Finite Group Databasebeta

← Group #12128015

Character table — Group #12128015

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222222888888888888882244444441616161616161616161616161616224444444161616161616161616161616161655101010101010104040404040404040404040404040
order1222244442288888888888851010101020202020101040404040404040404040404051010101020202020101040404040404040404040404022222444422888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1
χ411111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111
χ5111111111-1-111-1-111-1-111-1-1111111111-1-111-1-111-1-111-1-1111111111-1-111-1-111-1-111-1-1111111111-1-111-1-111-1-111-1-1
χ6111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111
χ7111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111
χ8111111111-1-1-1-111-1-11111-1-1111111111-1-1-1-111-1-11111-1-1111111111-1-1-1-111-1-11111-1-1111111111-1-1-1-111-1-11111-1-1
χ922222-2-2-2-22-200000000000022222-2-2-2-22-200000000000022222-2-2-2-22-200000000000022222-2-2-2-22-2000000000000
χ1022222-2-2-2-2-2200000000000022222-2-2-2-2-2200000000000022222-2-2-2-2-2200000000000022222-2-2-2-2-22000000000000
χ11222-2-222-2-20000000000002i−2i222-2-222-2-20000000000002i−2i222-2-222-2-20000000000002i−2i222-2-222-2-20000000000002i−2i
χ12222-2-222-2-2000000000000−2i2i222-2-222-2-2000000000000−2i2i222-2-222-2-2000000000000−2i2i222-2-222-2-2000000000000−2i2i
χ13222-2-2-2-22200000000002-200222-2-2-2-22200000000002-200222-2-2-2-22200000000002-200222-2-2-2-22200000000002-200
χ14222-2-2-2-2220000000000-2200222-2-2-2-2220000000000-2200222-2-2-2-2220000000000-2200222-2-2-2-2220000000000-2200
χ1522-22-22-22-2000000002i−2i000022-22-22-22-2000000002i−2i000022-22-22-22-2000000002i−2i000022-22-22-22-2000000002i−2i0000
χ1622-22-22-22-200000000−2i2i000022-22-22-22-200000000−2i2i000022-22-22-22-200000000−2i2i000022-22-22-22-200000000−2i2i0000
χ1722-22-2-22-220000002-200000022-22-2-22-220000002-200000022-22-2-22-220000002-200000022-22-2-22-220000002-2000000
χ1822-22-2-22-22000000-2200000022-22-2-22-22000000-2200000022-22-2-22-22000000-2200000022-22-2-22-22000000-22000000
χ1922-2-222-2-22002i−2i000000000022-2-222-2-22002i−2i000000000022-2-222-2-22002i−2i000000000022-2-222-2-22002i−2i0000000000
χ2022-2-222-2-2200−2i2i000000000022-2-222-2-2200−2i2i000000000022-2-222-2-2200−2i2i000000000022-2-222-2-2200−2i2i0000000000
χ2122-2-22-222-200002-20000000022-2-22-222-200002-20000000022-2-22-222-200002-20000000022-2-22-222-200002-200000000
χ2222-2-22-222-20000-220000000022-2-22-222-20000-220000000022-2-22-222-20000-220000000022-2-22-222-20000-2200000000
χ238-80000000000000000000008-80000000000000000000008-80000000000000000000008-8000000000000000000000
χ24111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ25111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ2611111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ2711111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ28111111111-1-111-1-111-1-111-1-1111111111-1-111-1-111-1-111-1-1111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ29111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ30111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ31111111111-1-1-1-111-1-11111-1-1111111111-1-1-1-111-1-11111-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ3222222-2-2-2-22-200000000000022222-2-2-2-22-200000000000022222-2-2-2-22-2000000000000-2-2-2-2-22222-22000000000000
