Finite Group Databasebeta

← Group #10693783

Character table — Group #10693783

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111111111111111122222222222222222222222244444444444444444444444444444444888888888888888888888888121212121212121212121212121212122424242424242424
order122222224444444434444444466666661212121212121212888888881212121212121212242424242424242424242424242424248888888824242424242424242424242424242424444444448888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ1722222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000022-2-222-2-20000000000000000
χ1822222222222222222-2-2-2-2-2-2-2-222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-222-2-2220000000000000000
χ192222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ202222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ212222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ2322222222-2-2-2-2-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000000000000000000000000000000022-2-2-2-2220000000000000000
χ2422222222-2-2-2-2-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000000000000000-2-22222-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-1111111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-22222-1-11111-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ292222-2-2-2-222-2-222-2-222222-2-2-2-2-2-2-2-22222222-2-2-2-2000000002222-2-2-2-2000000000000000000000000000000000000000000000000000000002-22-20000
χ302222-2-2-2-222-2-222-2-222222-2-2-2-2-2-2-2-22222222-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000000000000000000000000000-22-220000
χ312222-2-2-2-222-2-222-2-22-2-2-2-22222-2-2-2-22222222-2-2-2-200000000-2-2-2-2222200000000000000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ322222-2-2-2-222-2-222-2-22-2-2-2-22222-2-2-2-22222222-2-2-2-200000000-2-2-2-222220000000000000000−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ332222-2-2-2-222-2-222-2-2-1-2-2-2-222221111-1-1-1-1-1-1-11111000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32i−2i2i−2i0000−i−iii−i−iii33−3−333−3−3000000000000000000000000
χ342222-2-2-2-222-2-222-2-2-1-2-2-2-222221111-1-1-1-1-1-1-11111000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i0000ii−i−iii−i−i−3−333−3−333000000000000000000000000
χ352222-2-2-2-222-2-222-2-2-1-2-2-2-222221111-1-1-1-1-1-1-11111000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32i−2i2i−2i0000−i−iii−i−iii−3−333−3−333000000000000000000000000
χ362222-2-2-2-222-2-222-2-2-1-2-2-2-222221111-1-1-1-1-1-1-11111000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i0000ii−i−iii−i−i33−3−333−3−3000000000000000000000000
χ372222-2-2-2-2-2-222-2-222222-2-222-2-2-2-2-2-2222-2-2-2-222220000000022-2-222-2-2000000000000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-222-2-222222-2-222-2-2-2-2-2-2222-2-2-2-222220000000022-2-222-2-200000000000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-222-2-2222-2-222-2-222-2-2-2-2222-2-2-2-2222200000000-2-222-2-22200000000000000002-2-22000022-2-2-2-22200000000000000000000000000000000
χ402222-2-2-2-2-2-222-2-2222-2-222-2-222-2-2-2-2222-2-2-2-2222200000000-2-222-2-2220000000000000000-222-20000-2-22222-2-200000000000000000000000000000000
χ412222-2-2-2-2-2-222-2-222-1-2-222-2-2221111-1-1-11111-1-1-1-10000000011-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ422222-2-2-2-2-2-222-2-222-1-2-222-2-2221111-1-1-11111-1-1-1-10000000011-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ432222-2-2-2-2-2-222-2-222-1-2-222-2-2221111-1-1-11111-1-1-1-10000000011-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000000000
χ442222-2-2-2-2-2-222-2-222-1-2-222-2-2221111-1-1-11111-1-1-1-10000000011-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-222-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000000000
χ4522-2-222-2-222-2-2-2-22220000000022-2-22-2-222-2-222-2-2−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000002-2002-2−i2−i2i2i2−i2−i2i2i200000000
χ4622-2-222-2-222-2-2-2-22220000000022-2-22-2-222-2-222-2-2−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000-2200-22i2i2−i2−i2i2i2−i2−i200000000
χ4722-2-222-2-222-2-2-2-22220000000022-2-22-2-222-2-222-2-2i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000002-2002-2i2i2−i2−i2i2i2−i2−i200000000
χ4822-2-222-2-222-2-2-2-22220000000022-2-22-2-222-2-222-2-2i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000-2200-22−i2−i2i2i2−i2−i2i2i200000000
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χ5022-2-222-2-2-2-22222-2-220000000022-2-22-2-2-2-222-2-222−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000-22002-2i2i2−i2−i2−i2−i2i2i200000000
χ5122-2-222-2-2-2-22222-2-220000000022-2-22-2-2-2-222-2-222i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000002-200-22i2i2−i2−i2−i2−i2i2i200000000
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χ602-22-22-22-2−2i2i−2i2i−2i2i−2i2i2000000002-22-2-22-2−2i2i−2i2i−2i2i−2i2i−22−22−i2i2−i2i200000000−22−22−22−22−i2i2−i2i2−i2i2−i2i2000000000000000000000000-22002i−2i002−22−2i2−i2i2−i200000000
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χ622-2-222-2-222i−2i−2i2i−2i2i2i−2i22-22i−2i2i−2i2-22-2-22-2-222i−2i−2i2i2i−2i−2i2i000000002-22i−2i2i−2i2-2000000000000000000000000000000000000000000000000−2i2i2i−2i-222-200000000
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χ642-2-222-2-222i−2i−2i2i−2i2i2i−2i2-22−2i2i−2i2i-222-2-22-2-222i−2i−2i2i2i−2i−2i2i−2i2i2i−2i-222-2-22−2i2i−2i2i-22−2i2i2i−2i−2i2i2i−2i-222-2-222-2000000000000000000000000000000000000000000000000
χ652-2-222-2-222i−2i−2i2i−2i2i2i−2i-1-22−2i2i−2i2i-22-111-111-1−iii−i−iii−i2i−2i−2i2i2-2-221-1i−ii−i1-1−iii−i−iii−i-111-1-111-100000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.