Finite Group Databasebeta

← Group #10823159

Character table — Group #10823159

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212666688888888121212122424242424242424242424242424242444444444121212121212121212121212121212124444444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000000000002-22-2000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-20000000000000000000000000000000000000000-22-22000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-22-2-2-22222-2222222222222222-2-2-2-200000000-2-2-2-200000000000000000000000000000000000000002-2-22000000000000
χ2422222222-2-2-2-22-2-2-22222-2222222222222222-2-2-2-200000000-2-2-2-20000000000000000000000000000000000000000-222-2000000000000
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χ2622222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111111111112222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ2722222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1111111111111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ2822222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1111111111111-2-2-2-22222-1-1-1-111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ30222-2-2-2-2222-2-2222-222-2-2-2-2-2222-2-22222-2-2-2-222-2-20000000022-2-200000000000000000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i0000000000000000
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χ32222-2-2-2-2222-2-22-2-22-2-2222-2-2222-2-2-2-2-2-2222222-2-200000000-2-222000000000000000000000000000000000000000000000000-22-220000
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χ35222-2-2-2-2222-2-2-122-222-2-2-211-1-1-111-1-1-1-11111-1-11100000000-1-111−3−3−3−33333−3−3−3−3333300002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii0000000000000000
χ36222-2-2-2-2222-2-2-122-222-2-2-211-1-1-111-1-1-1-11111-1-11100000000-1-111−3−3−3−33333−3−3−3−333330000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i0000000000000000
χ37222-2-2-2-22-2-222222-2-2-222-2-2-2222-2-2-2-2-2-22222-2-2220000000022-2-2000000000000000000002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000
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χ40222-2-2-2-22-2-2222-2-2222-2-22-2-2222-2-22222-2-2-2-2-2-22200000000-2-222000000000000000000000000000000000000000000000000-222-20000
χ41222-2-2-2-22-2-222-122-2-2-222-211-1-1-1111111-1-1-1-111-1-100000000-1-1113333−3−3−3−3−3−3−3−3333300002i−2i−2i2i−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i0000000000000000
χ42222-2-2-2-22-2-222-122-2-2-222-211-1-1-1111111-1-1-1-111-1-100000000-1-1113333−3−3−3−3−3−3−3−333330000−2i2i2i−2ii3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii0000000000000000
χ43222-2-2-2-22-2-222-122-2-2-222-211-1-1-1111111-1-1-1-111-1-100000000-1-111−3−3−3−333333333−3−3−3−300002i−2i−2i2ii3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i0000000000000000
χ44222-2-2-2-22-2-222-122-2-2-222-211-1-1-1111111-1-1-1-111-1-100000000-1-111−3−3−3−333333333−3−3−3−30000−2i2i2i−2i−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii0000000000000000
χ452-2-222-2-222-22-222-222-22-2-2-2-22-2-22222-2-222-2-22-22-2000000002-22-200000000000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-2-222-2-222-22-222-222-22-2-2-2-22-2-22222-2-222-2-22-22-2000000002-22-20000000000000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
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χ482-2-222-2-222-22-22-22-2-22-222-2-22-2-222-2-222-2-2222-22-200000000-22-2200000000000000000000000000000000000000000000-22-2200000000
χ492-2-222-2-222-22-2-12-222-22-2-211-111-1-1-1-111-1-111-11-1100000000-11-1133−3−333−3−333−3−333−3−32i−2i2i−2i0000−ii−ii−ii−ii−i3i3−i3i3−i3i3−i3i30000000000000000
χ502-2-222-2-222-22-2-12-222-22-2-211-111-1-1-1-111-1-111-11-1100000000-11-1133−3−333−3−333−3−333−3−3−2i2i−2i2i0000i−ii−ii−ii−ii3−i3i3−i3i3−i3i3−i30000000000000000
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χ522-2-222-2-222-22-2-12-222-22-2-211-111-1-1-1-111-1-111-11-1100000000-11-11−3−333−3−333−3−333−3−333−2i2i−2i2i0000i−ii−ii−ii−i−i3i3−i3i3−i3i3−i3i30000000000000000
