Finite Group Databasebeta

← Group #13161987

Character table — Group #13161987

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size111122222222222222444444444444444444444444448888888888888888888888888888888888888181836363636363636363636363636363636363636363672727272727272
order1222333446666666663333366666666666666612121212121241212121212121212121212121212121212121212121212121212121212121212121212122244444668888121224242424242424244121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-111
χ92222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-20000000000000000000022-20000220000-2-2000000000000000
χ102222222-2-222222222222222222222222222222-2-2-2-2-2-20000000-2-2-2-2-2-2-2-2-2-200000000000000000000-2-220000-2-2000022000000000000000
χ11222222-12222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12220000-1-10000-1-1000000002-1-10000
χ12222222-12222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-200001100001100000000-2110000
χ13222222-12222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-2-2-211111111111111112220000-1-10000-1-100000000-2110000
χ14222222-12222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-21122-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2000011000011000000002-1-10000
χ15222222-1-2-222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000−i3i3-2-2111111110000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i322-20000-1-1000011000000000−i3i30000
χ16222222-1-2-222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000−i3i3-2-2111111110000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-220000110000-1-1000000000i3−i30000
χ17222222-1-2-222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i3-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i322-20000-1-1000011000000000i3−i30000
χ18222222-1-2-222-122-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i3-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-220000110000-1-1000000000−i3i30000
χ1922222-12222-122-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000022000022000000-1-1-1-100000-1-1
χ2022222-12222-122-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1222-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000-2-20000-2-200000011110000011
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χ2222222-12222-122-122-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1-2-2-211-2-2-1-122-1-1-1-1-1-11111-2-2111111-2-211111100000-2-2000022000000-1-1-1-10000011
χ232222-12222-122-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000220000220000-1-1-1-10000000-1-100
χ242222-12222-122-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-122-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000-2-20000-2-20000111100000001100
χ252222-12222-122-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-21111000220000-2-2000011110000000-1-100
χ262222-12222-122-122-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-21111000-2-20000220000-1-1-1-100000001100
χ2722-2-22222-2-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-2222222-22-2-2200000002-22-22-222-2-2000000000000000000000002i−2i0000000000000000000002i−2i00
χ2822-2-22222-2-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-2222222-22-2-2200000002-22-22-222-2-200000000000000000000000−2i2i000000000000000000000−2i2i00
χ2922-2-2222-22-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-222222-22-222-20000000-22-22-22-2-22200000000000000000000000002i−2i0000000000000000000002i−2i
χ3022-2-2222-22-2-2-2222-2-2-222222-2-2-2-2-2-2-2-2-2-222222-22-222-20000000-22-22-22-2-2220000000000000000000000000−2i2i000000000000000000000−2i2i
χ3122-2-22-12-22-21-22-12-21-2-12-1-1-111-2-2111111-12-1-1-1-2-1-2221000−i3i3001-1-221-111-1-1−i3−i3i3i300−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3000002i−2i00000000000033−3−300000−ii
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χ3322-2-22-12-22-21-22-12-21-2-12-1-1-111-2-2111111-12-1-1-1-2-1-2221000i3−i3001-1-221-111-1-1i3i3−i3−i300i3−i3i3i3−i3−i300i3−i3i3i3−i3−i3000002i−2i000000000000−3−33300000−ii
