Finite Group Databasebeta

← Group #72271482

Character table — Group #72271482

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1122222222222444444444444444444444444448888888888888888888888888888888816161616161616161616161616161616161616161616161648484848484848484848484848484848
order12222344446121244446668888888812121224242424242424242444668888121212121212121212122424242424242424242424241616161616161616484848484848484848484848484848482222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-11111
χ5111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-11-11-1-111-1-1-1-111
χ6111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-11-111-1-11111-1-1
χ7111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1
χ8111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111
χ91111111111111-1-1-1-1111-1-1-1-111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-11-11-1-1-1-11111-1-1
χ101111111111111-1-1-1-1111-1-1-1-111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11111-1-1-1-111
χ111111111111111-1-1-1-1111-1-1-1-111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ121111111111111-1-1-1-1111-1-1-1-111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ131111111111111-1-1-1-1111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ141111111111111-1-1-1-1111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ151111111111111-1-1-1-1111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1111-11-1-1-1-1-1-1-11111
χ161111111111111-1-1-1-1111-1-1-1-1111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-11111111-1-1-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ192222222222222-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ202222222222222-2-2-2-22222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222-12222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222-12222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ2322222-12222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-211-1-1-1-111111111-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222-12222-1-1-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-211-1-1-1-111111111-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2522222-12222-1-1-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111110000000033−3−333−3−333−3−333−3−30000000000000000
χ2622222-12222-1-1-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1111111112222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111111100000000−3−333−3−333−3−333−3−3330000000000000000
χ2722222-12222-1-1-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-111111111-2-2-2-211222211-1-1-1-11111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ2822222-12222-1-1-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-111111111-2-2-2-211222211-1-1-1-11111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ2922222-12222-1-1-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-11111111122-2-2-1-1-2-222-1-1111111111111-1-1-1-1-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3022222-12222-1-1-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-11111111122-2-2-1-1-2-222-1-1111111111111-1-1-1-1-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3122222-12222-1-1-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-111111111-2-2221122-2-2111111-1-1-1-1-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3222222-12222-1-1-1-2-2-2-2-1-1-12222-2-2-2-2-1-1-111111111-2-2221122-2-2111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ3322222-12222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-122-2-2-1-122-2-2-1-111111111-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3422222-12222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-122-2-2-1-122-2-2-1-111111111-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3522222-12222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-2-22211-2-222111111-1-1-1-111111111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3622222-12222-1-1-1-2-2-2-2-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-2-22211-2-222111111-1-1-1-111111111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ41222-2-22-222-2222−2i−2i2i2i2-2-22i2i−2i−2i-2-2222-2-2-2-2-2-22222000000000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000000000000000002i−2i0000-2200
