Finite Group Databasebeta

← Group #13161968

Character table — Group #13161968

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636363636363636363636363636727272727272
order12223334466666666622333336666666666666666666121212121212666666666666666666666666121212121212121212124412121212444888812121212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-111
χ5111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111111-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-111-1-1-1-111111111-1-1-1-1-11-1-111
χ8111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111-111-1-1
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χ102222222-2-222222222200222220000222222222222222-2-2-2-2-2-2000000000000000000000000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2002000022000000000000000000
χ11222222-1222222-1-122-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12220000-1-1-1-1-1-100000000000000
χ12222222-1222222-1-122-1222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-2-2000011111100000000000000
χ13222222-1222222-1-122-1-2-22-1-1-1-1111122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-2-2-2-2111111111111111122-1-1-1-1-1-1-1-122-1-1-1-1-2-220000-1-1111100000000000000
χ14222222-1222222-1-122-1-2-22-1-1-1-1111122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-2-2-2-2111111111111111122-1-1-1-1-1-1-1-1-2-2111122-2000011-1-1-1-100000000000000
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χ17222222-1-2-22222-1-122-1002-1-1-1-1i3i3−i3−i322-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-21111111122-1-1-1-100-2000011i3i3−i3−i300000000000000
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χ2022222-12222-12-1222-1222-12-1-1-12222-1-122-1-1-1-1-1-1-12-1-1-12-1222-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000-2-2000000000011110-20011
χ2122222-12222-12-1222-12-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-12-1-1-12-1222-1-2-2111111-2-2111111-2-2111111-1-122-1-1-1-1-1-100000000000220000000000-1-1-1-10-20011
χ2222222-12222-12-1222-12-2-2-12-1-1-1-2-2-2-2-1-122-1-1-1-1-1-1-12-1-1-12-1222-1-2-2111111-2-2111111-2-2111111-1-122-1-1-1-1-1-100000000000-2-2000000000011110200-1-1
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χ242222-12222-12-1222-12222-1-12-1-12222-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1000000000-2-20000000011110000-201100
χ252222-12222-12-1222-122-2-2-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1222-1211-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-10000000002200000000-1-1-1-10000-201100
χ262222-12222-12-1222-122-2-2-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1222-1211-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-1000000000-2-2000000001111000020-1-100
χ2722-2-22222-2-2-2222-2-2-2-22-2222222-22-2-2-2-2-2-2-2-2-2-2-222222222-2-2-22-22-222-2-22-22-222-2-22-22-222-2-22-22-22-222-2-2000000000000000000000000000000000
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χ3222-2-222-12-2-2-222-11-2-212-22-1-1-1-1-11-11-2-2111111112-1-1-1-122-11-2-22-22-222-2-2-11-11-1-111-11-11-1-1112-2-11-11-1-11100−3−3330000000−33−333−300000000000000
χ3322-2-222-12-2-2-222-11-2-21-222-1-1-1-11-11-1-2-2111111112-1-1-1-122-11-2-2-22-22-2-2221-11-111-1-11-11-111-1-12-2-11-11-1-1110033−3−300000003−3−333−300000000000000
χ3422-2-222-12-2-2-222-11-2-21-222-1-1-1-11-11-1-2-2111111112-1-1-1-122-11-2-2-22-22-2-2221-11-111-1-11-11-111-1-12-2-11-11-1-11100−3−3330000000−333−3−3300000000000000
