Finite Group Databasebeta

← Group #12137604

Character table — Group #12137604

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size112222222222244444444444444888888888816161616161616161616161616161616161616161616161616161616161620202020202020202020404040404040408080
order1222244445510101010101010102020202020202020224444888844101010102020202020202020202020202020202040404040404040402222444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111
χ51111111111111111111111111111-11-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1
χ61111111111111111111111111111-11-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11111
χ71111111111111111111111111111-11-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111-11-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
χ9111111111111111111111111111-11-1111-1-1-1-1-11-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-1-1111-1
χ10111111111111111111111111111-11-1111-1-1-1-1-11-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-111-1-1-11
χ11111111111111111111111111111-11-11-1-111-1-11-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-11
χ12111111111111111111111111111-11-11-1-111-1-11-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111111-1-1-1-11-1
χ13111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111111-1-1-1-1-11
χ14111111111111111111111111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-111111-1
χ15111111111111111111111111111-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-111-1-11-1
χ16111111111111111111111111111-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-11111-1-11-1-111-11
χ17222222222−1+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+52−1−52−1−52222222222222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000000
χ18222222222−1+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+52−1−52−1−522222-2-2-2-222-2-2−1+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+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000000
χ19222222222−1+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+52−1−52−1−522-22-22222-2-2-2-2−1+52−1−521−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000000
χ20222222222−1+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+52−1−52−1−522-22-2-2-2-2-2-2-222−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000000000000
χ21222222222−1+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+52−1−52−1−52-22-2222-2-2-2-2-221−521+52−1+52−1−521−521+52−1+52−1−521−521−521+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+520000000000000000000
χ22222222222−1+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+52−1−52−1−52-22-22-2-222-2-22-21−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000000000000
χ23222222222−1+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+52−1−52−1−52-2-2-2-222-2-2222-21−521+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+52−1+52−1+52−1−52−1−521−521−521+521+520000000000000000000
χ24222222222−1+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+52−1−52−1−52-2-2-2-2-2-22222-221−521+521−521+521−521+521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000000000000
χ25222222222−1−52−1+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+52222222222222−1−52−1+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+52−1−52−1−52−1+52−1+520000000000000000000
χ26222222222−1−52−1+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+522222-2-2-2-222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000000
χ27222222222−1−52−1+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+522-22-22222-2-2-2-2−1−52−1+521+521−52−1−52−1+521+521−521+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+520000000000000000000
χ28222222222−1−52−1+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+522-22-2-2-2-2-2-2-222−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000000000000