χ3322222-2-2-2-2-2200000000000022222-2-2-2-2-2200000000000022222-2-2-2-2-22000000000000-2-2-2-2-222222-2000000000000
χ34222-2-222-2-20000000000002i−2i222-2-222-2-20000000000002i−2i222-2-222-2-20000000000002i−2i-2-2-222-2-222000000000000−2i2i
χ35222-2-222-2-2000000000000−2i2i222-2-222-2-2000000000000−2i2i222-2-222-2-2000000000000−2i2i-2-2-222-2-2220000000000002i−2i
χ36222-2-2-2-22200000000002-200222-2-2-2-22200000000002-200222-2-2-2-22200000000002-200-2-2-22222-2-20000000000-2200
χ37222-2-2-2-2220000000000-2200222-2-2-2-2220000000000-2200222-2-2-2-2220000000000-2200-2-2-22222-2-200000000002-200
χ3822-22-22-22-2000000002i−2i000022-22-22-22-2000000002i−2i000022-22-22-22-2000000002i−2i0000-2-22-22-22-2200000000−2i2i0000
χ3922-22-22-22-200000000−2i2i000022-22-22-22-200000000−2i2i000022-22-22-22-200000000−2i2i0000-2-22-22-22-22000000002i−2i0000
χ4022-22-2-22-220000002-200000022-22-2-22-220000002-200000022-22-2-22-220000002-2000000-2-22-222-22-2000000-22000000
χ4122-22-2-22-22000000-2200000022-22-2-22-22000000-2200000022-22-2-22-22000000-22000000-2-22-222-22-20000002-2000000
χ4222-2-222-2-22002i−2i000000000022-2-222-2-22002i−2i000000000022-2-222-2-22002i−2i0000000000-2-222-2-222-200−2i2i0000000000
χ4322-2-222-2-2200−2i2i000000000022-2-222-2-2200−2i2i000000000022-2-222-2-2200−2i2i0000000000-2-222-2-222-2002i−2i0000000000
χ4422-2-22-222-200002-20000000022-2-22-222-200002-20000000022-2-22-222-200002-200000000-2-222-22-2-220000-2200000000
χ4522-2-22-222-20000-220000000022-2-22-222-20000-220000000022-2-22-222-20000-2200000000-2-222-22-2-2200002-200000000
χ468-80000000000000000000008-80000000000000000000008-8000000000000000000000-88000000000000000000000
χ4722222222222222222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000000000000
χ48222222222222222-2-2-2-2-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+521+521+5200000000000000000000000
χ4922222222222-2-2-2-22222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−521+521+521+521+5200000000000000000000000
χ5022222222222-2-2-2-2-2-2-2-22222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−521−521−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+521+521+52−1−52−1−52−1−52−1−5200000000000000000000000
χ51222222222-2-222-2-222-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−52−1−521+521+5200000000000000000000000
χ52222222222-2-222-2-2-2-222-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−52−1−5200000000000000000000000
χ53222222222-2-2-2-22222-2-2-2-222−1+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+521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−5200000000000000000000000
χ54222222222-2-2-2-222-2-22222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+52−1+52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−52−1−52−1−52−1−521+521+5200000000000000000000000
χ5544444-4-4-4-44-4000000000000−1+5−1+5−1+5−1+5−1+51−51−51−51−5−1+51−5000000000000−1−5−1−5−1−5−1−5−1−51+51+51+51+5−1−51+500000000000000000000000000000000000
