Finite Group Databasebeta

← Group #10690787

Character table — Group #10690787

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111111112222222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444242424242424242448484848
order12222222344444444444444446666666121212121212121212121212121212121212121212121212224444666688888888888888881212121212121212121212122424242424242424242424242424242424242424242424242424242424242424888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i-1-111
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−iiiii11-1-1
χ9111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-1-11
χ10111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-111-1
χ11111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1
χ12111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-11
χ13111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii1-11-1
χ14111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-11-11
χ15111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-11-11
χ16111111111-1-1-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i1-11-1
χ17222222222222222222222-2-2-2-22222222222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-222220000000000000000-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-22222-2-222222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ2122222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2222222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111000000000000
χ2322222222-1222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211110000000000000000111111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ2422222222-1222222222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211110000000000000000111111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ2522222222-12222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1000000000000000011111111-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−33333000000000000
χ2622222222-12222-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-1-1-1-1000000000000000011111111-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−3000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2222211112i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-222221111−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-1-1-1-1-1-1-1-11111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i000000000000
χ2922222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-2-2-2-22211112222-2-2-2-22222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ3022222222-1-2-2-2-222-2-2-2-2222222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-2-2-2-2221111-2-2-2-22222-2-2-2-22222-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ3122222222-1-2-2-2-222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-12222-2-2-1-1-1-100000000000000001111-1-1-1-11111−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ3222222222-1-2-2-2-222-2-2-2-222-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-12222-2-2-1-1-1-100000000000000001111-1-1-1-11111i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ3322222222-1-2-2-2-2-2-22222-2-22222-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-2-222-2-2111100000000000000001111-1-1-1-1-1-1-1-13333−3−3−3−3−3−3−3−33333−3−3−3−333333333−3−3−3−3000000000000
χ3422222222-1-2-2-2-2-2-22222-2-22222-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-2-222-2-2111100000000000000001111-1-1-1-1-1-1-1-1−3−3−3−333333333−3−3−3−33333−3−3−3−3−3−3−3−33333000000000000
χ3522222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111122-2-222-1-1-1-12i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i000000000000
χ3622222222-1-2-2-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111122-2-222-1-1-1-1−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ3722-22-22-2-220000002i2i−2i−2i002i2i−2i−2i22-2-22-2-20000000000002i2i2i2i−2i−2i−2i−2i0000002-20000001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000022-2-22i2i−2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ3822-22-22-2-220000002i2i−2i−2i002i2i−2i−2i22-2-22-2-20000000000002i2i2i2i−2i−2i−2i−2i0000002-2000000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000022-2-22i2i−2i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ3922-22-22-2-220000002i2i−2i−2i00−2i−2i2i2i22-2-22-2-20000000000002i2i2i2i−2i−2i−2i−2i000000-220000001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000-2-222−2i−2i2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i000000000000
χ4022-22-22-2-220000002i2i−2i−2i00−2i−2i2i2i22-2-22-2-20000000000002i2i2i2i−2i−2i−2i−2i000000-22000000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000-2-222−2i−2i2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
χ4122-22-22-2-22000000−2i−2i2i2i002i2i−2i−2i22-2-22-2-2000000000000−2i−2i−2i−2i2i2i2i2i000000-220000001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000-2-2222i2i−2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i000000000000
χ4222-22-22-2-22000000−2i−2i2i2i002i2i−2i−2i22-2-22-2-2000000000000−2i−2i−2i−2i2i2i2i2i000000-22000000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000-2-2222i2i−2i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i000000000000
χ4322-22-22-2-22000000−2i−2i2i2i00−2i−2i2i2i22-2-22-2-2000000000000−2i−2i−2i−2i2i2i2i2i0000002-20000001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000022-2-2−2i−2i2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i−1−i000000000000
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χ1062-2-222-2-22-10000220000-2-2-222-21111-1-1-1−i3−i3i3i3i3i3−i3−i3-1-1-1-1−i3−i3i3i3i3i3−i3−i311110000-22i3−i3−i3i3−2i2i2i−2i00002i−2i−2i2i00001-1-11i3−i3−i3i31-1-11i−i−iii−i−ii3−3−33−333−3−iii−i−iii−i−333−33−3−33000000000000
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χ1082-2-222-2-22-10000220000-2-2-222-21111-1-1-1i3i3−i3−i3−i3−i3i3i3-1-1-1-1i3i3−i3−i3−i3−i3i3i311110000-22−i3i3i3−i3−2i2i2i−2i00002i−2i−2i2i00001-1-11−i3i3i3−i31-1-11i−i−iii−i−ii−333−33−3−33−iii−i−iii−i3−3−33−333−3000000000000
χ1092-2-222-2-22-10000-2-20000222-2-221111-1-1-1−i3−i3i3i3i3i3−i3−i31111i3i3−i3−i3−i3−i3i3i3-1-1-1-10000-22−i3i3i3−i32-2-2200002-2-2200001-1-11i3−i3−i3i3-111-1-111-1-111-1i3−i3−i3i3−i3i3i3−i3-111-1-111-1i3−i3−i3i3−i3i3i3−i3000000000000
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χ1112-2-222-2-22-10000-2-20000222-2-221111-1-1-1i3i3−i3−i3−i3−i3i3i31111−i3−i3i3i3i3i3−i3−i3-1-1-1-10000-22i3−i3−i3i32-2-2200002-2-2200001-1-11−i3i3i3−i3-111-1-111-1-111-1−i3i3i3−i3i3−i3−i3i3-111-1-111-1−i3i3i3−i3i3−i3−i3i3000000000000
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χ117444-4-4-4-4444i−4i−4i4i000000000000-444-4-4-444i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ12744-4-44-44-4-20000−4i4i00004i−4i00002-22-22-22−2i32i32i3−2i32i3−2i3−2i32i32i−2i2i−2i−232323−2323−23−2323−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1314-44-444-4-4-2-44-444i−4i−4i4i−4i4i4i−4i0000-22-222-222-22-22-22-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1324-44-444-4-4-2-44-44−4i4i4i−4i4i−4i−4i4i0000-22-222-222-22-22-22-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1334-4-4-4-444440000004-4-440000004-4-44-4-440000000000004-44-4-44-4400000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1344-4-4-4-44444000000-444-40000004-4-44-4-44000000000000-44-444-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1354-4-4-4-4444-20000004-4-44000000-222-222-223−2323−23−2323−2323−232323−23-22-222-22-2−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1364-4-4-4-4444-20000004-4-44000000-222-222-2−2323−232323−2323−2323−23−2323-22-222-22-223−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1374-4-4-4-4444-2000000-444-4000000-222-222-223−2323−23−2323−232323−23−23232-22-2-22-2223−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1384-4-4-4-4444-2000000-444-4000000-222-222-2−2323−232323−2323−23−232323−232-22-2-22-22−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.