Finite Group Databasebeta

← Group #10690927

Character table — Group #10690927

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111111112222222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444242424242424242448484848
order1222222222223444444444444666666666666666121212121212121212121212121212124444444444444444444444121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212888888882444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ61111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ71111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-111-1
χ81111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111-1-11
χ911111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-1-111
χ1211111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii11-1-1
χ1311111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii1-11-1
χ1411111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-11-11
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-11-11
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i1-11-1
χ17222222222222222222222-2-2-2-22222222222222222222222222222222-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
χ19222222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ20222222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111000000000000
χ21222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-200000000000000001111111111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ22222222222222-122222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-200000000000000001111111111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ23222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-222222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000
χ24222222222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-2-2-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-22222000000000000000011111111-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-22222000000000000000011111111-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ2722222222-2-2-2-222222-2-2-2-222222222-2-2-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2-2222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-222222222-2-222-2-20000000000000000-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-2-2-2-22200000000000000001111-1-1-1-11111-1-1-1-13333−3−3−3−3−3−3−3−333333333−3−3−3−3−3−3−3−33333000000000000
χ3022222222-2-2-2-2-12222-2-2-2-22222-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-111111111-2-2-2-22200000000000000001111-1-1-1-11111-1-1-1-1−3−3−3−333333333−3−3−3−3−3−3−3−333333333−3−3−3−3000000000000
χ3122222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1111111112222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ3222222222-2-2-2-2-12222-2-2-2-2-2-2-2-2-1-1-1-1111111-1-1-111-1-1-1-1-1-1-1-1111111112222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i000000000000
χ3322222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1111111-1-1-11111111111-1-1-1-1-1-1-1-1-2-222-2-200000000000000001111-1-1-1-1-1-1-1-111113333−3−3−3−3−3−3−3−33333−3−3−3−333333333−3−3−3−3000000000000
χ3422222222-2-2-2-2-1-2-2-2-222222222-1-1-1-1111111-1-1-11111111111-1-1-1-1-1-1-1-1-2-222-2-200000000000000001111-1-1-1-1-1-1-1-11111−3−3−3−333333333−3−3−3−33333−3−3−3−3−3−3−3−33333000000000000
χ3522222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1111111-1-1-11111111111-1-1-1-1-1-1-1-122-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i000000000000
χ3622222222-2-2-2-2-1-2-2-2-22222-2-2-2-2-1-1-1-1111111-1-1-11111111111-1-1-1-1-1-1-1-122-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ3722-22-22-2-20000200002i2i−2i−2i2i2i−2i−2i22-2-20000002-2-200000000002i2i2i2i−2i−2i−2i−2i002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00002i2i−2i−2i22-2-200001+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
χ3822-22-22-2-20000200002i2i−2i−2i2i2i−2i−2i22-2-20000002-2-200000000002i2i2i2i−2i−2i−2i−2i002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i2i−2i−2i22-2-20000−1−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
χ3922-22-22-2-20000200002i2i−2i−2i−2i−2i2i2i22-2-20000002-2-200000000002i2i2i2i−2i−2i−2i−2i00-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2i−2i2i2i-2-22200001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−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
χ4022-22-22-2-20000200002i2i−2i−2i−2i−2i2i2i22-2-20000002-2-200000000002i2i2i2i−2i−2i−2i−2i00-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i−2i2i2i-2-2220000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+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
χ4122-22-22-2-2000020000−2i−2i2i2i2i2i−2i−2i22-2-20000002-2-20000000000−2i−2i−2i−2i2i2i2i2i00-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i2i−2i−2i-2-22200001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+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
χ4222-22-22-2-2000020000−2i−2i2i2i2i2i−2i−2i22-2-20000002-2-20000000000−2i−2i−2i−2i2i2i2i2i00-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00002i2i−2i−2i-2-2220000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−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
χ4322-22-22-2-2000020000−2i−2i2i2i−2i−2i2i2i22-2-20000002-2-20000000000−2i−2i−2i−2i2i2i2i2i002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i−2i2i2i22-2-200001−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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χ1032-2-222-2-22-2-222-1000000002-2-22111111-1-111-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-2200002-2-222-2-22000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3-111-1-111-1-111-1-111-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ1042-2-222-2-22-2-222-1000000002-2-22111111-1-111-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3-220000-222-2-222-2000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i31-1-111-1-111-1-111-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
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χ1132-2-2-2-2222-22-2222-22-2-22-2200002-22-2-22-2-2-22-22-2222-22-22-22-2-22-22-22-2200000000000000000000000000000000000000000000000000000000000000000000002−2−222−2−220000
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χ1324-44-444-4-40000-200004i−4i−4i4i0000-222-22i3−2i32i3−2i3−2i32i322-2−2i32i3−2323−232323−2323−23−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1334-44-444-4-40000-20000−4i4i4i−4i0000-222-2−2i32i3−2i32i32i3−2i322-22i3−2i3−2323−232323−2323−232i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1344-44-444-4-40000-20000−4i4i4i−4i0000-222-22i3−2i32i3−2i3−2i32i322-2−2i32i323−2323−23−2323−23232i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1354-4-4-4-44444-44-4-24-44-44-44-40000-22-22-22-2-2-222-2222-22-22-22-22-22-22-22-220000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1364-4-4-4-44444-44-4-2-44-44-44-440000-22-22-22-2-2-222-22222-22-22-22-22-22-22-22-20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1374-4-4-4-4444-44-44-24-44-4-44-440000-22-222-2222-22-22-2-2-22-22-22-222-22-22-22-20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1384-4-4-4-4444-44-44-2-44-444-44-40000-22-222-2222-22-22-2-22-22-22-22-2-22-22-22-220000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.