Finite Group Databasebeta

← Group #10690837

Character table — Group #10690837

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111111112222222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444242424242424242448484848
order12222222344444444444444446666666121212121212121212121212121212121212121212121212224444666688888888888888881212121212121212121212122424242424242424242424242424242424242424242424242424242424242424888888884444
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
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−i1-11-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-11-11
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i-11-11
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−iiiii1-11-1
χ9111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ11111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ12111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ13111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiii−i−i−i−iii1-1-11
χ14111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−iiiii−i−i-111-1
χ15111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iii−i−i−i−iii-111-1
χ16111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222-2-2222222-2-22222222222222222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222222-2-222-2-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000000000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2-2-222-2-22222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-2-22222220000000000000000-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-2222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-222220000000000000000-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
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
χ2322222222-1222222-2-2222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211110000000000000000111111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ2422222222-1222222-2-2222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211110000000000000000111111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ2522222222-12222-2-222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222111100000000000000001111-1-1-1-1-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−33333000000000000
χ2622222222-12222-2-222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222111100000000000000001111-1-1-1-1-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−3000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-2-1-1-1-12i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-2-1-1-1-1−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i000000000000
χ2922222222-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-2-222-2-211112222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ3022222222-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-2-222-2-21111-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ3122222222-1-2-2-2-222-2-2-2-2-2-222-2-2-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-122-2-222-1-1-1-1000000000000000011111111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ3222222222-1-2-2-2-222-2-2-2-2-2-222-2-2-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-122-2-222-1-1-1-1000000000000000011111111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ3322222222-1-2-2-2-2-2-2222222-2-222-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111122-2-2-2-2-1-1-1-100000000000000001111-1-1-1-111113333−3−3−3−3−3−3−3−33333−3−3−3−333333333−3−3−3−3000000000000
χ3422222222-1-2-2-2-2-2-2222222-2-222-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111122-2-2-2-2-1-1-1-100000000000000001111-1-1-1-11111−3−3−3−333333333−3−3−3−33333−3−3−3−3−3−3−3−33333000000000000
χ3522222222-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-2-2222211112i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i000000000000
χ3622222222-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-2-222221111−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii000000000000
χ37222-2-2-2-2222i2i−2i−2i002-20000002-222-2-22-2-22i2i2i2i−2i−2i−2i−2i000000000000000000002i−2i000022−2−2−i2−i2i2i222−2−2−i2−i2i2i2000022-2-22i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ38222-2-2-2-2222i2i−2i−2i002-20000002-222-2-22-2-22i2i2i2i−2i−2i−2i−2i000000000000000000002i−2i0000−2−222i2i2−i2−i2−2−222i2i2−i2−i2000022-2-22i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ39222-2-2-2-2222i2i−2i−2i00-22000000-2222-2-22-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000−2i2i0000−i2−i2i2i2−2−222i2i2−i2−i222−2−20000-2-222−2i−2i2i2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ40222-2-2-2-2222i2i−2i−2i00-22000000-2222-2-22-2-22i2i2i2i−2i−2i−2i−2i00000000000000000000−2i2i0000i2i2−i2−i222−2−2−i2−i2i2i2−2−2220000-2-222−2i−2i2i2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ41222-2-2-2-222−2i−2i2i2i002-20000002-222-2-22-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000−2i2i000022−2−2i2i2−i2−i222−2−2i2i2−i2−i2000022-2-2−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ42222-2-2-2-222−2i−2i2i2i002-20000002-222-2-22-2-2−2i−2i−2i−2i2i2i2i2i00000000000000000000−2i2i0000−2−222−i2−i2i2i2−2−222−i2−i2i2i2000022-2-2−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ43222-2-2-2-222−2i−2i2i2i00-22000000-2222-2-22-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000002i−2i0000−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000-2-2222i2i−2i−2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ44222-2-2-2-222−2i−2i2i2i00-22000000-2222-2-22-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000002i−2i0000i2i2−i2−i2−2−222−i2−i2i2i222−2−20000-2-2222i2i−2i−2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ45222-2-2-2-22-12i2i−2i−2i002-20000002-2-1-111-111−i−i−i−iiiii33−3−3−i3−i3−i3−i3i3i3i3i333−3−300002i−2i−i3−i3i3i322−2−2−i2−i2i2i222−2−2−i2−i2i2i233−3−3-1-111−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23000000000000
χ46222-2-2-2-22-12i2i−2i−2i002-20000002-2-1-111-111−i−i−i−iiiii33−3−3−i3−i3−i3−i3i3i3i3i333−3−300002i−2i−i3−i3i3i3−2−222i2i2−i2−i2−2−222i2i2−i2−i233−3−3-1-111−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23000000000000
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χ1344-44-4-444-4400000000−4i4i4i−4i0000-444-4-4-44000000000000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1354-44-4-444-4-2000000004i−4i−4i4i00002-2-2222-2−2i32i32i3−2i3−2i32i32i3−2i3−232323−23−2i2i2i−2i−2i2i2i−2i23−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1364-44-4-444-4-2000000004i−4i−4i4i00002-2-2222-22i3−2i3−2i32i32i3−2i3−2i32i323−23−2323−2i2i2i−2i−2i2i2i−2i−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1374-44-4-444-4-200000000−4i4i4i−4i00002-2-2222-2−2i32i32i3−2i3−2i32i32i3−2i323−23−23232i−2i−2i2i2i−2i−2i2i−232323−230000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1384-44-4-444-4-200000000−4i4i4i−4i00002-2-2222-22i3−2i3−2i32i32i3−2i3−2i32i3−232323−232i−2i−2i2i2i−2i−2i2i23−23−23230000000000000000000000000000000000000000000000000000000000000000000000000000000000

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