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χ3622-2-222-1-22-2-222-11-2-21002-1-1-1-1−i3i3i3−i3-2-2111111112-1-1-1-1-2-21-12200000000−i3i3−i3i3−i3−i3i3i3i3−i3i3−i3i3i3−i3−i3-221-11-111-1-100−3−333−2i2i000003−3i−ii−i00000000000000
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χ3922-2-22-122-2-212-12-2-21-22-2-12-1-1-12-22-211-2-2111111-12-1-1-12-12-2-212-2-11-1-1112-2-11-1-1112-2-11-1-111-112-2-11-1-1110000000000000000000000033−3−300003−3
χ4022-2-22-122-2-212-12-2-21-22-2-12-1-1-12-22-211-2-2111111-12-1-1-12-12-2-212-2-11-1-1112-2-11-1-1112-2-11-1-111-112-2-11-1-11100000000000000000000000−3−3330000−33
χ4122-2-22-122-2-212-12-2-21-2-22-12-1-1-1-22-2211-2-2111111-12-1-1-12-12-2-21-221-111-1-1-221-111-1-1-221-111-1-1-112-2-11-1-1110000000000000000000000033−3−30000−33
χ4222-2-22-122-2-212-12-2-21-2-22-12-1-1-1-22-2211-2-2111111-12-1-1-12-12-2-21-221-111-1-1-221-111-1-1-221-111-1-1-112-2-11-1-11100000000000000000000000−3−33300003−3
χ4322-2-2-1222-21-2-122-21-2-22-2-1-12-1-12-22-21111-2-21111-1-12-1-1-122-21-2-112-2-1-111-112-2-1-111-112-2-1-111-11-112-2-1-111000000000000000000033−3−30000003−300
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χ4622-2-2-1222-21-2-122-21-2-2-22-1-12-1-1-22-221111-2-21111-1-12-1-1-122-21-21-1-2211-1-11-1-2211-1-11-1-2211-1-1-11-112-2-1-1110000000000000000000−3−3330000003−300
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χ664444-2-2-244-2-2-2-2-2-2-2-2-244111−1+3i32−1−3i32-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-211111111−1+3i32−1−3i32−1+3i32−1−3i321111−1−3i32−1+3i32−1−3i32−1+3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000
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χ684444-2-2-244-2-2-2-2-2-2-2-2-2-4-4111−1+3i32−1−3i322222111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-22222-1-1-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-11+3i321−3i321+3i321−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000
χ694444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1−3i32−1+3i32−2i3−2i32i32i3111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i3222222200003-33-3i3i3i3i3−3−i323−i32−3−i323−i32−i3−i3−i3−i3−3+i323+i32−3+i323+i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000
χ704444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1−3i32−1+3i322i32i3−2i3−2i3111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i322222220000-33-33−i3−i3−i3−i33+i32−3+i323+i32−3+i32i3i3i3i33−i32−3−i323−i32−3−i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000
χ714444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1+3i32−1−3i32−2i3−2i32i32i3111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i322222220000-33-33i3i3i3i33−i32−3−i323−i32−3−i32−i3−i3−i3−i33+i32−3+i323+i32−3+i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000
χ724444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1+3i32−1−3i322i32i3−2i3−2i3111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i3222222200003-33-3−i3−i3−i3−i3−3+i323+i32−3+i323+i32i3i3i3i3−3−i323−i32−3−i323−i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000
χ7344-4-44-24-44-424-24-4-42-400-24-2-2-2000022-4-4222222-24-2-2-2-42-444-20000000000000000000000002-2-442-222-2-2000000000000000000000000000000000
χ7444-4-44-2-24-4-424-2-22-4224-4-2-2111-22-222222-1-1-1-1-1-1-2-21114-2-22-424-4-22-2-222-221-111-1-1-221-111-1-1-22-221-111-1-1000000000000000000000000000000000
