Finite Group Databasebeta

← Group #10694404

Character table — Group #10694404

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111111112222222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444242424242424242448484848
order122222223444444446666666888888881212121212121212242424242424242424242424242424244444444444888888888888121212121212121212121212121212121212121212121212242424242424242424242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ91-1-11-1-1111-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iii−i−i1-11-1
χ101-1-11-1-1111-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-111-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−iii-11-11
χ111-1-11-1-1111-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iii−i−i-11-11
χ121-1-11-1-1111-11111-1-1-1-1-1111-1-11111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-111-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−iii1-11-1
χ131-1-11-1-1111-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i1-1-1-111−i−i−i−iiiii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii1-1-11
χ141-1-11-1-1111-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i1-1-1-111−i−i−i−iiiii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-111-1
χ151-1-11-1-1111-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii1-1-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-111-1
χ161-1-11-1-1111-11111-1-1-1-1-1111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii1-1-1-111iiii−i−i−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i1-1-11
χ172222222222-2-2222-2-222222222222222222222222222222222222222200000000-2-2-2-2-2-200000000-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222-2-2222-2-22222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222200000000-2-2-2-2-2-2-2-20000000000000000222222220000000000000000000000000000
χ19222222222-222-2-2-222222222200000000-2-2-2-2-2-2-2-2000000000000000022-2-222-2-2-2-200000000000022-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222-222-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000000000-2-222-2-222-2-200000000000022-2-222-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-20000000000000000000000002200002i2i−2i−2i2i2i−2i−2i-2-222-2-2220000000000000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-2222222200000000-2-2-2-2-2-2-2-2000000000000000000000000220000−2i−2i2i2i−2i−2i2i2i-2-222-2-222000000000000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111000000000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2-2-2-2-222-2-2-2-222222222-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2722222222-12-2-2222-2-2-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-20000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i311111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ2822222222-12-2-2222-2-2-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2-2-20000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i311111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ2922222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-2-222220000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ3022222222-12-2-2222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000-2-222220000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ3122222222-1-222-2-2-222-1-1-1-1-1-1-100000000111111113333−3−3−3−33333−3−3−3−322-2-222-2-2-2-2000000000000-1-111-1-111-1-1-1-11111-1-1-1-1111133−3−333−3−333−3−3−3−33333−3−3−3−333000000000000
χ3222222222-1-222-2-2-222-1-1-1-1-1-1-100000000111111113333−3−3−3−33333−3−3−3−3-2-222-2-222-2-2000000000000-1-111-1-1111111-1-1-1-11111-1-1-1-133−3−333−3−3−3−33333−3−3−3−33333−3−3000000000000
χ3322222222-1-222-2-2-222-1-1-1-1-1-1-10000000011111111−3−3−3−33333−3−3−3−3333322-2-222-2-2-2-2000000000000-1-111-1-111-1-1-1-11111-1-1-1-11111−3−333−3−333−3−33333−3−3−3−33333−3−3000000000000
χ3422222222-1-222-2-2-222-1-1-1-1-1-1-10000000011111111−3−3−3−33333−3−3−3−33333-2-222-2-222-2-2000000000000-1-111-1-1111111-1-1-1-11111-1-1-1-1−3−333−3−33333−3−3−3−33333−3−3−3−333000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-100000000111111113333−3−3−3−33333−3−3−3−3000000002200002i2i−2i−2i2i2i−2i−2i11-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−3−333−3−333−i−i−i−iiiii−i−i−i−iiiii000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-100000000111111113333−3−3−3−33333−3−3−3−300000000220000−2i−2i2i2i−2i−2i2i2i11-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−3−333−3−333iiii−i−i−i−iiiii−i−i−i−i000000000000
χ3722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000000011111111−3−3−3−33333−3−3−3−33333000000002200002i2i−2i−2i2i2i−2i−2i11-1-111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i333−3−333−3−3−i−i−i−iiiii−i−i−i−iiiii000000000000
χ3822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-10000000011111111−3−3−3−33333−3−3−3−3333300000000220000−2i−2i2i2i−2i−2i2i2i11-1-111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i333−3−333−3−3iiii−i−i−i−iiiii−i−i−i−i000000000000
χ392222-2-2-2-222002-2-200222-2-2-2-222-2-222-2-22222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000000000000000000000000000000000000000000000000002−22−22−22−20000
χ402222-2-2-2-222002-2-200222-2-2-2-222-2-222-2-22222-2-2-2-222-2-222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000000000000000000000−22−22−22−220000
χ412222-2-2-2-222002-2-200222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000000000000000002−22−2−22−220000
χ422222-2-2-2-222002-2-200222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000000000000000000000000000000000000000000000000000000000−22−222−22−20000
χ4322-2-22-22-2202-20002-22-2-22-22-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i00−i2i2−i2i22−22−22−22−22-2002-20000002i−2i2i−2i00002i−2i2i−2i−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−2000000000000
χ4422-2-22-22-2202-20002-22-2-22-22-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i00−i2i2−i2i2−22−22−22−222-2002-2000000−2i2i−2i2i0000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22−22−22−22−22000000000000
χ4522-2-22-22-2202-20002-22-2-22-22-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i00i2−i2i2−i2−22−22−22−222-2002-20000002i−2i2i−2i00002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−22000000000000
χ4622-2-22-22-2202-20002-22-2-22-22-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i00i2−i2i2−i22−22−22−22−22-2002-2000000−2i2i−2i2i0000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−2000000000000
χ4722-2-22-22-220-22000-222-2-22-22-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22-2002-20000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2-2200-22002-22-200002-22-20000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4822-2-22-22-220-22000-222-2-22-22-2−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2-2200-220000i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2-2200-2200-22-220000-22-220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4922-2-22-22-220-22000-222-2-22-22-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22-2002-20000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2-2200-22002-22-200002-22-20000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ5022-2-22-22-220-22000-222-2-22-22-2i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2-2200-220000−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2-2200-2200-22-220000-22-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
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χ12244-4-4-44-444000000004-4-4-44-44−2i22i22i2−2i2−2i22i22i2−2i200000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12344-4-4-44-444000000004-4-4-44-442i2−2i2−2i22i22i2−2i2−2i22i2000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12444-4-4-44-44-200000000-2222-22-2−2i22i22i2−2i2−2i22i22i2−2i223−2323−23−2323−23232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12544-4-4-44-44-200000000-2222-22-2−2i22i22i2−2i2−2i22i22i2−2i2−2323−232323−2323−232ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1294-44-44-4-44400000000-44-4-444-42i2−2i2−2i22i2−2i22i22i2−2i2000000002i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1304-44-44-4-44-2000000002-222-2-22−2i22i22i2−2i22i2−2i2−2i22i223−23−232323−23−23232ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1314-44-44-4-44-2000000002-222-2-22−2i22i22i2−2i22i2−2i2−2i22i2−232323−23−232323−232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1334-44-44-4-44-2000000002-222-2-222i2−2i2−2i22i2−2i22i22i2−2i2−232323−23−232323−23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1384-4-4444-4-4-2-4004-440022-222-2-2-4-44444-4-422-2-222-2-222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000000000000000000000000000000000

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