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χ542-2-222-2-22-22-2222-22-22-22-2-2-22-2-222-2-222-2-222-22-22000000002-22-20000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ552-2-222-2-22-22-222-22-22-22-22-2-22-2-22222-2-222-2-2-22-2200000000-22-22000000000000000000000000000000000000000000002-2-2200000000
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χ572-2-222-2-22-22-22-12-22-22-22-211-111-1-111-1-111-1-11-11-100000000-11-1133−3−333−3−3−3−333−3−3332i−2i−2i2i0000−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i30000000000000000
χ582-2-222-2-22-22-22-12-22-22-22-211-111-1-111-1-111-1-11-11-100000000-11-1133−3−333−3−3−3−333−3−333−2i2i2i−2i0000i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i30000000000000000
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χ612-2-2-2-22222-2-2222-2-22-2-222222-2-2-2-222-2-2-2-2222-2-2222-2-222-2-22-2-2222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ622-2-2-2-22222-2-2222-2-22-2-222222-2-2-2-222-2-2-2-2222-2-22-2-222-2-2222-2-22-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
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χ652-2-2-2-22222-2-22-12-2-22-2-222-1-1-11111-1-11111-1-1-111-122-2-222-2-2-111-1-1-11111-1-1-1-11111-1-1000000003−3−333−3−33−333−3−333−30000000000000000
χ662-2-2-2-22222-2-22-12-2-22-2-222-1-1-11111-1-11111-1-1-111-122-2-222-2-2-111-1-1-11111-1-1-1-11111-1-100000000−333−3−333−33−3−333−3−330000000000000000
χ672-2-2-2-22222-2-22-12-2-22-2-222-1-1-11111-1-11111-1-1-111-1-2-222-2-222-111-111-1-1-1-11111-1-1-1-111000000003−3−333−3−333−3−333−3−330000000000000000
χ682-2-2-2-22222-2-22-12-2-22-2-222-1-1-11111-1-11111-1-1-111-1-2-222-2-222-111-111-1-1-1-11111-1-1-1-11100000000−333−3−333−3−333−3−333−30000000000000000
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χ9244-4-44-44-40000-2000000002-22-222-2−2323−232323−2323−230000−2222−2222000000002−22−2−22−22−66−666−66−60000000000000000000000000000000000000000
χ934-444-4-44-40000400000000-44-4-444-400000000000022−22−22220000000022−22−222222−22−2222000000000000000000000000000000000000000000000000
χ944-444-4-44-40000400000000-44-4-444-4000000000000−222222−2200000000−222222−22−222222−22000000000000000000000000000000000000000000000000
χ954-444-4-44-40000-2000000002-222-2-2223−23−232323−23−2323000022−22−222200000000−222−2−222−2−666−6−666−60000000000000000000000000000000000000000
χ964-444-4-44-40000-2000000002-222-2-2223−23−232323−23−23230000−222222−22000000002−2−222−2−226−6−666−6−660000000000000000000000000000000000000000
χ974-444-4-44-40000-2000000002-222-2-22−232323−23−232323−23000022−22−222200000000−222−2−222−26−6−666−6−660000000000000000000000000000000000000000
χ984-444-4-44-40000-2000000002-222-2-22−232323−23−232323−230000−222222−22000000002−2−222−2−22−666−6−666−60000000000000000000000000000000000000000
χ994-44-444-4-400004000000004-4-4-44-44000000000000000022−22−222200000000000022−22−2222−222222−220000000000000000000000000000000000000000
χ1004-44-444-4-400004000000004-4-4-44-440000000000000000−222222−22000000000000−222222−2222−22−22220000000000000000000000000000000000000000
χ1014-44-444-4-40000-200000000-2222-22-223−23−2323−232323−230000000022−22−222200006−6−66−666−6−222−22−2−220000000000000000000000000000000000000000
χ1024-44-444-4-40000-200000000-2222-22-223−23−2323−232323−2300000000−222222−220000−666−66−6−662−2−22−222−20000000000000000000000000000000000000000
χ1034-44-444-4-40000-200000000-2222-22-2−232323−2323−23−23230000000022−22−22220000−666−66−6−66−222−22−2−220000000000000000000000000000000000000000
χ1044-44-444-4-40000-200000000-2222-22-2−232323−2323−23−232300000000−222222−2200006−6−66−666−62−2−22−222−20000000000000000000000000000000000000000
χ1054-4-444-4-444-44-4-2-44-4-44-44422-222-2-222-2-222-2-2-22-22000000002-22-200000000000000000000000000000000000000000000000000000000
χ1064-4-444-4-44-44-44-2-44-44-44-4422-222-2-2-2-222-2-2222-22-2000000002-22-200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4-44444-4-44-2-444-444-4-4-2-2-2222222-2-2-2-222-222-2000000002-2-2200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4-4444-444-4-2-4444-4-44-4-2-2-22222-2-22222-2-22-2-22000000002-2-2200000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).