Finite Group Databasebeta

← Group #10702689

Character table — Group #10702689

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121266668888888812121212242424242424242424242424242424242244666688881212121224242424242424248888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111
χ121111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111iiiiiiii−i−i−i−i−i−i−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1
χ131111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiiiii−i−iii−i−i-1-111-1-111
χ141111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii−i−iii−i−iii11-1-111-1-1
χ151111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-111-1-1-1-1111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111−i−i−i−i−i−i−i−iiiiiiiii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111
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
χ212222222222-2-2-2-22-2-222-2-2222222222222222-2-2-2-200000000-2-2-2-200000000000000002-22-222-2-2000022-2-2000000000000000000000000
χ222222222222-2-2-2-22-2-222-2-2222222222222222-2-2-2-200000000-2-2-2-20000000000000000-22-22-2-2220000-2-222000000000000000000000000
χ232222222222-2-2-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-2-1-1110000-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ242222222222-2-2-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2211-1-1000011-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-2-2-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-2-1-1110000-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-2-2-2-2-1-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2211-1-1000011-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-222-2-222-2-2-22-222-2-2-2-2222-2-222-2-222-2-20000000022-2-2000000000000000000000000000000000000000000002-22-200000000
χ2822222222-2-222-2-222-2-2-22-222-2-2-2-2222-2-222-2-222-2-20000000022-2-200000000000000000000000000000000000000000000-22-2200000000
χ2922222222-2-2-2-2222-22-2-2-2222-2-2-2-2222-2-222-2-2-2-22200000000-2-22200000000000000000000000000000000000000002-22-2000000000000
χ3022222222-2-2-2-2222-22-2-2-2222-2-2-2-2222-2-222-2-2-2-22200000000-2-2220000000000000000000000000000000000000000-22-22000000000000
χ312222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000002-2-2222-2-20000-2-222000000000000000000000000
χ322222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000-222-2-2-222000022-2-2000000000000000000000000
χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−3−3−3−3−333332-2-22-1-111000011-1-133−3−3−3−3330000000000000000
χ342222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-10000000011113333−3−3−3−3−3−3−3−33333-222-211-1-10000-1-111−3−33333−3−30000000000000000
χ352222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−32-2-22-1-111000011-1-1−3−33333−3−30000000000000000
χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1000000001111−3−3−3−333333333−3−3−3−3-222-211-1-10000-1-11133−3−3−3−3330000000000000000
χ372222-2-2-2-222-2-2-2-2-122-2-222-1-1-1-1-1-1-11111111111112i2i2i2i−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
χ382222-2-2-2-222-2-2-2-2-122-2-222-1-1-1-1-1-1-11111111111112i2i2i2i−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
χ392222-2-2-2-222-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111111111−2i−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
χ402222-2-2-2-222-2-2-2-2-122-2-222-1-1-1-1-1-1-1111111111111−2i−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
χ412222-2-2-2-2-2-222-2-22-2222-2222-2-2-2-22-2-222-2-22222-2-200000000-2-22200000000000000000000000000000000000000002i−2i−2i2i000000000000
