Finite Group Databasebeta

← Group #65413

Character table — Group #65413

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222222222222244444444444444444444444444442020202020202020
order1244222444551010101010102020202020202020888810101010202020204040404040404040404040404040404088888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ611111-1-1-1-1111-1-1-1-111-1-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ811111-1-1-1-1111-1-1-1-111-1-1-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911-1-1-11-11-1111111111-1-1-1-1-1-1-1-1i−ii−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−ii−ii−i1-11-1
χ1011-1-1-11-11-1111111111-1-1-1-1-1-1-1-1i−ii−i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−ii−ii-11-11
χ1111-1-1-11-11-1111111111-1-1-1-1-1-1-1-1−ii−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiii−ii−i-11-11
χ1211-1-1-11-11-1111111111-1-1-1-1-1-1-1-1−ii−ii-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii−ii−ii1-11-1
χ1311-1-1-1-11-11111-1-1-1-1111111-1-1-1-1i−i−ii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii1-1-11
χ1411-1-1-1-11-11111-1-1-1-1111111-1-1-1-1i−i−ii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i-111-1
χ1511-1-1-1-11-11111-1-1-1-1111111-1-1-1-1−iii−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii-111-1
χ1611-1-1-1-11-11111-1-1-1-1111111-1-1-1-1−iii−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i1-1-11
χ172222222222−1+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+52−1−52−1−522222−1+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+52−1−52−1−5200000000
χ182222222222−1+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+52−1−52−1−52-2-2-2-2−1+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+521−521−521+521+5200000000
χ192222222222−1−52−1+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+522222−1−52−1+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+5200000000
χ202222222222−1−52−1+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+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000
χ2122222-2-2-2-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5222-2-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000
χ2222222-2-2-2-22−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52-2-222−1+52−1−521−521+52−1+52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ2322222-2-2-2-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5222-2-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000
χ2422222-2-2-2-22−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52-2-222−1−52−1+521+521−52−1−52−1+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+5200000000
χ252222-22-2-22-222222222222222220000-2-2-2-2-2-2-2-2000000000000000000000000
χ262222-22-2-22-2−1+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+52−1−52−1−5200001−521+521−521+521−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ272222-22-2-22-2−1+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+52−1−52−1−5200001−521+521−521+521−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ282222-22-2-22-2−1−52−1+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+52−1+5200001+521−521+521−521+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ292222-22-2-22-2−1−52−1+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+52−1+5200001+521−521+521−521+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ302222-2-222-2-222-2-2-2-222-2-2-2-222220000-2-222-2-222000000000000000000000000
χ312222-2-222-2-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−521+52−1+52−1−521−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ1800000000
χ322222-2-222-2-2−1+52−1−521−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−521+52−1+52−1−521−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ1800000000
χ332222-2-222-2-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200001+521−52−1−52−1+521+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ1400000000
χ342222-2-222-2-2−1−52−1+521+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200001+521−52−1−52−1+521+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ1400000000
χ3522-2-2222-2-2-222222222-2-2-2-2-2-2-2-200002222-2-2-2-2000000000000000000000000
χ3622-2-2222-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−521−521+521−521+52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ700000000
χ3722-2-2222-2-2-2−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−521−521+521−521+52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ700000000
χ3822-2-2222-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+521+521−521+521−52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ1900000000
χ3922-2-2222-2-2-2−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+521+521−521+521−52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ1900000000
χ4022-2-22-2-222-222-2-2-2-2222222-2-2-2-2000022-2-2-2-222000000000000000000000000
χ4122-2-22-2-222-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−1+52−1−521−521+521−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ700000000
χ4222-2-22-2-222-2−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−1+52−1−521−521+521−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ700000000
χ4322-2-22-2-222-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000−1−52−1+521+521−521+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ1900000000
χ4422-2-22-2-222-2−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000−1−52−1+521+521−521+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ1900000000
χ4522-2-2-22-22-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+522i−2i2i−2i1−521+521−521+52−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700000000
χ4622-2-2-22-22-22−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−2i2i−2i2i1−521+521−521+52−1+52−1−52−1+52−1−52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700000000
χ4722-2-2-22-22-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−522i−2i2i−2i1+521−521+521−52−1−52−1+52−1−52−1+52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900000000
χ4822-2-2-22-22-22−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−2i2i−2i2i1+521−521+521−52−1−52−1+52−1−52−1+52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900000000
χ4922-2-2-2-22-222−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+522i−2i−2i2i1−521+52−1+52−1−52−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ700000000
χ5022-2-2-2-22-222−1+52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−2i2i2i−2i1−521+52−1+52−1−52−1+52−1−521−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ700000000
χ5122-2-2-2-22-222−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−522i−2i−2i2i1+521−52−1−52−1+52−1−52−1+521+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900000000
χ5222-2-2-2-22-222−1−52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−2i2i2i−2i1+521−52−1−52−1+52−1−52−1+521+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900000000
χ534-44i−4i000000440000-4-400004i−4i4i−4i000000000000000000000000000000000000
χ544-44i−4i000000−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000000
χ554-44i−4i000000−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000000000
χ564-44i−4i000000−1−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000000
χ574-44i−4i000000−1−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000000000
χ584-4−4i4i000000440000-4-40000−4i4i−4i4i000000000000000000000000000000000000
χ594-4−4i4i000000−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000000
χ604-4−4i4i000000−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000000000
χ614-4−4i4i000000−1−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000000
χ624-4−4i4i000000−1−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000000000

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