χ29222222222−1−52−1+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+52-22-2222-2-2-2-2-221+521−52−1−52−1+521+521−52−1−52−1+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+521−521−520000000000000000000
χ30222222222−1−52−1+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+52-22-22-2-222-2-22-21+521−52−1−52−1+521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000000000000
χ31222222222−1−52−1+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+52-2-2-2-222-2-2222-21+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+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000000000000
χ32222222222−1−52−1+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+52-2-2-2-2-2-22222-221+521−521+521−521+521−521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000000000000
χ33222-2-222-2-2222222-2-2-2-22222-2-2-2-200002i−2i0000000000000000002i−2i2i−2i000000000000002200-2-2000002i−2i0000
χ34222-2-222-2-2222222-2-2-2-22222-2-2-2-200002i−2i0000000000000000002i−2i2i−2i00000000000000-2-2002200000−2i2i0000
χ35222-2-222-2-2222222-2-2-2-22222-2-2-2-20000−2i2i000000000000000000−2i2i−2i2i000000000000002200-2-200000−2i2i0000
χ36222-2-222-2-2222222-2-2-2-22222-2-2-2-20000−2i2i000000000000000000−2i2i−2i2i00000000000000-2-20022000002i−2i0000
χ37222-2-2-2-222222222-2-2-2-2-2-2-2-22222020-200000000002200-2-2000000000000000000002-2002-20000000002-200
χ38222-2-2-2-222222222-2-2-2-2-2-2-2-22222020-200000000002200-2-200000000000000000000-2200-22000000000-2200
χ39222-2-2-2-222222222-2-2-2-2-2-2-2-222220-2020000000000-2-20022000000000000000000002-2002-2000000000-2200
χ40222-2-2-2-222222222-2-2-2-2-2-2-2-222220-2020000000000-2-2002200000000000000000000-2200-220000000002-200
χ4122-22-2-22-222222-2-22-22-22-22-22-22-220-20000000002200-2-200000000000000000000002-22-2-222-200000000000
χ4222-22-2-22-222222-2-22-22-22-22-22-22-220-20000000002200-2-20000000000000000000000-22-222-2-2200000000000
χ4322-22-2-22-222222-2-22-22-22-22-22-22-2-202000000000-2-2002200000000000000000000002-2-22-22-2200000000000
χ4422-22-2-22-222222-2-22-22-22-22-22-22-2-202000000000-2-200220000000000000000000000-222-22-22-200000000000
χ4522-2-222-2-222222-2-2-22-22-22-222-22-2000000002-200000000000000000000002-22-200002200-2-200002-20000000
χ4622-2-222-2-222222-2-2-22-22-22-222-22-2000000002-200000000000000000000002-22-20000-2-200220000-220000000
χ4722-2-222-2-222222-2-2-22-22-22-222-22-200000000-220000000000000000000000-22-2200002200-2-20000-220000000
χ4822-2-222-2-222222-2-2-22-22-22-222-22-200000000-220000000000000000000000-22-220000-2-2002200002-20000000
χ4922-2-22-222-22222-2-2-22-222-22-2-22-220000002-200000000000000000000000000002-22-2002-200-222200-2000000
χ5022-2-22-222-22222-2-2-22-222-22-2-22-220000002-200000000000000000000000000002-22-200-22002-2-2-2002000000
χ5122-2-22-222-22222-2-2-22-222-22-2-22-22000000-220000000000000000000000000000-22-22002-200-22-2-2002000000
χ5222-2-22-222-22222-2-2-22-222-22-2-22-22000000-220000000000000000000000000000-22-2200-22002-22200-2000000
χ5344444-4-4-4-44444444444-4-4-4-4-4-4-4-400000000000000000000000000000000000000000000000000000000000
χ5444444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+500000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000000000000
χ5544444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−51−51−51+51+51−51−51+51+50000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000000000000
χ5644444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−50000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000000
χ5744444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+51+51+51−51−51+51+51−51−500000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000000
χ58444-4-444-4-4−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+5−1+5−1+5−1−5−1−51−51−51+51+500004i−4i000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000
