Finite Group Databasebeta

← Group #3963

Character table — Group #3963

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111111112222222222222222222222222222222222221010101010101010
order1222222244445510101010101010101010101010102020202020202020202020202020202044444444
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ6111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ7111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ8111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ911-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ1011-11-1-11-1i−ii−i1111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ1111-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ1211-11-1-11-1−ii−ii1111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ1311-1-11-1-11i−i−ii1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1
χ1411-1-11-1-11i−i−ii1111-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11
χ1511-1-11-1-11−iii−i1111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11
χ1611-1-11-1-11−iii−i1111-1-1-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1
χ17222222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ18222222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+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
χ1922222222-2-2-2-2−1+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+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000
χ2022222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000
χ21222-2-22-2-222-2-2−1+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+52−1−52−1−521−521−521+521+521−521−521+521+5200000000
χ22222-2-22-2-222-2-2−1−52−1+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+521+521+521−521−521+521+521−521−5200000000
χ23222-2-22-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000
χ24222-2-22-2-2-2-222−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000
χ2522-22-2-22-22i−2i2i−2i−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+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
χ2622-22-2-22-22i−2i2i−2i−1−52−1+52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ1900000000
χ2722-22-2-22-2−2i2i−2i2i−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+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
χ2822-22-2-22-2−2i2i−2i2i−1−52−1+52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ1900000000
χ2922-2-22-2-222i−2i−2i2i−1+52−1−52−1+52−1−521−521+521−521−521+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
χ3022-2-22-2-222i−2i−2i2i−1−52−1+52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+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
χ3122-2-22-2-22−2i2i2i−2i−1+52−1−52−1+52−1−521−521+521−521−521+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
χ3222-2-22-2-22−2i2i2i−2i−1−52−1+52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+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
χ332-2222-2-2-2000022-2-2222-22-22-22-2-2-2000000000000000000000000
χ342-2222-2-2-20000−1+52−1−521−521+52−1+52−1−52−1+521−52−1−521+52−1+521−52−1−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000000
χ352-2222-2-2-20000−1+52−1−521−521+52−1+52−1−52−1+521−52−1−521+52−1+521−52−1−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000000
χ362-2222-2-2-20000−1−52−1+521+521−52−1−52−1+52−1−521+52−1+521−52−1−521+52−1+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000000
χ372-2222-2-2-20000−1−52−1+521+521−52−1−52−1+52−1−521+52−1+521−52−1−521+52−1+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000000
χ382-22-2-2-222000022-2-222-22-22-22-22-2-2000000000000000000000000
χ392-22-2-2-2220000−1+52−1−521−521+52−1+52−1−521−52−1+521+52−1−521−52−1+521+52−1−521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ700000000
χ402-22-2-2-2220000−1+52−1−521−521+52−1+52−1−521−52−1+521+52−1−521−52−1+521+52−1−521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ700000000
χ412-22-2-2-2220000−1−52−1+521+521−52−1−52−1+521+52−1−521−52−1+521+52−1−521−52−1+521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ1900000000
χ422-22-2-2-2220000−1−52−1+521+521−52−1−52−1+521+52−1−521−52−1+521+52−1−521−52−1+521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ1900000000
χ432-2-22-22-22000022-2-2-2-22-22-2-22-2222000000000000000000000000
χ442-2-22-22-220000−1+52−1−521−521+521−521+52−1+521−52−1−521+521−52−1+521+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ1800000000
χ452-2-22-22-220000−1+52−1−521−521+521−521+52−1+521−52−1−521+521−52−1+521+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ1800000000
χ462-2-22-22-220000−1−52−1+521+521−521+521−52−1−521+52−1+521−521+52−1−521−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ1400000000
χ472-2-22-22-220000−1−52−1+521+521−521+521−52−1−521+52−1+521−521+52−1−521−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ1400000000
χ482-2-2-2222-2000022-2-2-2-2-22-222-22-222000000000000000000000000
χ492-2-2-2222-20000−1+52−1−521−521+521−521+521−52−1+521+52−1−52−1+521−52−1−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ1800000000
χ502-2-2-2222-20000−1+52−1−521−521+521−521+521−52−1+521+52−1−52−1+521−52−1−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ1800000000
χ512-2-2-2222-20000−1−52−1+521+521−521+521−521+52−1−521−52−1+52−1−521+52−1+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ1400000000
χ522-2-2-2222-20000−1−52−1+521+521−521+521−521+52−1−521−52−1+52−1−521+52−1+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ1400000000

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