χ422222-2-2-2-2-2-222-2-22-2222-2222-2-2-2-22-2-222-2-22222-2-200000000-2-2220000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ432222-2-2-2-2-2-2-2-22222-2222-222-2-2-2-22-2-222-2-222-2-2220000000022-2-2000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ442222-2-2-2-2-2-2-2-22222-2222-222-2-2-2-22-2-222-2-222-2-2220000000022-2-200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ452-2-2222-2-22-22-22-2222-22-2-2-2-222-2-2222-2-2-2-2222-22-2000000002-22-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-2222-2-22-22-22-2222-22-2-2-2-222-2-2222-2-2-2-2222-22-2000000002-22-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-2222-2-22-2-22-222-2-2-2222-2-222-2-2222-2-2-2-222-22-2200000000-22-220000000000000000000000000000000000000000000000002-22-20000
χ482-2-2222-2-22-2-22-222-2-2-2222-2-222-2-2222-2-2-2-222-22-2200000000-22-22000000000000000000000000000000000000000000000000-22-220000
χ492-2-2222-2-2-222-2-2222-22-2-22-2-2-2-22222222-2-2-2-22-2-222i2i−2i−2i2i2i−2i−2i2-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ502-2-2222-2-2-222-2-2222-22-2-22-2-2-2-22222222-2-2-2-22-2-22−2i−2i2i2i−2i−2i2i2i2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ512-2-2222-2-2-222-2-22-12-22-2-221111-1-1-1-1-1-1-11111-111-12i2i−2i−2i2i2i−2i−2i-111-1−i−iii−i−iii−i−iii−i−iii0000−i3i3−i3i30000−i3i3−i3i33−33−33−33−30000000000000000
χ522-2-2222-2-2-222-2-22-12-22-2-221111-1-1-1-1-1-1-11111-111-12i2i−2i−2i2i2i−2i−2i-111-1−i−iii−i−iii−i−iii−i−iii0000i3−i3i3−i30000i3−i3i3−i3−33−33−33−330000000000000000
χ532-2-2222-2-2-222-2-22-12-22-2-221111-1-1-1-1-1-1-11111-111-1−2i−2i2i2i−2i−2i2i2i-111-1ii−i−iii−i−iii−i−iii−i−i0000−i3i3−i3i30000−i3i3−i3i3−33−33−33−330000000000000000
χ542-2-2222-2-2-222-2-22-12-22-2-221111-1-1-1-1-1-1-11111-111-1−2i−2i2i2i−2i−2i2i2i-111-1ii−i−iii−i−iii−i−iii−i−i0000i3−i3i3−i30000i3−i3i3−i33−33−33−33−30000000000000000
χ552-2-2222-2-2-22-222-22-222-22-2-2-2-2-22222222-2-2-2-2-222-200000000-222-20000000000000000000000002i−2i2i−2i00002i−2i−2i2i2i−2i−2i2i0000000000000000
χ562-2-2222-2-2-22-222-22-222-22-2-2-2-2-22222222-2-2-2-2-222-200000000-222-2000000000000000000000000−2i2i−2i2i0000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ572-2-2222-2-2-22-222-2-1-222-22-21111-1-1-1-1-1-1-111111-1-11000000001-1-1133−3−3−3−33333−3−3−3−3330000−i3i3i3−i32i−2i2i−2i−i3i3i3−i3−iii−i−iii−i0000000000000000
χ582-2-2222-2-2-22-222-2-1-222-22-21111-1-1-1-1-1-1-111111-1-11000000001-1-1133−3−3−3−33333−3−3−3−3330000i3−i3−i3i3−2i2i−2i2ii3−i3−i3i3i−i−iii−i−ii0000000000000000
χ592-2-2222-2-2-22-222-2-1-222-22-21111-1-1-1-1-1-1-111111-1-11000000001-1-11−3−33333−3−3−3−33333−3−30000−i3i3i3−i3−2i2i−2i2i−i3i3i3−i3i−i−iii−i−ii0000000000000000
χ602-2-2222-2-2-22-222-2-1-222-22-21111-1-1-1-1-1-1-111111-1-11000000001-1-11−3−33333−3−3−3−33333−3−30000i3−i3−i3i32i−2i2i−2ii3−i3−i3i3−iii−i−iii−i0000000000000000
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χ622-2-22-2-2222-22-22-22-2-22-222-2-222-2-22-2-22222-2-22-22-200000000-22-22000000000000000000000000000000000000000000000000-222-20000
χ632-2-22-2-2222-2-22-222222-2-2-2-2-222-2-22-2-22222-2-2-22-22000000002-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ642-2-22-2-2222-2-22-222222-2-2-2-2-222-2-22-2-22222-2-2-22-22000000002-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ652-2-22-2-222-222-2-222-22-222-2-2-2-2-2222-2-2-2-222222-2-2200000000-222-20000000000000000000000002-2-2200002-2-22-222-20000000000000000
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χ712-2-22-2-222-22-222-222-2-22-22-2-2-2-2222-2-2-2-22222-222-222-2-2-2-2222-2-2222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ722-2-22-2-222-22-222-222-2-22-22-2-2-2-2222-2-2-2-22222-222-2-2-22222-2-22-2-22-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.