Finite Group Databasebeta

← Group #10702096

Character table — Group #10702096

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121266668888888812121212242424242424242424242424242424242244666688881212121224242424242424242244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111
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χ101-1-1111-1-1111-1-1-1111-1-11-111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-111-1-1ii−i−i11-1-1iiii−i−i−i−i-11−i−iii-11−i−iii-1-111
χ111-1-1111-1-1111-1-1-1111-1-11-111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11-1-111−i−iii-1-111−i−i−i−iiiii1-1−i−iii1-1ii−i−i-1-111
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χ131-1-1111-1-1111-1-1-1111-1-11-111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii1-1−i−iii1-1−i−iii11-1-1
χ141-1-1111-1-1111-1-1-1111-1-11-111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-111-1-1−i−iii11-1-1−i−i−i−iiiii-11ii−i−i-11ii−i−i-1-111
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χ161-1-1111-1-1111-1-1-1111-1-11-111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11-1-111ii−i−i-1-111iiii−i−i−i−i-11−i−iii-11ii−i−i11-1-1
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
χ21222222222-2-22-2-222-2-22-2-2222222222222222-2-2-2-200000000-2-2-2-20000000000000000000000002-22-2000022-2-222-2-20000000000000000
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χ26222222222-2-22-2-2-12-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111000000001111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i30000i3−i3i3−i32-22-2i3−i3i3−i3-1-111-1-1110000000000000000
χ2722222222-22-2-22-22-22-2-2-22-2-222-2-2222-2-222-2-22-22-2000000002-22-20000000000000000000000000000000000000000000000002-22-20000
χ2822222222-22-2-22-22-22-2-2-22-2-222-2-2222-2-222-2-22-22-2000000002-22-2000000000000000000000000000000000000000000000000-22-220000
χ2922222222-2-22-2-222-2-22-22-2-2-222-2-2222-2-222-2-2-22-2200000000-22-2200000000000000000000000000000000000000000000000000002-22-2
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χ332222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-12i2i−2i−2i2i2i−2i−2i1111−i−iii−i−iii−i−iii−i−iii0000−i3i3−i3i30000i3−i3i3−i33−33−33−33−30000000000000000
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χ362222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1−2i−2i2i2i−2i−2i2i2i1111ii−i−iii−i−iii−i−iii−i−i0000i3−i3i3−i30000−i3i3−i3i33−33−33−33−30000000000000000
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χ382222-2-2-2-22-2-22-2-22-222-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-222-2-2-2-200002222000000000000000000000000
χ392222-2-2-2-22-2-22-2-2-1-222-222-1-1-1-1-1-1-111111111111100000000-1-1-1-133−3−3−3−33333−3−3−3−33322-2-2-1-1-1-1000011113−3−333−3−330000000000000000
χ402222-2-2-2-22-2-22-2-2-1-222-222-1-1-1-1-1-1-111111111111100000000-1-1-1-133−3−3−3−33333−3−3−3−333-2-22211110000-1-1-1-1−333−3−333−30000000000000000
χ412222-2-2-2-22-2-22-2-2-1-222-222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−33333−3−3−3−33333−3−322-2-2-1-1-1-100001111−333−3−333−30000000000000000
χ422222-2-2-2-22-2-22-2-2-1-222-222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−3−33333−3−3−3−33333−3−3-2-22211110000-1-1-1-13−3−333−3−330000000000000000
χ432222-2-2-2-2-22-2-22-222-2222-2-2-222-2-22-2-222-2-2222-22-200000000-22-220000000000000000000000000000000000000000220000-2-200000000
χ442222-2-2-2-2-22-2-22-222-2222-2-2-222-2-22-2-222-2-2222-22-200000000-22-220000000000000000000000000000000000000000-2-200002200000000
χ452222-2-2-2-2-2-22-2-22222-22-22-2-222-2-22-2-222-2-222-22-22000000002-22-20000000000000000000000000000000000000000002-22-20000000000
χ462222-2-2-2-2-2-22-2-22222-22-22-2-222-2-22-2-222-2-222-22-22000000002-22-2000000000000000000000000000000000000000000-22-220000000000
χ472-2-2222-2-2222-2-2-2-122-2-22-2-1-11111-1-1-1-1-11111-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii2-22-2-1-1112i2i−2i−2i-1-111−i−i−i−iiiii0000000000000000
χ482-2-2222-2-2222-2-2-2-122-2-22-2-1-11111-1-1-1-1-11111-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-22-2211-1-1−2i−2i2i2i11-1-1iiii−i−i−i−i0000000000000000
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χ502-2-2222-2-2222-2-2-2-122-2-22-2-1-11111-1-1-1-1-11111-1-111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-22-2211-1-12i2i−2i−2i11-1-1−i−i−i−iiiii0000000000000000
χ512-2-2222-2-22-2-2-22222-22-2-2222-2-2-2-222222-2-2-2-2-2-22200000000-2-2220000000000000000000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000
χ522-2-2222-2-22-2-2-22222-22-2-2222-2-2-2-222222-2-2-2-2-2-22200000000-2-222000000000000000000000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ532-2-2222-2-22-2-2-222-12-22-2-22-1-11111-1-1-1-1-1111111-1-10000000011-1-13333−3−3−3−3−3−3−3−333330000−i3i3i3−i32i−2i−2i2i−i3i3i3−i3−i−iiiii−i−i0000000000000000
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χ552-2-2222-2-22-2-2-222-12-22-2-22-1-11111-1-1-1-1-1111111-1-10000000011-1-1−3−3−3−333333333−3−3−3−30000−i3i3i3−i3−2i2i2i−2i−i3i3i3−i3ii−i−i−i−iii0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.