χ59444-4-444-4-4−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+5−1+5−1+5−1−5−1−51−51−51+51+50000−4i4i0000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000
χ60444-4-444-4-4−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−5−1−5−1−5−1+5−1+51+51+51−51−500004i−4i000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000
χ61444-4-444-4-4−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−5−1−5−1−5−1+5−1+51+51+51−51−50000−4i4i0000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000
χ62444-4-4-4-444−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+5−1+5−1+5−1−5−1−5040-40000000000−1+5−1−5001−51+5000000000000000000000000000000000000000
χ63444-4-4-4-444−1+5−1−5−1+5−1−5−1+5−1−51−51−51+51+51−51−51+51+5−1+5−1+5−1−5−1−50-40400000000001−51+500−1+5−1−5000000000000000000000000000000000000000
χ64444-4-4-4-444−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+5040-40000000000−1−5−1+5001+51−5000000000000000000000000000000000000000
χ65444-4-4-4-444−1−5−1+5−1−5−1+5−1−5−1+51+51+51−51−51+51+51−51−5−1−5−1−5−1+5−1+50-40400000000001+51−500−1−5−1+5000000000000000000000000000000000000000
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χ6844-44-44-44-4−1+5−1−5−1+5−1−51−51+5−1+51−5−1−51+51−5−1+51+5−1−51−5−1+51+5−1−500000000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000
χ6944-44-44-44-4−1−5−1+5−1−5−1+51+51−5−1−51+5−1+51−51+5−1−51−5−1+51+5−1−51−5−1+500000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000
χ7044-44-44-44-4−1−5−1+5−1−5−1+51+51−5−1−51+5−1+51−51+5−1−51−5−1+51+5−1−51−5−1+5000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000
χ7144-44-4-44-44−1+5−1−5−1+5−1−51−51+5−1+51−5−1−51+5−1+51−5−1−51+5−1+51−5−1−51+540-4000000000−1+5−1−5001−51+500000000000000000000000000000000000000000
χ7244-44-4-44-44−1+5−1−5−1+5−1−51−51+5−1+51−5−1−51+5−1+51−5−1−51+5−1+51−5−1−51+5-4040000000001−51+500−1+5−1−500000000000000000000000000000000000000000
χ7344-44-4-44-44−1−5−1+5−1−5−1+51+51−5−1−51+5−1+51−5−1−51+5−1+51−5−1−51+5−1+51−540-4000000000−1−5−1+5001+51−500000000000000000000000000000000000000000
χ7444-44-4-44-44−1−5−1+5−1−5−1+51+51−5−1−51+5−1+51−5−1−51+5−1+51−5−1−51+5−1+51−5-4040000000001+51−500−1−5−1+500000000000000000000000000000000000000000
χ7544-4-444-4-44−1+5−1−5−1+5−1−51−51+51−5−1+51+5−1−51−5−1+51+5−1−5−1+51−5−1−51+5000000004-40000000000000000000000−1+51−5−1−51+500000000000000000000000
χ7644-4-444-4-44−1+5−1−5−1+5−1−51−51+51−5−1+51+5−1−51−5−1+51+5−1−5−1+51−5−1−51+500000000-4400000000000000000000001−5−1+51+5−1−500000000000000000000000
χ7744-4-444-4-44−1−5−1+5−1−5−1+51+51−51+5−1−51−5−1+51+5−1−51−5−1+5−1−51+5−1+51−5000000004-40000000000000000000000−1−51+5−1+51−500000000000000000000000
χ7844-4-444-4-44−1−5−1+5−1−5−1+51+51−51+5−1−51−5−1+51+5−1−51−5−1+5−1−51+5−1+51−500000000-4400000000000000000000001+5−1−51−5−1+500000000000000000000000
χ7944-4-44-444-4−1+5−1−5−1+5−1−51−51+51−5−1+51+5−1−5−1+51−5−1−51+51−5−1+51+5−1−50000004-40000000000000000000000000000−1+51−5−1−51+50000000000000000000
χ8044-4-44-444-4−1+5−1−5−1+5−1−51−51+51−5−1+51+5−1−5−1+51−5−1−51+51−5−1+51+5−1−5000000-4400000000000000000000000000001−5−1+51+5−1−50000000000000000000
χ8144-4-44-444-4−1−5−1+5−1−5−1+51+51−51+5−1−51−5−1+5−1−51+5−1+51−51+5−1−51−5−1+50000004-40000000000000000000000000000−1−51+5−1+51−50000000000000000000
χ8244-4-44-444-4−1−5−1+5−1−5−1+51+51−51+5−1−51−5−1+5−1−51+5−1+51−51+5−1−51−5−1+5000000-4400000000000000000000000000001+5−1−51−5−1+50000000000000000000
χ838-8000000088-8-8000000000000000000000000000000000000000000000000000000000000004-4000000000
χ848-8000000088-8-800000000000000000000000000000000000000000000000000000000000000-44000000000
χ8516-160000000−4+45−4−454−454+450000000000000000000000000000000000000000000000000000000000000000000000000
χ8616-160000000−4−45−4+454+454−450000000000000000000000000000000000000000000000000000000000000000000000000

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