χ42222-2-22-222-2222−2i−2i2i2i2-2-22i2i−2i−2i-2-2222-2-2-2-2-2-22222000000000000−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000000000000000−2i2i00002-200
χ43222-2-22-222-2222−2i−2i2i2i2-2-2−2i−2i2i2i22-2-22-2-22222-2-2-2-2000000000000−2i−2i2i2i00000000−2i−2i2i2i000000000000000000000000000000020-200000000−2i2i
χ44222-2-22-222-2222−2i−2i2i2i2-2-2−2i−2i2i2i22-2-22-2-22222-2-2-2-2000000000000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000000000000-202000000002i−2i
χ4522-22-2222-2-22222i−2i2i−2i-22-22i−2i2i−2i2-22-2-22-222-2-222-2-20000000000002i−2i2i−2i000000002i−2i2i−2i000000002i−2i2-2000000002i−2i2i−2i2-22-20000000000000000
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χ4822-22-2222-2-22222i−2i2i−2i-22-2−2i2i−2i2i-22-22-22-2-2-222-2-2220000000000002i−2i2i−2i00000000−2i2i−2i2i0000-22−2i2i0000-22-22−2i2i−2i2i000000000000000000000000
χ4922-22-2222-2-2222−2i2i−2i2i-22-22i−2i2i−2i-22-22-22-2-2-222-2-222000000000000−2i2i−2i2i000000002i−2i2i−2i00002-2−2i2i00002-22-2−2i2i−2i2i000000000000000000000000
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χ5122-22-2222-2-2222−2i2i−2i2i-22-2−2i2i−2i2i2-22-2-22-222-2-222-2-2000000000000−2i2i−2i2i00000000−2i2i−2i2i000000002i−2i-22000000002i−2i2i−2i-22-220000000000000000
χ5222-22-2222-2-2222−2i2i−2i2i-22-2−2i2i−2i2i2-22-2-22-222-2-222-2-2000000000000−2i2i−2i2i00000000−2i2i−2i2i00000000−2i2i2-200000000−2i2i−2i2i2-22-20000000000000000
χ5322-22-2-122-2-2-1-1-12i−2i2i−2i1-112i−2i2i−2i2-22-21-11-1-111-1-1110000−i3i30000−i3i3−ii−ii33−3−3−i3−i3i3i3−ii−ii33−3−300002i−2i2-23−3−33i3−i3−i3i3−ii−ii-11-110000000000000000
χ5422-22-2-122-2-2-1-1-12i−2i2i−2i1-112i−2i2i−2i2-22-21-11-1-111-1-1110000−i3i30000−i3i3−ii−ii33−3−3−i3−i3i3i3−ii−ii33−3−30000−2i2i-22−333−3−i3i3i3−i3i−ii−i1-11-10000000000000000
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χ5722-22-2-122-2-2-1-1-12i−2i2i−2i1-11−2i2i−2i2i-22-221-1111-1-111-1-10000−i3i30000−i3i3−ii−ii33−3−3i3i3−i3−i3i−ii−i−3−3332-22i−2i0000-11-11−ii−ii−i3i3i3−i3−333−30000000000000000
χ5822-22-2-122-2-2-1-1-12i−2i2i−2i1-11−2i2i−2i2i-22-221-1111-1-111-1-10000−i3i30000−i3i3−ii−ii33−3−3i3i3−i3−i3i−ii−i−3−333-22−2i2i00001-11-1i−ii−ii3−i3−i3i33−3−330000000000000000
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χ6022-22-2-122-2-2-1-1-12i−2i2i−2i1-11−2i2i−2i2i-22-221-1111-1-111-1-10000i3−i30000i3−i3−ii−ii−3−333−i3−i3i3i3i−ii−i33−3−3-22−2i2i00001-11-1i−ii−i−i3i3i3−i3−333−30000000000000000
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χ6922-2-222-22-222222-2-22-2-222-2-222-2-22-2-2222-2-2-2-2220000000000002-2-22000000002-2-2200000000000000000000000000000020-2000002-20000
χ7022-2-222-22-222222-2-22-2-222-2-222-2-22-2-2222-2-2-2-2220000000000002-2-22000000002-2-22000000000000000000000000000000-20200000-220000
χ7122-2-222-22-222222-2-22-2-22-222-2-222-2-2-22-2-22222-2-20000000000002-2-2200000000-222-200000000000000000000000000002-20000002-2000000
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χ7422-2-222-22-22222-222-2-2-222-2-22-222-2-2-22-2-22222-2-2000000000000-222-2000000002-2-220000000000000000000000000000-220000002-2000000
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χ7944444-2-4-4-4-4-2220000-2-2-20000000022223−2323−2323−2323−23004-4000000000000-22-220000000023−2323−230000000000000000000000000000000000000000
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χ8144444-2-4-4-4-4-2220000-2-2-200000000222−2323−2323−2323−2323004-4000000000000-22-2200000000−2323−23230000000000000000000000000000000000000000