χ5644444-4-4-4-4-44000000000000−1+5−1+5−1+5−1+5−1+51−51−51−51−51−5−1+5000000000000−1−5−1−5−1−5−1−5−1−51+51+51+51+51+5−1−500000000000000000000000000000000000
χ57444-4-444-4-40000000000004i−4i−1+5−1+5−1+51−51−5−1+5−1+51−51−5000000000000−2ζ11−2ζ192ζ11+2ζ19−1−5−1−5−1−51+51+5−1−5−1−51+51+5000000000000−2ζ3−2ζ72ζ3+2ζ700000000000000000000000
χ58444-4-444-4-4000000000000−4i4i−1+5−1+5−1+51−51−5−1+5−1+51−51−50000000000002ζ11+2ζ19−2ζ11−2ζ19−1−5−1−5−1−51+51+5−1−5−1−51+51+50000000000002ζ3+2ζ7−2ζ3−2ζ700000000000000000000000
χ59444-4-4-4-44400000000004-400−1+5−1+5−1+51−51−51−51−5−1+5−1+50000000000−1+51−500−1−5−1−5−1−51+51+51+51+5−1−5−1−50000000000−1−51+50000000000000000000000000
χ60444-4-4-4-4440000000000-4400−1+5−1+5−1+51−51−51−51−5−1+5−1+500000000001−5−1+500−1−5−1−5−1−51+51+51+51+5−1−5−1−500000000001+5−1−50000000000000000000000000
χ6144-44-44-44-4000000004i−4i0000−1+5−1+51−5−1+51−5−1+51−5−1+51−500000000−2ζ11−2ζ192ζ11+2ζ190000−1−5−1−51+5−1−51+5−1−51+5−1−51+500000000−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000
χ6244-44-44-44-400000000−4i4i0000−1+5−1+51−5−1+51−5−1+51−5−1+51−5000000002ζ11+2ζ19−2ζ11−2ζ190000−1−5−1−51+5−1−51+5−1−51+5−1−51+5000000002ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000
χ6344-44-4-44-440000004-4000000−1+5−1+51−5−1+51−51−5−1+51−5−1+5000000−1+51−5000000−1−5−1−51+5−1−51+51+5−1−51+5−1−5000000−1−51+500000000000000000000000000000
χ6444-44-4-44-44000000-44000000−1+5−1+51−5−1+51−51−5−1+51−5−1+50000001−5−1+5000000−1−5−1−51+5−1−51+51+5−1−51+5−1−50000001+5−1−500000000000000000000000000000
χ6544-4-444-4-44004i−4i0000000000−1+5−1+51−51−5−1+5−1+51−51−5−1+500−2ζ11−2ζ192ζ11+2ζ190000000000−1−5−1−51+51+5−1−5−1−51+51+5−1−500−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000
χ6644-4-444-4-4400−4i4i0000000000−1+5−1+51−51−5−1+5−1+51−51−5−1+5002ζ11+2ζ19−2ζ11−2ζ190000000000−1−5−1−51+51+5−1−5−1−51+51+5−1−5002ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000
χ6744-4-44-444-400004-400000000−1+5−1+51−51−5−1+51−5−1+5−1+51−50000−1+51−500000000−1−5−1−51+51+5−1−51+5−1−5−1−51+50000−1−51+50000000000000000000000000000000
χ6844-4-44-444-40000-4400000000−1+5−1+51−51−5−1+51−5−1+5−1+51−500001−5−1+500000000−1−5−1−51+51+5−1−51+5−1−5−1−51+500001+5−1−50000000000000000000000000000000
χ6916-16000000000000000000000−4+454−45000000000000000000000−4−454+4500000000000000000000000000000000000000000000
χ7022222222222222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+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+5200000000000000000000000
χ71222222222222222-2-2-2-2-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−521−521−5200000000000000000000000
χ7222222222222-2-2-2-22222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+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+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+521−521−521−521−5200000000000000000000000
χ7322222222222-2-2-2-2-2-2-2-22222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+521+521+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+521−521−521−521−521−521−521−521−52−1+52−1+52−1+52−1+5200000000000000000000000
