Finite Group Databasebeta

← Group #10690785

Character table — Group #10690785

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order12222222344444444444444446666666121212121212121222444466661212121212121212121212121212121212121212888888882424242424242424242424242424242488888888888888882444
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
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-111
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-111
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii11-1-1
χ9111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11
χ10111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1
χ11111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-1
χ12111111111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11
χ13111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-11-1
χ14111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11
χ15111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11
χ16111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1
χ172222222222222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222222200000000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-22222-2-222222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-222222222-2-2222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ2122222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2322222222-12222222222-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-10000000033−3−333−3−333−3−333−3−300000000000000000000
χ2422222222-12222222222-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-211111111-1-1-1-11111-1-1-1-1-1-1-1-100000000−3−333−3−333−3−333−3−33300000000000000000000
χ2522222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-1-1-1-111111111111100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2622222222-12222-2-2-2-2-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-11111-1-1-1-111111111111100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-222221111-1-1-1-1-1-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-222221111-1-1-1-1-1-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2922222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-111111111-1-1-1-1111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ3022222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-1-1-1-111111111-1-1-1-11111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ3122222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-111110000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ3222222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1111100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ3322222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2111111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3422222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2111111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-1-1-1-1-1-1-1-1111111111111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ3722-22-22-2-220000002i2i−2i−2i2i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i002-20000000000000022-2-200002i2i−2i−2i0000000000000000000000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000
χ3822-22-22-2-220000002i2i−2i−2i2i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i002-20000000000000022-2-200002i2i−2i−2i000000000000000000000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000
χ3922-22-22-2-220000002i2i−2i−2i−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00-2200000000000000-2-22200002i2i−2i−2i0000000000000000000000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000
χ4022-22-22-2-220000002i2i−2i−2i−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i00-2200000000000000-2-22200002i2i−2i−2i000000000000000000000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000
χ4122-22-22-2-22000000−2i−2i2i2i2i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i00-2200000000000000-2-2220000−2i−2i2i2i0000000000000000000000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000
χ4222-22-22-2-22000000−2i−2i2i2i2i2i−2i−2i0022-2-22-2-22i2i2i2i−2i−2i−2i−2i00-2200000000000000-2-2220000−2i−2i2i2i000000000000000000000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000
χ4322-22-22-2-22000000−2i−2i2i2i−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000000000000022-2-20000−2i−2i2i2i0000000000000000000000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000
χ4422-22-22-2-22000000−2i−2i2i2i−2i−2i2i2i0022-2-22-2-2−2i−2i−2i−2i2i2i2i2i002-20000000000000022-2-20000−2i−2i2i2i000000000000000000000000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000
χ452-222-2-22-222i2i−2i−2i0000002i−2i2i−2i00-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-2000022-2-200002i2i−2i−2i0000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000
χ462-222-2-22-222i2i−2i−2i0000002i−2i2i−2i00-2-2222-2-22i2i−2i−2i2i2i−2i−2i2-2000022-2-200002i2i−2i−2i000000000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000
χ472-222-2-22-222i2i−2i−2i000000−2i2i−2i2i00-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-220000-2-22200002i2i−2i−2i0000000000000000000000000000000000001−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i0000
χ482-222-2-22-222i2i−2i−2i000000−2i2i−2i2i00-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-220000-2-22200002i2i−2i−2i000000000000000000000000000000000000−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i0000
χ492-222-2-22-22−2i−2i2i2i0000002i−2i2i−2i00-2-2222-2-22i2i−2i−2i2i2i−2i−2i-220000-2-2220000−2i−2i2i2i0000000000000000000000000000000000001+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i0000
χ502-222-2-22-22−2i−2i2i2i0000002i−2i2i−2i00-2-2222-2-22i2i−2i−2i2i2i−2i−2i-220000-2-2220000−2i−2i2i2i000000000000000000000000000000000000−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i0000
χ512-222-2-22-22−2i−2i2i2i000000−2i2i−2i2i00-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-2000022-2-20000−2i−2i2i2i0000000000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000
χ522-222-2-22-22−2i−2i2i2i000000−2i2i−2i2i00-2-2222-2-2−2i−2i2i2i−2i−2i2i2i2-2000022-2-20000−2i−2i2i2i000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000
χ532-22-222-2-222-22-22i−2i2i−2i2i−2i00002i−2i2-22-2-22-200000000000000000000002-22-200002i2i−2i−2i2i−2i2i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i00000000000000000000
χ542-22-222-2-222-22-22i−2i2i−2i2i−2i00002i−2i2-22-2-22-200000000000000000000002-22-200002i2i−2i−2i2i−2i2i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i00000000000000000000
χ552-22-222-2-222-22-2−2i2i−2i2i−2i2i0000−2i2i2-22-2-22-200000000000000000000002-22-20000−2i−2i2i2i−2i2i−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i00000000000000000000
χ562-22-222-2-222-22-2−2i2i−2i2i−2i2i0000−2i2i2-22-2-22-200000000000000000000002-22-20000−2i−2i2i2i−2i2i−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i00000000000000000000
χ572-22-222-2-22-22-222i−2i−2i2i−2i2i00002i−2i2-22-2-22-20000000000000000000000-22-2200002i2i−2i−2i−2i2i−2i2i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000000000000000
χ582-22-222-2-22-22-222i−2i−2i2i−2i2i00002i−2i2-22-2-22-20000000000000000000000-22-2200002i2i−2i−2i−2i2i−2i2i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000000000000000
χ592-22-222-2-22-22-22−2i2i2i−2i2i−2i0000−2i2i2-22-2-22-20000000000000000000000-22-220000−2i−2i2i2i2i−2i2i−2i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.