Finite Group Databasebeta

← Group #13167433

Character table — Group #13167433

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122224444444488888888181818181818181818181818181818181818363636363636363636363636111122224444444488888888181818181818181818181818181818181818363636363636363636363636
order1244361212336612121212336612121212244444661212121212121212121224668812122424242422446612126666121212126666121212122444446612121212121212121212246688121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
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χ611-1-111-1-11111-1-1-1-11111-1-1-1-1-11ii−i−i-1-111iiii−i−i−i−i-11-1-1−ii11−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1-11ii−i−i-1-111iiii−i−i−i−i-11-1-1−ii11−i−iii
χ711-1-111-1-11111-1-1-1-11111-1-1-1-1-11−i−iii-1-111−i−i−i−iiiii1-111−ii-1-1−i−iii11-1-111-1-11111-1-1-1-11111-1-1-1-1-11−i−iii-1-111−i−i−i−iiiii1-111−ii-1-1−i−iii
χ811-1-111-1-11111-1-1-1-11111-1-1-1-1-11−i−iii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−i11-1-111-1-11111-1-1-1-11111-1-1-1-1-11−i−iii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−i
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χ112222-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111110000000000002222-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-111111111000000000000
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χ212-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+i−i3i33−3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ140000000000002-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+i−i3i33−3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ222-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+ii3−i3−33−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ220000000000002-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+ii3−i3−33−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ232-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−i−i3i33−3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ140000000000002-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−i−i3i33−3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ242-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−ii3−i3−33ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ220000000000002-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−ii3−i3−33ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ252-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000002-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
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χ282-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i001−i−1+i1+i−1−ii3−i33−3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ220000000000002-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i001−i−1+i1+i−1−ii3−i33−3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ292-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+i−i3i3−33ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ140000000000002-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+i−i3i3−33ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ302-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+ii3−i33−3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ220000000000002-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+ii3−i33−3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ31444444441-21-2-2-2111-21-21-21-200000000000000000000002200-1-1-1-1444444441-21-2-2-2111-21-21-21-200000000000000000000002200-1-1-1-1
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χ3344444444-21-2111-2-2-21-21-21-2100000000000000000022-1-100-1-1000044444444-21-2111-2-2-21-21-21-2100000000000000000022-1-100-1-10000
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χ5811111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1-1
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χ6211-1-111-1-11111-1-1-1-11111-1-1-1-1-11−i−iii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−i-1-111-1-111-1-1-1-11111-1-1-1-111111-1ii−i−i11-1-1iiii−i−i−i−i1-111−ii-1-1−i−iii
