-2-22-22i2i−2i2i−2i−2i−2i2i222-2-22i2i−2i−2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i00000000000000000000000022-2-22i2i−2i−2i0000-22−2i2i00000000-22-22−2i2i−2i2i000000000000000000000000
χ4722-22-2-22-22i2i−2i2i−2i−2i−2i2i2-2-222−2i−2i2i2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-2-222−2i−2i2i2i2-22i−2i00002-22-22i−2i2i−2i00000000000000000000000000000000
χ4822-22-2-22-22i2i−2i2i−2i−2i−2i2i2-2-222−2i−2i2i2i2-22-2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-2-222−2i−2i2i2i-22−2i2i0000-22-22−2i2i−2i2i00000000000000000000000000000000
χ4922-22-2-22-22i2i−2i2i−2i−2i−2i2i-122-2-22i2i−2i−2i-11-111-11−i−iii−i−iii00000000−i3−i3i3i3−i3i3−i3i333−3−33−33−3-1-111−i−iii00002-22i−2i−i3i3i3−i33−3−33-11-11−ii−ii000000000000000000000000
χ5022-22-2-22-22i2i−2i2i−2i−2i−2i2i-122-2-22i2i−2i−2i-11-111-11−i−iii−i−iii00000000−i3−i3i3i3−i3i3−i3i333−3−33−33−3-1-111−i−iii0000-22−2i2ii3−i3−i3i3−333−31-11-1i−ii−i000000000000000000000000
χ5122-22-2-22-22i2i−2i2i−2i−2i−2i2i-122-2-22i2i−2i−2i-11-111-11−i−iii−i−iii00000000i3i3−i3−i3i3−i3i3−i3−3−333−33−33-1-111−i−iii00002-22i−2ii3−i3−i3i3−333−3-11-11−ii−ii000000000000000000000000
χ5222-22-2-22-22i2i−2i2i−2i−2i−2i2i-122-2-22i2i−2i−2i-11-111-11−i−iii−i−iii00000000i3i3−i3−i3i3−i3i3−i3−3−333−33−33-1-111−i−iii0000-22−2i2i−i3i3i3−i33−3−331-11-1i−ii−i000000000000000000000000
χ5322-22-2-22-22i2i−2i2i−2i−2i−2i2i-1-2-222−2i−2i2i2i-11-111-11−i−iii−i−iii00000000−i3−i3i3i3i3−i3i3−i333−3−3−33−3311-1-1ii−i−i2-22i−2i0000-11-11−ii−ii−i3i3i3−i33−3−33000000000000000000000000
χ5422-22-2-22-22i2i−2i2i−2i−2i−2i2i-1-2-222−2i−2i2i2i-11-111-11−i−iii−i−iii00000000−i3−i3i3i3i3−i3i3−i333−3−3−33−3311-1-1ii−i−i-22−2i2i00001-11-1i−ii−ii3−i3−i3i3−333−3000000000000000000000000
χ5522-22-2-22-22i2i−2i2i−2i−2i−2i2i-1-2-222−2i−2i2i2i-11-111-11−i−iii−i−iii00000000i3i3−i3−i3−i3i3−i3i3−3−3333−33−311-1-1ii−i−i2-22i−2i0000-11-11−ii−iii3−i3−i3i3−333−3000000000000000000000000
χ5622-22-2-22-22i2i−2i2i−2i−2i−2i2i-1-2-222−2i−2i2i2i-11-111-11−i−iii−i−iii00000000i3i3−i3−i3−i3i3−i3i3−3−3333−33−311-1-1ii−i−i-22−2i2i00001-11-1i−ii−i−i3i3i3−i33−3−33000000000000000000000000
χ5722-22-2-22-2−2i−2i2i−2i2i2i2i−2i222-2-2−2i−2i2i2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000022-2-2−2i−2i2i2i00002-2−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000
χ5822-22-2-22-2−2i−2i2i−2i2i2i2i−2i222-2-2−2i−2i2i2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000022-2-2−2i−2i2i2i0000-222i−2i00000000-22-222i−2i2i−2i000000000000000000000000
χ5922-22-2-22-2−2i−2i2i−2i2i2i2i−2i2-2-2222i2i−2i−2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-2-2222i2i−2i−2i2-2−2i2i00002-22-2−2i2i−2i2i00000000000000000000000000000000
χ6022-22-2-22-2−2i−2i2i−2i2i2i2i−2i2-2-2222i2i−2i−2i2-22-2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-2-2222i2i−2i−2i-222i−2i0000-22-222i−2i2i−2i00000000000000000000000000000000
χ6122-22-2-22-2−2i−2i2i−2i2i2i2i−2i-122-2-2−2i−2i2i2i-11-111-11ii−i−iii−i−i00000000−i3−i3i3i3−i3i3−i3i3−3−333−33−33-1-111ii−i−i00002-2−2i2i−i3i3i3−i3−333−3-11-11i−ii−i000000000000000000000000
χ6222-22-2-22-2−2i−2i2i−2i2i2i2i−2i-122-2-2−2i−2i2i2i-11-111-11ii−i−iii−i−i00000000−i3−i3i3i3−i3i3−i3i3−3−333−33−33-1-111ii−i−i0000-222i−2ii3−i3−i3i33−3−331-11-1−ii−ii000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.