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χ84444-4-444-4-444-4-400004-4-400000000-44400000000000000−4i4i000000000000−4i4i−4i4i000000000000000000000000000000000000000000000000
χ85444-4-4-24-4-44-2220000-222000000002-2-223−2323−23−2323−23230000−2i32i34i−4i002i3−2i300000000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ86444-4-4-24-4-44-2220000-222000000002-2-223−2323−23−2323−232300002i3−2i3−4i4i00−2i32i3000000002i−2i2i−2i000000000000000000000000000000000000000000000000
χ87444-4-4-24-4-44-2220000-222000000002-2-2−2323−232323−2323−230000−2i32i3−4i4i002i3−2i3000000002i−2i2i−2i000000000000000000000000000000000000000000000000
χ88444-4-4-24-4-44-2220000-222000000002-2-2−2323−232323−2323−2300002i3−2i34i−4i00−2i32i300000000−2i2i−2i2i000000000000000000000000000000000000000000000000
χ89444-4-4-2-444-4-2-2-24i4i−4i−4i-2224i4i−4i−4i44-4-4-222-2-2-2-22222000000000000−2i−2i2i2i00000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ90444-4-4-2-444-4-2-2-24i4i−4i−4i-222−4i−4i4i4i-4-444-2222222-2-2-2-2000000000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000000000000000000000000000
χ91444-4-4-2-444-4-2-2-2−4i−4i4i4i-2224i4i−4i−4i-4-444-2222222-2-2-2-20000000000002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000000000000000000000000000
χ92444-4-4-2-444-4-2-2-2−4i−4i4i4i-222−4i−4i4i4i44-4-4-222-2-2-2-222220000000000002i2i−2i−2i000000002i2i−2i−2i00000000000000000000000000000000000000000000
χ9344-44-44-4-4444-4-40000-44-4000000004-4400000000000000004-40000000000000000004-4-440000000000000000000000000000000000000000
χ9444-44-44-4-4444-4-40000-44-4000000004-440000000000000000-44000000000000000000-444-40000000000000000000000000000000000000000
χ9544-44-4-2-4-444-22200002-2200000000-22-223−23−232323−23−2323000000004-4000000−232323−2300000000-222-20000000000000000000000000000000000000000
χ9644-44-4-2-4-444-22200002-2200000000-22-223−23−232323−23−232300000000-4400000023−23−2323000000002-2-220000000000000000000000000000000000000000
χ9744-44-4-2-4-444-22200002-2200000000-22-2−232323−23−232323−23000000004-400000023−23−232300000000-222-20000000000000000000000000000000000000000
χ9844-44-4-2-4-444-22200002-2200000000-22-2−232323−23−232323−2300000000-44000000−232323−23000000002-2-220000000000000000000000000000000000000000
χ9944-4-4444-44-44-4-40000-4-440000000044-4000000004-400440000-4-4000000000000000000000000000000000000000000000000000000000000
χ10044-4-4444-44-44-4-40000-4-440000000044-400000000-4400-4-4000044000000000000000000000000000000000000000000000000000000000000
χ10144-4-44-24-44-4-222000022-200000000-2-2223−23−2323−232323−234-400-2-20000220000000023−23−2323000000000000000000000000000000000000000000000000
χ10244-4-44-24-44-4-222000022-200000000-2-2223−23−2323−232323−23-4400220000-2-200000000−232323−23000000000000000000000000000000000000000000000000
χ10344-4-44-24-44-4-222000022-200000000-2-22−232323−2323−23−23234-400-2-200002200000000−232323−23000000000000000000000000000000000000000000000000
χ10444-4-44-24-44-4-222000022-200000000-2-22−232323−2323−23−2323-4400220000-2-20000000023−23−2323000000000000000000000000000000000000000000000000
χ10544-4-44-2-44-44-2-2-24-4-4422-24-4-444-4-4422-2-2-22222-2-2000000000000-222-200000000-222-200000000000000000000000000000000000000000000
χ10644-4-44-2-44-44-2-2-24-4-4422-2-444-4-444-422-222-2-2-2-222000000000000-222-2000000002-2-2200000000000000000000000000000000000000000000
χ10744-4-44-2-44-44-2-2-2-444-422-24-4-44-444-422-222-2-2-2-2220000000000002-2-2200000000-222-200000000000000000000000000000000000000000000
χ10844-4-44-2-44-44-2-2-2-444-422-2-444-44-4-4422-2-2-22222-2-20000000000002-2-22000000002-2-2200000000000000000000000000000000000000000000
χ10916-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11016-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ11116-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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