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χ642222-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-21111-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2111111111111000000000000
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χ662222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-20000111133−3−333−3−3000000000000-2-2-2-21111-2-2-2-2-2-2-2-211111111220000-1-1-1-1−3−333−3−333000000000000
χ672222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-200001111−3−333−3−333000000000000-2-2-2-21111-2-2-2-2-2-2-2-211111111220000-1-1-1-133−3−333−3−3000000000000
χ6822-2-222-2-22222-2-2-2-22222-2-2-2-22-2000022-2-200000000000000000000-2-222-2-222-2-2-2-22222-2-2-2-22222-220000-2-22200000000000000000000
χ6922-2-2-1-1112222-2-2-2-2-1-1-1-111112-20000-1-111−i3−i3i3i3i3i3−i3−i3000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-1-22000011-1-1i3i3−i3−i3−i3−i3i3i3000000000000
χ7022-2-2-1-1112222-2-2-2-2-1-1-1-111112-20000-1-111i3i3−i3−i3−i3−i3i3i3000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-1-22000011-1-1−i3−i3i3i3i3i3−i3−i3000000000000
χ7122-2-2-1-1112222-2-2-2-2-1-1-1-11111-222i2i−2i−2i11-1-1−i−i−i−iiiii000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-12-2−2i−2i2i2i-1-111iiii−i−i−i−i000000000000
χ7222-2-2-1-1112222-2-2-2-2-1-1-1-11111-22−2i−2i2i2i11-1-1iiii−i−i−i−i000000000000-2-22211-1-1-2-2-2-222221111-1-1-1-12-22i2i−2i−2i-1-111−i−i−i−iiiii000000000000
χ732-22i−2i2-22i−2i22-2-22i−2i2i−2i22-2-22i2i−2i−2i001+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000-22−2i2i-22−2i2i-2-222−2i2i−2i2i-2-222−2i−2i2i2i00−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ742-22i−2i2-22i−2i22-2-22i−2i2i−2i22-2-22i2i−2i−2i00−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000-22−2i2i-22−2i2i-2-222−2i2i−2i2i-2-222−2i−2i2i2i001+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ752-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+i−i3i33−3−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000-22−2i2i1-1i−i-2-222−2i2i−2i2i11-1-1ii−i−i00−1−i1+i−1+i1−ii3−i3−33ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ762-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii001+i−1−i1−i−1+ii3−i3−33−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000-22−2i2i1-1i−i-2-222−2i2i−2i2i11-1-1ii−i−i00−1−i1+i−1+i1−i−i3i33−3ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ772-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−i−i3i33−3ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000-22−2i2i1-1i−i-2-222−2i2i−2i2i11-1-1ii−i−i001+i−1−i1−i−1+ii3−i3−33−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ782-22i−2i-11−ii22-2-22i−2i2i−2i-1-111−i−iii00−1−i1+i−1+i1−ii3−i3−33ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000-22−2i2i1-1i−i-2-222−2i2i−2i2i11-1-1ii−i−i001+i−1−i1−i−1+i−i3i33−3−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ792-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000-222i−2i-222i−2i-2-2222i−2i2i−2i-2-2222i2i−2i−2i00−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ802-2−2i2i2-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i−2i2i2i00−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000-222i−2i-222i−2i-2-2222i−2i2i−2i-2-2222i2i−2i−2i001−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ812-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i001−i−1+i1+i−1−i−i3i3−33−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000-222i−2i1-1−ii-2-2222i−2i2i−2i11-1-1−i−iii00−1+i1−i−1−i1+ii3−i33−3ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ822-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i001−i−1+i1+i−1−ii3−i33−3−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000-222i−2i1-1−ii-2-2222i−2i2i−2i11-1-1−i−iii00−1+i1−i−1−i1+i−i3i3−33ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ832-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+i−i3i3−33ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000-222i−2i1-1−ii-2-2222i−2i2i−2i11-1-1−i−iii001−i−1+i1+i−1−ii3−i33−3−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ842-2−2i2i-11i−i22-2-2−2i2i−2i2i-1-111ii−i−i00−1+i1−i−1−i1+ii3−i33−3ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000-222i−2i1-1−ii-2-2222i−2i2i−2i11-1-1−i−iii001−i−1+i1+i−1−i−i3i3−33−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ85444444441-21-2-2-2111-21-21-21-200000000000000000000002200-1-1-1-1-4-4-4-4-4-4-4-4-12-1222-1-1-12-12-12-120000000000000000000000-2-2001111
