Finite Group Databasebeta

← Group #12131835

Character table — Group #12131835

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1122222222222222244444444444444888888888888888881616161616161616161616161616161616161616161616161616202020202020202040404040404040408080
order1222244445510102020202044101010101010202020202020244444488202020202020202048101020202020202020202020202020204040404040404040224444442224448848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-111
χ51111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-111-1-1-1-1
χ61111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111
χ71111111111111111111111111111111-1-11-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111-1-11-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-11-1
χ1011111111111111111-1-111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-111-11
χ1111111111111111111-1-111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11
χ1211111111111111111-1-111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1
χ1311111111111111111-1-1111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-11
χ1411111111111111111-1-1111111111111-1-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11-1
χ1511111111111111111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-1-1-1111-1
χ1611111111111111111-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-1111-1-1-11
χ17222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222222222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ18222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52222-2-2-2-222−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ19222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222222-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000000
χ20222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-22-2-2-2-2-2-2−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52221−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ21222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-222-2-2-2-21−521−521−521−521+521+521+521+522-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ22222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-222-2-21−521−521−521−521+521+521+521+52-22−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ23222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-222-2-2221−521−521−521−521+521+521+521+52-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ24222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-222221−521−521−521−521+521+521+521+522-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ25222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222222222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ26222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52222-2-2-2-222−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ27222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222222-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-2-21+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000000
χ28222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-22-2-2-2-2-2-2−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52221+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ29222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-222-2-2-2-21+521+521+521+521−521−521−521−522-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ30222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-222-2-21+521+521+521+521−521−521−521−52-22−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ31222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-222-2-2221+521+521+521+521−521−521−521−52-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ32222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2-222221+521+521+521+521−521−521−521−522-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ3322222-2-2-2-22222-2-2-2-200222222-2-2-2-2-2-20002-200000000000000000000002-22-20000000000002-22-2000000002-20000
χ3422222-2-2-2-22222-2-2-2-200222222-2-2-2-2-2-20002-200000000000000000000002-22-2000000000000-22-2200000000-220000
χ3522222-2-2-2-22222-2-2-2-200222222-2-2-2-2-2-2000-220000000000000000000000-22-220000000000002-22-200000000-220000
χ3622222-2-2-2-22222-2-2-2-200222222-2-2-2-2-2-2000-220000000000000000000000-22-22000000000000-22-22000000002-20000
χ37222-2-222-2-22222222200-2-222-2-22-22-2-2-200000002i−2i0000000000000000000000000000002i−2i2i−2i00002i2i−2i−2i200-2000000
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χ4122-22-22-22-22222-2-2-2-20022-2-2-2-22222-2-22-20000000000000000022-2-20000000000000000000000002i−2i2i−2i0000002i−2i00
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χ4322-22-22-22-22222-2-2-2-20022-2-2-2-22222-2-2-2200000000000000000-2-2220000000000000000000000002i−2i2i−2i000000−2i2i00
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χ4522-2-222-2-222222-2-2-2-222-2-2-2-2222-22-22200-200000022-2-222-2-2000000000000000000000000002-2-222-2-220000000000
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χ4722-2-222-2-222222-2-2-2-2-2-2-2-2-2-2222-22-222002000000-2-222-2-222000000000000000000000000002-2-22-222-20000000000
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χ4922-2-22-222-22222222200-2-2-2-222-22-22-2-2000002-20000000000000000000000002-22-20000000022-2-2000002-20000000
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χ5344444-4-4-4-4−1+5−1−5−1+5−1−51−51−51+51+500−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+51−51+50004-40000000000000000000000−1+51−5−1−51+5000000000000000000000000000000
