Finite Group Databasebeta

← Group #10690852

Character table — Group #10690852

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138
size111111112222222222222222222222222222222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444242424242424242448484848
order1222222222223444444444444666666666666666121212121212121212121212121212124444448888888888888888121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424888888882244
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
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−i1-11-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii-11-11
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiii−i−i−i−i-11-11
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−iiiii1-11-1
χ911111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ1211111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ1311111111-1-1-1-11-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-111-1-111iiii−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−iii1-1-11
χ1411111111-1-1-1-11-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-111-1-111iiii−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-111-1
χ1511111111-1-1-1-11-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-111-1-111−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-111-1
χ1611111111-1-1-1-11-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-111-1-111−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−i1-1-11
χ172222222222222222-2-222222-2-22222222222222222222222222222222-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000
χ182222222222222-2-2-222-2-2-2-2-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000
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
χ21222222222222-1222-2-222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-200000000000000001111111111111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3000000000000
χ22222222222222-1222-2-222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-200000000000000001111111111111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3000000000000
χ23222222222222-1-2-2-222-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222000000000000000011111111-1-1-1-1-1-1-1-13333−3−3−3−33333−3−3−3−3−3−3−3−33333−3−3−3−33333000000000000
χ24222222222222-1-2-2-222-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-222000000000000000011111111-1-1-1-1-1-1-1-1−3−3−3−33333−3−3−3−333333333−3−3−3−33333−3−3−3−3000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-22i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111112222-2-2−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i-1-1-1-1-1-1-1-111111111iiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-22-2-22222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222220000000000000000-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-2222222-2222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-222222222-2-2-2-222-2-20000000000000000-2-2-2-222222222-2-2-2-200000000000000000000000000000000000000000000
χ2922222222-2-2-2-2-122222-2-2-2-2222-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-22222-2-2-2-22222-2-2-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111000000000000
χ3022222222-2-2-2-2-122222-2-2-2-2222-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-1-122-2-2-2-2-2-2-2-22222-2-2-2-22222-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000
χ3122222222-2-2-2-2-1222-2-2-2-2-2-22-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-1-1-2-2222200000000000000001111-1-1-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3000000000000
χ3222222222-2-2-2-2-1222-2-2-2-2-2-22-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-111111111-1-1-2-2222200000000000000001111-1-1-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3000000000000
χ3322222222-2-2-2-2-1-2-2-2222222-222-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-111-2-222-2-200000000000000001111-1-1-1-1-1-1-1-111113333−3−3−3−3−3−3−3−33333−3−3−3−333333333−3−3−3−3000000000000
χ3422222222-2-2-2-2-1-2-2-2222222-222-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-111-2-222-2-200000000000000001111-1-1-1-1-1-1-1-11111−3−3−3−333333333−3−3−3−33333−3−3−3−3−3−3−3−33333000000000000
χ3522222222-2-2-2-2-1-2-2-2-2-22222-2-2-2-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-11122-2-2222i2i2i2i−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
χ3622222222-2-2-2-2-1-2-2-2-2-22222-2-2-2-1-1-1-111111111-1-1-1111111-1-1-1-1-1-1-1-11122-2-222−2i−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
χ37222-22-2-2-2000020002-22i2i−2i−2i02-222-2-2000000002-2-20000002i2i2i2i−2i−2i−2i−2i00002i−2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i200002i2i−2i−2i22-2-2000022−2−222−2−2−i2−i2i2i2−i2−i2i2i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ38222-22-2-2-2000020002-22i2i−2i−2i02-222-2-2000000002-2-20000002i2i2i2i−2i−2i−2i−2i00002i−2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i200002i2i−2i−2i22-2-20000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ39222-22-2-2-2000020002-2−2i−2i2i2i02-222-2-2000000002-2-2000000−2i−2i−2i−2i2i2i2i2i0000−2i2i0022−2−2i2i2−i2−i222−2−2i2i2−i2−i20000−2i−2i2i2i22-2-2000022−2−222−2−2i2i2−i2−i2i2i2−i2−i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ40222-22-2-2-2000020002-2−2i−2i2i2i02-222-2-2000000002-2-2000000−2i−2i−2i−2i2i2i2i2i0000−2i2i00−2−222−i2−i2i2i2−2−222−i2−i2i2i20000−2i−2i2i2i22-2-20000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ41222-22-2-2-200002000-222i2i−2i−2i0-2222-2-2000000002-2-20000002i2i2i2i−2i−2i−2i−2i0000−2i2i00−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000−2i−2i2i2i-2-2220000−i2−i2i2i2−i2−i2i2i222−2−222−2−2i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ42222-22-2-2-200002000-222i2i−2i−2i0-2222-2-2000000002-2-20000002i2i2i2i−2i−2i−2i−2i0000−2i2i00i2i2−i2−i2−2−222−i2−i2i2i222−2−20000−2i−2i2i2i-2-2220000i2i2−i2−i2i2i2−i2−i2−2−222−2−222−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ43222-22-2-2-200002000-22−2i−2i2i2i0-2222-2-2000000002-2-2000000−2i−2i−2i−2i2i2i2i2i00002i−2i00−i2−i2i2i2−2−222i2i2−i2−i222−2−200002i2i−2i−2i-2-2220000−i2−i2i2i2−i2−i2i2i2−2−222−2−222i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ44222-22-2-2-200002000-22−2i−2i2i2i0-2222-2-2000000002-2-2000000−2i−2i−2i−2i2i2i2i2i00002i−2i00i2i2−i2−i222−2−2−i2−i2i2i2−2−22200002i2i−2i−2i-2-2220000i2i2−i2−i2i2i2−i2−i222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ45222-22-2-2-20000-10002-22i2i−2i−2i02-2-1-111−i3−i3−i3−i3i3i3i3i3-111333−3−3−3−i−i−i−iiiii3−3002i−2i0022−2−2−i2−i2i2i222−2−2−i2−i2i2i233−3−3−i−iii-1-111−i3−i3i3i3ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+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−ζ7000000000000
χ46222-22-2-2-20000-10002-22i2i−2i−2i02-2-1-111−i3−i3−i3−i3i3i3i3i3-111333−3−3−3−i−i−i−iiiii3−3002i−2i00−2−222i2i2−i2−i2−2−222i2i2−i2−i233−3−3−i−iii-1-111−i3−i3i3i3−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−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+ζ7000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.