χ7544-4-44-2-24-4-424-2-22-422-44-2-21112-22-22222-1-1-1-1-1-1-2-21114-2-22-42-442-222-2-22-2-11-1-1112-2-11-1-111-22-221-111-1-1000000000000000000000000000000000
χ7644-4-44-2-2-44-424-2-22-42200-2-2111−2i32i32i3−2i32222-1-1-1-1-1-1-2-2111-422-24-200000000−2i32i3i3−i3i3i3−i3−i32i3−2i3−i3i3−i3−i3i3i32-22-2-11-1-111000000000000000000000000000000000
χ7744-4-44-2-2-44-424-2-22-42200-2-21112i3−2i3−2i32i32222-1-1-1-1-1-1-2-2111-422-24-2000000002i3−2i3−i3i3−i3−i3i3i3−2i32i3i3−i3i3i3−i3−i32-22-2-11-1-111000000000000000000000000000000000
χ7844-4-4-244-442-4-244-42-4-400-2-24-2-200002222-4-42222-2-24-2-22-4-44-240000000000000000000000002-22-2-4422-2-2000000000000000000000000000000000
χ7944-4-4-24-24-42-4-24-222-424-4-21-211-22-2222-1-122-1-1-1-1-21-211-24-222-4-224-4-2-2221-1-2211-1-11-1-2211-1-1-221-1-2211-1-1000000000000000000000000000000000
χ8044-4-4-24-24-42-4-24-222-42-44-21-2112-22-222-1-122-1-1-1-1-21-211-24-222-42-2-4422-2-2-112-2-1-111-112-2-1-111-221-1-2211-1-1000000000000000000000000000000000
χ8144-4-4-24-2-442-4-24-222-4200-21-211−2i32i32i3−2i322-1-122-1-1-1-1-21-2112-42-2-2400000000i3−i3−2i32i3i3i3−i3−i3−i3i32i3−2i3−i3−i3i3i32-2-112-2-1-111000000000000000000000000000000000
χ8244-4-4-24-2-442-4-24-222-4200-21-2112i3−2i3−2i32i322-1-122-1-1-1-1-21-2112-42-2-2400000000−i3i32i3−2i3−i3−i3i3i3i3−i3−2i32i3i3i3−i3−i32-2-112-2-1-111000000000000000000000000000000000
χ8344-4-4-2-244-422-2-24-422-44-41-2-2114-44-4-1-12222-1-1-1-11-2-211-2-24-422-22-2211-1-1-22-2211-1-1-22-2211-1-11-1-22-2211-1-1000000000000000000000000000000000
χ8444-4-4-2-244-422-2-24-422-4-441-2-211-44-44-1-12222-1-1-1-11-2-211-2-24-4222-22-2-1-1112-22-2-1-1112-22-2-1-1111-1-22-2211-1-1000000000000000000000000000000000
χ8544-4-4-2-24-4422-2-24-422-4001-2-2110000-1-12222-1-1-1-11-2-21122-44-2-200003-3-3300003-3-3300003-3-33-112-22-2-1-111000000000000000000000000000000000
χ8644-4-4-2-24-4422-2-24-422-4001-2-2110000-1-12222-1-1-1-11-2-21122-44-2-20000-333-30000-333-30000-333-3-112-22-2-1-111000000000000000000000000000000000
χ8744-4-4-2-2-24-422-2-2-222224-4111−1−3i32−1+3i32-22-22-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-2-2-2222-22-2211-1-11-11-1−1−3i32−1+3i321+3i321−3i321-11-1−1+3i32−1−3i321−3i321+3i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000000
χ8844-4-4-2-2-24-422-2-2-222224-4111−1+3i32−1−3i32-22-22-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-2-2-2222-22-2211-1-11-11-1−1+3i32−1−3i321−3i321+3i321-11-1−1−3i32−1+3i321+3i321−3i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000
χ8944-4-4-2-2-24-422-2-2-22222-44111−1−3i32−1+3i322-22-2-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-2-2-22222-22-2-1-111-11-111+3i321−3i32−1−3i32−1+3i32-11-111−3i321+3i32−1+3i32−1−3i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000000
χ9044-4-4-2-2-24-422-2-2-22222-44111−1+3i32−1−3i322-22-2-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-2-2-22222-22-2-1-111-11-111−3i321+3i32−1+3i32−1−3i32-11-111+3i321−3i32−1−3i32−1+3i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000