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χ5544444-4-4-4-4−1−5−1+5−1−5−1+51+51+51−51−500−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−51+51−50004-40000000000000000000000−1−51+5−1+51−5000000000000000000000000000000
χ5644444-4-4-4-4−1−5−1+5−1−5−1+51+51+51−51−500−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−51+51−5000-4400000000000000000000001+5−1−51−5−1+5000000000000000000000000000000
χ57444-4-444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+5−1+5−1−51−51+5−1+51−5−1−51+51−51+500000004i−4i000000000000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000
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χ6644-44-44-44-4−1+5−1−5−1+5−1−51−51−51+51+500−1+5−1−51−51+51−51+5−1+5−1+5−1−5−1−51−51+54-400000000000000000−1+5−1−51−51+500000000000000000000000000000000000000
χ6744-44-44-44-4−1+5−1−5−1+5−1−51−51−51+51+500−1+5−1−51−51+51−51+5−1+5−1+5−1−5−1−51−51+5-44000000000000000001−51+5−1+5−1−500000000000000000000000000000000000000
χ6844-44-44-44-4−1−5−1+5−1−5−1+51+51+51−51−500−1−5−1+51+51−51+51−5−1−5−1−5−1+5−1+51+51−54-400000000000000000−1−5−1+51+51−500000000000000000000000000000000000000
χ6944-44-44-44-4−1−5−1+5−1−5−1+51+51+51−51−500−1−5−1+51+51−51+51−5−1−5−1−5−1+5−1+51+51−5-44000000000000000001+51−5−1−5−1+500000000000000000000000000000000000000
χ7044-44-4-44-44444444440044-4-4-4-4-4-4-4-4440000000000000000000000000000000000000000000000000000000000000
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χ7244-44-4-44-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500−1+5−1−51−51+51−51+51−51−51+51+5−1+5−1−5000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000000000
χ7344-44-4-44-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500−1−5−1+51+51−51+51−51+51+51−51−5−1−5−1+5000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000000000
χ7444-44-4-44-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500−1−5−1+51+51−51+51−51+51+51−51−5−1−5−1+500000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000000000
χ7544-4-444-4-44−1+5−1−5−1+5−1−51−51−51+51+5441−51+51−51+5−1+5−1−5−1+51−5−1−51+5−1+5−1−500-4000000−1+5−1+51−51−5−1−5−1−51+51+500000000000000000000000000000000000000000000
χ7644-4-444-4-44−1+5−1−5−1+5−1−51−51−51+51+5-4-41−51+51−51+5−1+5−1−5−1+51−5−1−51+5−1+5−1−50040000001−51−5−1+5−1+51+51+5−1−5−1−500000000000000000000000000000000000000000000
χ7744-4-444-4-44−1−5−1+5−1−5−1+51+51+51−51−5441+51−51+51−5−1−5−1+5−1−51+5−1+51−5−1−5−1+500-4000000−1−5−1−51+51+5−1+5−1+51−51−500000000000000000000000000000000000000000000
χ7844-4-444-4-44−1−5−1+5−1−5−1+51+51+51−51−5-4-41+51−51+51−5−1−5−1+5−1−51+5−1+51−5−1−5−1+50040000001+51+5−1−5−1−51−51−5−1+5−1+500000000000000000000000000000000000000000000
χ7944-4-44-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+5−1+5−1−51−5−1+51+5−1−51−51+5000004-4000000000000000000000000−1+51−5−1−51+500000000000000000000000000
χ8044-4-44-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5001−51+51−51+5−1+5−1−51−5−1+51+5−1−51−51+500000-440000000000000000000000001−5−1+51+5−1−500000000000000000000000000
χ8144-4-44-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−5−1−5−1+51+5−1−51−5−1+51+51−5000004-4000000000000000000000000−1−51+5−1+51−500000000000000000000000000
χ8244-4-44-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5001+51−51+51−5−1−5−1+51+5−1−51−5−1+51+51−500000-440000000000000000000000001+5−1−51−5−1+500000000000000000000000000
χ838-8000000088-8-800004i−4i0000000000000000000004i−4i004i−4i0000000000000000000000000000000000000000000000
χ848-8000000088-8-80000−4i4i000000000000000000000−4i4i00−4i4i0000000000000000000000000000000000000000000000
χ858-80000000−2+25−2−252−252+25−4ζ11+4ζ194ζ11−4ζ194ζ3−4ζ7−4ζ3+4ζ74i−4i000000000000000000000−2ζ11−2ζ192ζ11+2ζ192ζ6−2ζ14−2ζ6+2ζ14−2ζ3−2ζ72ζ3+2ζ7−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000000000
χ868-80000000−2+25−2−252−252+25−4ζ11+4ζ194ζ11−4ζ194ζ3−4ζ7−4ζ3+4ζ7−4i4i0000000000000000000002ζ11+2ζ19−2ζ11−2ζ19−2ζ6+2ζ142ζ6−2ζ142ζ3+2ζ7−2ζ3−2ζ72ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000000000
χ878-80000000−2+25−2−252−252+254ζ11−4ζ19−4ζ11+4ζ19−4ζ3+4ζ74ζ3−4ζ74i−4i000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ6+2ζ142ζ6−2ζ14−2ζ3−2ζ72ζ3+2ζ72ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000000000
χ888-80000000−2+25−2−252−252+254ζ11−4ζ19−4ζ11+4ζ19−4ζ3+4ζ74ζ3−4ζ7−4i4i0000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ6−2ζ14−2ζ6+2ζ142ζ3+2ζ7−2ζ3−2ζ7−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000000000
χ898-80000000−2−25−2+252+252−254ζ3−4ζ7−4ζ3+4ζ74ζ11−4ζ19−4ζ11+4ζ194i−4i000000000000000000000−2ζ3−2ζ72ζ3+2ζ72ζ2−2ζ18−2ζ2+2ζ18−2ζ11−2ζ192ζ11+2ζ192ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000000
χ908-80000000−2−25−2+252+252−254ζ3−4ζ7−4ζ3+4ζ74ζ11−4ζ19−4ζ11+4ζ19−4i4i0000000000000000000002ζ3+2ζ7−2ζ3−2ζ7−2ζ2+2ζ182ζ2−2ζ182ζ11+2ζ19−2ζ11−2ζ19−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000
χ918-80000000−2−25−2+252+252−25−4ζ3+4ζ74ζ3−4ζ7−4ζ11+4ζ194ζ11−4ζ194i−4i000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ2+2ζ182ζ2−2ζ18−2ζ11−2ζ192ζ11+2ζ19−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000000
χ928-80000000−2−25−2+252+252−25−4ζ3+4ζ74ζ3−4ζ7−4ζ11+4ζ194ζ11−4ζ19−4i4i0000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ2−2ζ18−2ζ2+2ζ182ζ11+2ζ19−2ζ11−2ζ192ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.