Finite Group Databasebeta

← Group #66047

Character table — Group #66047

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222222222224444444444444444488888888101010101010101020202020
order1222444455101010101010222242020202020202020202020201010101010101010444444444444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1
χ6111111-1-11111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-11
χ7111111-1-111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11
χ8111111-1-111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-1
χ91111-1-111111111111-11-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111111-1-1-1
χ101111-1-111111111111-11-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1111
χ111111-1-11111111111-11-11-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11-111
χ121111-1-11111111111-11-11-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111111-11-1-1
χ131111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-11-11
χ141111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1111-11-1
χ151111-1-1-1-111111111-111-11-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111-111-1
χ161111-1-1-1-111111111-111-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11-1-11
χ1722222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222222−1+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+52−1−52000000000000
χ1822222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-2-2-22−1+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+52000000000000
χ1922222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5222222−1−52−1−52−1+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+52000000000000
χ2022222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-2-2-22−1−52−1−52−1+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+521−52000000000000
χ21222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5222-2-2-2−1+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+52000000000000
χ22222222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-2-222-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521+521−521+52−1+52−1−52−1+52−1−52000000000000
χ23222222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5222-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521−521+521−52000000000000
χ24222222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-2-222-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521−521+521−52−1−52−1+52−1−52−1+52000000000000
χ252222-2-222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+52000000000000
χ262222-2-222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-22-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−521−521+52−1+52−1−52000000000000
χ272222-2-222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-22-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−52000000000000
χ282222-2-222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-22-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+521+521−52−1−52−1+52000000000000
χ292222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1−52000000000000
χ302222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52-222-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−52−1+52−1−521−521+52000000000000
χ312222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+52000000000000
χ322222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52-222-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+52−1−52−1+521+521−52000000000000
χ3322-2-2002-2222-2-22-2-20000000002-22-200000000000000002i−2i2i−2i0000
χ3422-2-2002-2222-2-22-2-20000000002-22-20000000000000000−2i2i−2i2i0000
χ3522-2-200-22222-2-22-2-2000000000-22-2200000000000000002i−2i−2i2i0000
χ3622-2-200-22222-2-22-2-2000000000-22-220000000000000000−2i2i2i−2i0000
χ372-22-22-20022-22-2-22-2000002-22-200000000000000002i−2i2i−2i00000000
χ382-22-22-20022-22-2-22-2000002-22-20000000000000000−2i2i−2i2i00000000
χ392-22-2-220022-22-2-22-200000-22-2200000000000000002i−2i−2i2i00000000
χ402-22-2-220022-22-2-22-200000-22-220000000000000000−2i2i2i−2i00000000
χ4144-4-4004-4−1+5−1−5−1+51−51−5−1−51+51+5000000000−1+51−5−1−51+5000000000000000000000000
χ4244-4-4004-4−1−5−1+5−1−51+51+5−1+51−51−5000000000−1−51+5−1+51−5000000000000000000000000
χ4344-4-400-44−1+5−1−5−1+51−51−5−1−51+51+50000000001−5−1+51+5−1−5000000000000000000000000
χ4444-4-400-44−1−5−1+5−1−51+51+5−1+51−51−50000000001+5−1−51−5−1+5000000000000000000000000
χ454-44-44-400−1+5−1−51−5−1+51−51+5−1−51+500000−1+51−5−1−51+50000000000000000000000000000
χ464-44-44-400−1−5−1+51+5−1−51+51−5−1+51−500000−1−51+5−1+51−50000000000000000000000000000
χ474-44-4-4400−1+5−1−51−5−1+51−51+5−1−51+5000001−5−1+51+5−1−50000000000000000000000000000
χ484-44-4-4400−1−5−1+51+5−1−51+51−5−1+51−5000001+5−1−51−5−1+50000000000000000000000000000
χ494-4-44000044-4-44-4-440000000000000000000000000000000000000
χ504-4-440000−1+5−1−51−51−5−1+51+51+5−1−500000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000
χ514-4-440000−1+5−1−51−51−5−1+51+51+5−1−50000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000
χ524-4-440000−1−5−1+51+51+5−1−51−51−5−1+50000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000
χ534-4-440000−1−5−1+51+51+5−1−51−51−5−1+500000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000

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