χ3422-2-22-12-22-21-22-12-21-2-12-1-1-111-2-2111111-12-1-1-1-2-1-2221000i3−i3001-1-221-111-1-1i3i3−i3−i300i3−i3i3i3−i3−i300i3−i3i3i3−i3−i300000−2i2i00000000000033−3−300000i−i
χ3522-2-2-1222-21-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-1-1-22-2120−i3i30000-11-112-2-1-111−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i30002i−2i000000000033−3−30000000−ii00
χ3622-2-2-1222-21-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-1-1-22-2120−i3i30000-11-112-2-1-111−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3000−2i2i0000000000−3−3330000000i−i00
χ3722-2-2-1222-21-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-1-1-22-2120i3−i30000-11-112-2-1-111i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i30002i−2i0000000000−3−3330000000−ii00
χ3822-2-2-1222-21-2-2-1221-2-2-1-12-1-11111-2-21111-1-12-1-1-1-22-2120i3−i30000-11-112-2-1-111i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i3000−2i2i000000000033−3−30000000i−i00
χ392-2-2222200-2-22-2-2-222-2222222-22-22-222-2-2-2-2-2-2-200000000000000000000000000000000000000000002-2000002-2−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000
χ402-2-2222200-2-22-2-2-222-2222222-22-22-222-2-2-2-2-2-2-200000000000000000000000000000000000000000002-2000002-2i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000
χ412-2-2222200-2-22-2-2-222-2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000000000000000000000000-2200000-22−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000000
χ422-2-2222200-2-22-2-2-222-2222222-22-22-222-2-2-2-2-2-2-20000000000000000000000000000000000000000000-2200000-22i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000000
χ4344444-24-4-44-244-244-24-24-2-2-2-2-244-2-2-2-2-2-2-24-2-2-2-42-4-4-42000000022-4-422222200000000000000000000000000000000000000000000000000
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χ514444-24-2-4-4-24-2-24-2-24-2-21-211-2-211-2-21111-21-2112-4222-400000−2i32i322-1-122-1-1-1-10000i3i3−2i3−2i3i3i3i3i3−i3−i32i32i3−i3−i3−i3−i3000000000000000000000000000000
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χ574444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-24-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i3211111111−1−3i32−1+3i32−1+3i32−1−3i321111−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000000000
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χ594444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-24-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i3211111111−1+3i32−1−3i32−1−3i32−1+3i321111−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000000000
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χ7444-4-4-24-24-42-42-24-22-42-21-21122-1-122-1-1-1-1-21-211-2-4-222402i3−2i30000-221-1-2211-1-12i3−2i32i3−2i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i3000000000000000000000000000000
χ7544-4-4-24-2-442-42-24-22-42-21-21122-1-122-1-1-1-1-21-211242-2-2-400000002-2-112-2-1-11100003-3003-33-3-3300-33-33000000000000000000000000000000
χ7644-4-4-24-2-442-42-24-22-42-21-21122-1-122-1-1-1-1-21-211242-2-2-400000002-2-112-2-1-1110000-3300-33-333-3003-33-3000000000000000000000000000000
χ7744-4-4-2-244-422-4-2-2422-41-2-211-1-12222-1-1-1-11-2-211-224-42-20−2i32i300001-1-22-2211-1-1i3−i3i3−i3−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i3000000000000000000000000000000
χ7844-4-4-2-244-422-4-2-2422-41-2-211-1-12222-1-1-1-11-2-211-224-42-202i3−2i300001-1-22-2211-1-1−i3i3−i3i32i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i3000000000000000000000000000000
χ7944-4-4-2-24-4422-4-2-2422-41-2-211-1-12222-1-1-1-11-2-2112-2-44-22000−2i32i300-112-22-2-1-111i3i3−i3−i300−2i32i3i3i3−i3−i300−2i32i3i3i3−i3−i3000000000000000000000000000000
χ8044-4-4-2-24-4422-4-2-2422-41-2-211-1-12222-1-1-1-11-2-2112-2-44-220002i3−2i300-112-22-2-1-111−i3−i3i3i3002i3−2i3−i3−i3i3i3002i3−2i3−i3−i3i3i3000000000000000000000000000000
χ8144-4-4-2-2-24-4222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-20−2i32i300001-11-11-1−1−3i32−1+3i321+3i321−3i32i3−i3i3−i3i3−i33-3−3−i32−3+i323−i323+i32i3−i3-333−i323+i32−3−i32−3+i32000000000000000000000000000000