χ74222222222-2-222-2-222-2-222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+52−1−52−1−521+521+52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−52−1+52−1+521−521−52−1+52−1+521−521−5200000000000000000000000
χ75222222222-2-222-2-2-2-222-2-222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+52−1+5200000000000000000000000
χ76222222222-2-2-2-22222-2-2-2-222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+5200000000000000000000000
χ77222222222-2-2-2-222-2-22222-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1−52−1−52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1+52−1+52−1+52−1+521−521−5200000000000000000000000
χ7844444-4-4-4-44-4000000000000−1−5−1−5−1−5−1−5−1−51+51+51+51+5−1−51+5000000000000−1+5−1+5−1+5−1+5−1+51−51−51−51−5−1+51−500000000000000000000000000000000000
χ7944444-4-4-4-4-44000000000000−1−5−1−5−1−5−1−5−1−51+51+51+51+51+5−1−5000000000000−1+5−1+5−1+5−1+5−1+51−51−51−51−51−5−1+500000000000000000000000000000000000
χ80444-4-444-4-40000000000004i−4i−1−5−1−5−1−51+51+5−1−5−1−51+51+5000000000000−2ζ3−2ζ72ζ3+2ζ7−1+5−1+5−1+51−51−5−1+5−1+51−51−5000000000000−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000
χ81444-4-444-4-4000000000000−4i4i−1−5−1−5−1−51+51+5−1−5−1−51+51+50000000000002ζ3+2ζ7−2ζ3−2ζ7−1+5−1+5−1+51−51−5−1+5−1+51−51−50000000000002ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000
χ82444-4-4-4-44400000000004-400−1−5−1−5−1−51+51+51+51+5−1−5−1−50000000000−1−51+500−1+5−1+5−1+51−51−51−51−5−1+5−1+50000000000−1+51−50000000000000000000000000
χ83444-4-4-4-4440000000000-4400−1−5−1−5−1−51+51+51+51+5−1−5−1−500000000001+5−1−500−1+5−1+5−1+51−51−51−51−5−1+5−1+500000000001−5−1+50000000000000000000000000
χ8444-44-44-44-4000000004i−4i0000−1−5−1−51+5−1−51+5−1−51+5−1−51+500000000−2ζ3−2ζ72ζ3+2ζ70000−1+5−1+51−5−1+51−5−1+51−5−1+51−500000000−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000
χ8544-44-44-44-400000000−4i4i0000−1−5−1−51+5−1−51+5−1−51+5−1−51+5000000002ζ3+2ζ7−2ζ3−2ζ70000−1+5−1+51−5−1+51−5−1+51−5−1+51−5000000002ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000
χ8644-44-4-44-440000004-4000000−1−5−1−51+5−1−51+51+5−1−51+5−1−5000000−1−51+5000000−1+5−1+51−5−1+51−51−5−1+51−5−1+5000000−1+51−500000000000000000000000000000
χ8744-44-4-44-44000000-44000000−1−5−1−51+5−1−51+51+5−1−51+5−1−50000001+5−1−5000000−1+5−1+51−5−1+51−51−5−1+51−5−1+50000001−5−1+500000000000000000000000000000
χ8844-4-444-4-44004i−4i0000000000−1−5−1−51+51+5−1−5−1−51+51+5−1−500−2ζ3−2ζ72ζ3+2ζ70000000000−1+5−1+51−51−5−1+5−1+51−51−5−1+500−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000
χ8944-4-444-4-4400−4i4i0000000000−1−5−1−51+51+5−1−5−1−51+51+5−1−5002ζ3+2ζ7−2ζ3−2ζ70000000000−1+5−1+51−51−5−1+5−1+51−51−5−1+5002ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000
χ9044-4-44-444-400004-400000000−1−5−1−51+51+5−1−51+5−1−5−1−51+50000−1−51+500000000−1+5−1+51−51−5−1+51−5−1+5−1+51−50000−1+51−50000000000000000000000000000000
χ9144-4-44-444-40000-4400000000−1−5−1−51+51+5−1−51+5−1−5−1−51+500001+5−1−500000000−1+5−1+51−51−5−1+51−5−1+5−1+51−500001−5−1+50000000000000000000000000000000
χ9216-16000000000000000000000−4−454+45000000000000000000000−4+454−4500000000000000000000000000000000000000000000

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