χ9144-4-4-2-2-2-4422-2-2-2222200111−1−3i32−1+3i32−2i32i32i3−2i3-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32222-2-2-200003-3-33i3−i3i3−i3−3−i323−i323+i32−3+i32−i3i3−i3i3−3+i323+i323−i32−3−i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ9244-4-4-2-2-2-4422-2-2-2222200111−1−3i32−1+3i322i3−2i3−2i32i3-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32222-2-2-20000-333-3−i3i3−i3i33+i32−3+i32−3−i323−i32i3−i3i3−i33−i32−3−i32−3+i323+i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ9344-4-4-2-2-2-4422-2-2-2222200111−1+3i32−1−3i32−2i32i32i3−2i3-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32222-2-2-20000-333-3i3−i3i3−i33−i32−3−i32−3+i323+i32−i3i3−i3i33+i32−3+i32−3−i323−i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ9444-4-4-2-2-2-4422-2-2-2222200111−1+3i32−1−3i322i3−2i3−2i32i3-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32222-2-2-200003-3-33−i3i3−i3i3−3+i323+i323−i32−3−i32i3−i3i3−i3−3−i323−i323+i32−3+i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ954-44-444-20044-4-422-4-4-2004-2-2-2-200004-4-22-22-2-222-4222200000000000000000000000000000000000000004-4-22-22000000000000000000000000000
χ964-44-444-20044-4-422-4-4-2004-2-2-2-200004-4-22-22-2-222-422220000000000000000000000000000000000000000-442-22-2000000000000000000000000000
χ974-44-44-24004-2-42-4-4-42400-24-2-2-20000-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000000−2i22i20000000000i2−i2i2−i2000000
χ984-44-44-24004-2-42-4-4-42400-24-2-2-20000-224-4-22-2-2222-42220000000000000000000000000000000000000000000000000002i2−2i20000000000−i2i2−i2i2000000
χ994-44-4-24400-242-4-4-42-4400-2-24-2-20000-22-224-4-2-22222-4220000000000000000000000000000000000000000000000000−2i22i200000000i2−i2i2−i20000000000
χ1004-44-4-24400-242-4-4-42-4400-2-24-2-20000-22-224-4-2-22222-42200000000000000000000000000000000000000000000000002i2−2i200000000−i2i2−i2i20000000000
χ1014-4-4444400-4-4-4-4-4444-400444440000-44-44-44-4-444-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-200-4-4-4-42-2442004-2-2-2-20000-442-22-222-2-2-4222200000000000000000000000000000000000000000023−23−2323000000000000000000000000000
χ1034-4-4444-200-4-4-4-42-2442004-2-2-2-20000-442-22-222-2-2-42222000000000000000000000000000000000000000000−232323−23000000000000000000000000000
χ1044-4-444-2400-42-42-444-2-400-24-2-2-200002-2-442-222-2-22-4222000000000000000000000000000000000000000000000000000000000000000i6−i6−i6i6000000
χ1054-4-444-2400-42-42-444-2-400-24-2-2-200002-2-442-222-2-22-4222000000000000000000000000000000000000000000000000000000000000000−i6i6i6−i6000000
χ1064-4-44-244002-42-4-44-24-400-2-24-2-200002-22-2-4422-2-222-42200000000000000000000000000000000000000000000000000000000000i6−i6−i6i60000000000
χ1074-4-44-244002-42-4-44-24-400-2-24-2-200002-22-2-4422-2-222-42200000000000000000000000000000000000000000000000000000000000−i6i6i6−i60000000000
χ1088-88-88-4-4008-4-8444-84-400-4-42220000-44-442-222-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-48-400-484-8444-8-400-42-4220000-442-2-4422-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4800-4-444-8-8448002-4-42200002-2-44-4422-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-400-4-4444444-400222−1−3i3−1+3i300002-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-400-4-4444444-400222−1+3i3−1−3i300002-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-888-4-400-84-844-48-4400-4-422200004-44-4-22-2-22244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-4004-84-84-4-48400-42-42200004-4-224-4-2-2224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48004444-88-4-4-8002-4-4220000-224-44-4-2-222-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044444-4-4-4400222−1−3i3−1+3i30000-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044444-4-4-4400222−1+3i3−1−3i30000-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000

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