Finite Group Databasebeta

← Group #10702239

Character table — Group #10702239

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121266668888888812121212242424242424242424242424242424242244666688881212121224242424242424244444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i-1-111ii−i−i−i−iii11-1-1
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-21111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2111122221111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-2-2-2-22-2-2-222-2222222222222222-2-2-2-200000000-2-2-2-20000000000000000000000002-22-2000022-2-222-2-20000000000000000
χ222222222222-2-2-2-22-2-2-222-2222222222222222-2-2-2-200000000-2-2-2-2000000000000000000000000-22-220000-2-222-2-2220000000000000000
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χ262222222222-2-2-2-2-1-2-2-222-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3i3−i3−i32-22-2i3i3−i3−i3-1-111-1-1110000000000000000
χ2722222222-2-222-2-222-2-2-2-2222-2-2-2-2222-2-222-2-222-2-20000000022-2-200000000000000000000000000000000000000002-22-2000000000000
χ2822222222-2-222-2-222-2-2-2-2222-2-2-2-2222-2-222-2-222-2-20000000022-2-20000000000000000000000000000000000000000-22-22000000000000
χ2922222222-2-2-2-2222-222-2-2-222-2-2-2-2222-2-222-2-2-2-22200000000-2-2220000000000000000000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2222-222-2-2-222-2-2-2-2222-2-222-2-2-2-22200000000-2-222000000000000000000000000000000000000000000000000-22-220000
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χ352222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−30000−i3−i3i3i3−2i2i2i−2ii3i3−i3−i3ii−i−i−i−iii0000000000000000
χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−30000i3i3−i3−i32i−2i−2i2i−i3−i3i3i3−i−iiiii−i−i0000000000000000
χ372222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii0000000000000000
χ382222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i0000000000000000
χ392222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i0000000000000000
χ402222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii0000000000000000
χ412222-2-2-2-2-2-222-2-22-22222-222-2-2-2-22-2-222-2-22222-2-200000000-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-222-2-22-22222-222-2-2-2-22-2-222-2-22222-2-200000000-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-2-22222-2-222222-2-2-2-22-2-222-2-222-2-2220000000022-2-200000000000000000000000000000000000000002-2-22000000000000
χ442222-2-2-2-2-2-2-2-22222-2-222222-2-2-2-22-2-222-2-222-2-2220000000022-2-20000000000000000000000000000000000000000-222-2000000000000
χ4522-2-222-2-22-22-22-2222-22-2-2-2-222-2-222222-2-2-2-22-22-2000000002-22-200000000000000002-22-22-22-200002-22-2000000000000000000000000
χ4622-2-222-2-22-22-22-2222-22-2-2-2-222-2-222222-2-2-2-22-22-2000000002-22-20000000000000000-22-22-22-220000-22-22000000000000000000000000
χ4722-2-222-2-22-22-22-2-122-22-2-211-1-111-1-1-1-1-11111-11-1100000000-11-1133−3−333−3−333−3−333−3−32-22-2-11-110000-11-113−33−33−33−30000000000000000
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χ5022-2-222-2-22-22-22-2-122-22-2-211-1-111-1-1-1-1-11111-11-1100000000-11-11−3−333−3−333−3−333−3−333-22-221-11-100001-11-13−33−33−33−30000000000000000
χ5122-2-222-2-22-2-22-222-2-222-22-2-222-2-222222-2-2-2-2-22-222i2i−2i−2i2i2i−2i−2i-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5222-2-222-2-22-2-22-222-2-222-22-2-222-2-222222-2-2-2-2-22-22−2i−2i2i2i−2i−2i2i2i-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ5822-2-222-2-2-222-2-2222-22-22-2-2-2-2-222222-2-2-2-2222-2-22000000002-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
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χ6222-2-2-2-2222-22-22-22-2-22-222-2-222-2-22-2-2-2-222222-22-2-2-22222-2-2-22-22-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ6322-2-2-2-2222-22-22-2-1-2-22-22211-1-111-11111-1-1-1-1-11-1122-2-2-2-2221-11-1-1-11111-1-111-1-1-1-1110000−i3i3i3−i30000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i30000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.