χ8244-4-4-2-2-24-4222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-202i3−2i300001-11-11-1−1−3i32−1+3i321+3i321−3i32−i3i3−i3i3−i3i3-333+i323−i32−3+i32−3−i32−i3i33-3−3+i32−3−i323+i323−i32000000000000000000000000000000
χ8344-4-4-2-2-24-4222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-22-222-20−2i32i300001-11-11-1−1+3i32−1−3i321−3i321+3i32i3−i3i3−i3i3−i3-333−i323+i32−3−i32−3+i32i3−i33-3−3−i32−3+i323−i323+i32000000000000000000000000000000
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χ8544-4-4-2-2-2-44222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-22000−2i32i300-11-11-111+3i321−3i32−1−3i32−1+3i32i3i3−i3−i33-3i3−i3−3−i323−i32−3+i323+i32-33i3−i33−i32−3−i323+i32−3+i32000000000000000000000000000000
χ8644-4-4-2-2-2-44222-2-2-2222111−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-220002i3−2i300-11-11-111+3i321−3i32−1−3i32−1+3i32−i3−i3i3i3-33−i3i33+i32−3+i323−i32−3−i323-3−i3i3−3+i323+i32−3−i323−i32000000000000000000000000000000
χ8744-4-4-2-2-2-44222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-22000−2i32i300-11-11-111−3i321+3i32−1+3i32−1−3i32i3i3−i3−i3-33i3−i33−i32−3−i323+i32−3+i323-3i3−i3−3−i323−i32−3+i323+i32000000000000000000000000000000
χ8844-4-4-2-2-2-44222-2-2-2222111−1+3i32−1−3i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-220002i3−2i300-11-11-111−3i321+3i32−1+3i32−1−3i32−i3−i3i3i33-3−i3i3−3+i323+i32−3−i323−i32-33−i3i33+i32−3+i323−i32−3−i32000000000000000000000000000000
χ894-44-44440044-4-4-4-4-4-4444444-44-44-44-4-444-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000
χ904-44-444-200442-4-42-4-4-24-2-2-2-2-442-22-222-2-2-422220000000000000000000000000000000000000000000000000000000023−23000000000000000
χ914-44-444-200442-4-42-4-4-24-2-2-2-2-442-22-222-2-2-4222200000000000000000000000000000000000000000000000000000000−2323000000000000000
χ924-44-44-24004-2-4-42-4-424-24-2-2-22-2-442-222-2-22-422200000000000000000000000000000000000000000000000000000000000000i6−i6−i6i60000000
χ934-44-44-24004-2-4-42-4-424-24-2-2-22-2-442-222-2-22-422200000000000000000000000000000000000000000000000000000000000000−i6i6i6−i60000000
χ944-44-4-24400-24-42-4-42-44-2-24-2-22-22-2-4422-2-222-4220000000000000000000000000000000000000000000000000000000000i6−i6−i6i600000000000
χ954-44-4-24400-24-42-4-42-44-2-24-2-22-22-2-4422-2-222-4220000000000000000000000000000000000000000000000000000000000−i6i6i6−i600000000000
χ964-4-4444-200-4-4-2-4-424424-2-2-2-24-4-22-22-2-222-4222200000000000000000000000000000000000000000004-400000-22000000000000000000000
χ974-4-4444-200-4-4-2-4-424424-2-2-2-24-4-22-22-2-222-422220000000000000000000000000000000000000000000-44000002-2000000000000000000000
χ984-4-444-2400-424-42-44-2-4-24-2-2-2-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000000000−2i22i2000000i2−i2i2−i20000000
χ994-4-444-2400-424-42-44-2-4-24-2-2-2-224-4-22-2-2222-42220000000000000000000000000000000000000000000000000000002i2−2i2000000−i2i2−i2i20000000
χ1004-4-44-244002-442-4-4-24-4-2-24-2-2-22-224-4-2-22222-4220000000000000000000000000000000000000000000000000000−2i22i20000i2−i2i2−i200000000000
χ1014-4-44-244002-442-4-4-24-4-2-24-2-2-22-224-4-2-22222-42200000000000000000000000000000000000000000000000000002i2−2i20000−i2i2−i2i200000000000
χ1028-88-88-4-4008-44-844-84-4-4-42224-44-4-22-2-22244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-48-400-4844-844-8-4-42-4224-4-224-4-2-2224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4800-4-4-844-84482-4-422-224-44-4-2-222-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-400-4-4444444-4222−1−3i3−1+3i3-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-400-4-4444444-4222−1+3i3−1−3i3-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-400-84-4-8448-44-4-4222-44-442-222-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-4004-8-44-84-484-42-422-442-2-4422-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-480044844-8-4-4-82-4-4222-2-44-4422-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044-4444-4-44222−1−3i3−1+3i32-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044-4444-4-44222−1+3i3−1−3i32-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000

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