χ86444444441-21-2-2-2111-21-21-21-20000000000000000000000-2-2001111-4-4-4-4-4-4-4-4-12-1222-1-1-12-12-12-1200000000000000000000002200-1-1-1-1
χ8744444444-21-2111-2-2-21-21-21-2100000000000000000022-1-100-1-10000-4-4-4-4-4-4-4-42-12-1-1-1222-12-12-12-1000000000000000000-2-21100110000
χ8844444444-21-2111-2-2-21-21-21-21000000000000000000-2-21100110000-4-4-4-4-4-4-4-42-12-1-1-1222-12-12-12-100000000000000000022-1-100-1-10000
χ8944-4-444-4-41-21-222-1-11-21-2-12-1200000000000000000000002i−2i00−i−iii-4-444-4-444-12-12-2-211-12-121-21-20000000000000000000000−2i2i00ii−i−i
χ9044-4-444-4-41-21-222-1-11-21-2-12-120000000000000000000000−2i2i00ii−i−i-4-444-4-444-12-12-2-211-12-121-21-200000000000000000000002i−2i00−i−iii
χ9144-4-444-4-4-21-21-1-122-21-212-12-10000000000000000002-2-1-100110000-4-444-4-4442-12-111-2-22-12-1-21-21000000000000000000-221100-1-10000
χ9244-4-444-4-4-21-21-1-122-21-212-12-1000000000000000000-221100-1-10000-4-444-4-4442-12-111-2-22-12-1-21-210000000000000000002-2-1-100110000
χ934-44i−4i4-44i−4i1-2-12−2i2ii−i1-2-12i−2i−i2i00000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13-44−4i4i-44−4i4i-121-22i−2i−ii-121-2−i2ii−2i00000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ944-44i−4i4-44i−4i1-2-12−2i2ii−i1-2-12i−2i−i2i00000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13-44−4i4i-44−4i4i-121-22i−2i−ii-121-2−i2ii−2i00000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ954-44i−4i4-44i−4i-212-1i−i−2i2i-212-1−2ii2i−i00000000000000000000−i3i3003−30000-44−4i4i-44−4i4i2-1-21−ii2i−2i2-1-212i−i−2ii00000000000000000000i3−i300−330000
χ964-44i−4i4-44i−4i-212-1i−i−2i2i-212-1−2ii2i−i00000000000000000000i3−i300−330000-44−4i4i-44−4i4i2-1-21−ii2i−2i2-1-212i−i−2ii00000000000000000000−i3i3003−30000
χ974-4−4i4i4-4−4i4i1-2-122i−2i−ii1-2-12−i2ii−2i00000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23-444i−4i-444i−4i-121-2−2i2ii−i-121-2i−2i−i2i00000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ984-4−4i4i4-4−4i4i1-2-122i−2i−ii1-2-12−i2ii−2i00000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23-444i−4i-444i−4i-121-2−2i2ii−i-121-2i−2i−i2i00000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ994-4−4i4i4-4−4i4i-212-1−ii2i−2i-212-12i−i−2ii00000000000000000000−i3i300−330000-444i−4i-444i−4i2-1-21i−i−2i2i2-1-21−2ii2i−i00000000000000000000i3−i3003−30000
χ1004-4−4i4i4-4−4i4i-212-1−ii2i−2i-212-12i−i−2ii00000000000000000000i3−i3003−30000-444i−4i-444i−4i2-1-21i−i−2i2i2-1-21−2ii2i−i00000000000000000000−i3i300−330000
χ1018888-4-4-4-42-42-4-4-422-12-12-12-12000000000000000000000000000000-8-8-8-84444-24-2444-2-21-21-21-21-2000000000000000000000000000000
χ1028888-4-4-4-4-42-4222-4-42-12-12-12-1000000000000000000000000000000-8-8-8-844444-24-2-2-244-21-21-21-21000000000000000000000000000000
χ10388-8-8-4-4442-42-444-2-2-12-121-21-2000000000000000000000000000000-8-88844-4-4-24-24-4-4221-21-2-12-12000000000000000000000000000000
χ10488-8-8-4-444-42-42-2-2442-12-1-21-21000000000000000000000000000000-8-88844-4-44-24-222-4-4-21-212-12-1000000000000000000000000000000
χ1058-88i−8i-44−4i4i2-4-24−4i4i2i−2i-121-2−i2ii−2i000000000000000000000000000000-88−8i8i4-44i−4i-242-44i−4i−2i2i1-2-12i−2i−i2i000000000000000000000000000000
χ1068-88i−8i-44−4i4i-424-22i−2i−4i4i2-1-212i−i−2ii000000000000000000000000000000-88−8i8i4-44i−4i4-2-42−2i2i4i−4i-212-1−2ii2i−i000000000000000000000000000000
χ1078-8−8i8i-444i−4i2-4-244i−4i−2i2i-121-2i−2i−i2i000000000000000000000000000000-888i−8i4-4−4i4i-242-4−4i4i2i−2i1-2-12−i2ii−2i000000000000000000000000000000
χ1088-8−8i8i-444i−4i-424-2−2i2i4i−4i2-1-21−2ii2i−i000000000000000000000000000000-888i−8i4-4−4i4i4-2-422i−2i−4i4i-212-12i−i−2ii000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.