Finite Group Databasebeta

← Group #4075

Character table — Group #4075

Order 160.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222222222222222222222222222222220202020
order1222224444551010101010101010101010101010202020202020202020202020202020202444
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1
χ3111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11
χ4111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1
χ51111-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1
χ61111-1-111-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ71111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-1
χ81111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11
χ92222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000
χ102222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000
χ11222222-2-2-2-2−1+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+520000
χ12222222-2-2-2-2−1−52−1+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+521−521−521−521−520000
χ132222-2-222-2-2−1+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+520000
χ142222-2-222-2-2−1−52−1+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+521−521−521−521−520000
χ152222-2-2-2-222−1+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+52−1−52−1−52−1−52−1−520000
χ162222-2-2-2-222−1−52−1+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+520000
χ1722-2-200002i−2i222-22-200000000-2-2000000002i2i−2i−2i2i2i−2i−2i0000
χ1822-2-200002i−2i−1+52−1−52−1+521−52−1−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521+52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ70000
χ1922-2-200002i−2i−1+52−1−52−1+521−52−1−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521+52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ70000
χ2022-2-200002i−2i−1−52−1+52−1−521+52−1+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521−52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ190000
χ2122-2-200002i−2i−1−52−1+52−1−521+52−1+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ141+521−52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ190000
χ2222-2-20000−2i2i222-22-200000000-2-200000000−2i−2i2i2i−2i−2i2i2i0000
χ2322-2-20000−2i2i−1+52−1−52−1+521−52−1−521+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ181−521+52ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ70000
χ2422-2-20000−2i2i−1+52−1−52−1+521−52−1−521+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ181−521+52−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ70000
χ2522-2-20000−2i2i−1−52−1+52−1−521+52−1+521−52−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ141+521−52ζ3−ζ7ζ3−ζ7−ζ3+ζ7−ζ3+ζ7ζ11−ζ19ζ11−ζ19−ζ11+ζ19−ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ190000
χ2622-2-20000−2i2i−1−52−1+52−1−521+52−1+521−52ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ141+521−52−ζ3+ζ7−ζ3+ζ7ζ3−ζ7ζ3−ζ7−ζ11+ζ19−ζ11+ζ19ζ11−ζ19ζ11−ζ19ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ190000
χ272-22-2002i−2i0022-22-2200000000-2-22i−2i2i−2i2i−2i2i−2i000000000000
χ282-22-2002i−2i00−1+52−1−521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ181−521+52−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ70000
χ292-22-2002i−2i00−1+52−1−521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ181−521+52−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ70000
χ302-22-2002i−2i00−1−52−1+521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ141+521−52−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ190000
χ312-22-2002i−2i00−1−52−1+521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ141+521−52−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ190000
χ322-22-200−2i2i0022-22-2200000000-2-2−2i2i−2i2i−2i2i−2i2i000000000000
χ332-22-200−2i2i00−1+52−1−521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ181−521+52ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ70000
χ342-22-200−2i2i00−1+52−1−521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ181−521+52ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ70000
χ352-22-200−2i2i00−1−52−1+521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ141+521−52ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ11−ζ19−ζ11+ζ190000
χ362-22-200−2i2i00−1−52−1+521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ141+521−52ζ3+ζ7−ζ3−ζ7ζ3+ζ7−ζ3−ζ7ζ11+ζ19−ζ11−ζ19ζ11+ζ19−ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ11+ζ19ζ11−ζ190000
χ372-2-222-2000022-2-2-2-22-2-222-2-222200000000000000000000
χ382-2-222-20000−1+52−1−521−521−521+521+52−1+521−521−52−1+52−1−521+521+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ180000
χ392-2-222-20000−1+52−1−521−521−521+521+52−1+521−521−52−1+52−1−521+521+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ180000
χ402-2-222-20000−1−52−1+521+521+521−521−52−1−521+521+52−1−52−1+521−521−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ140000
χ412-2-222-20000−1−52−1+521+521+521−521−52−1−521+521+52−1−52−1+521−521−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ140000
χ422-2-22-22000022-2-2-2-2-222-2-222-22200000000000000000000
χ432-2-22-220000−1+52−1−521−521−521+521+521−52−1+52−1+521−521+52−1−52−1−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ180000
χ442-2-22-220000−1+52−1−521−521−521+521+521−52−1+52−1+521−521+52−1−52−1−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ180000
χ452-2-22-220000−1−52−1+521+521+521−521−521+52−1−52−1−521+521−52−1+52−1+521−52−1−52−1+52−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ140000
χ462-2-22-220000−1−52−1+521+521+521−521−521+52−1−52−1−521+521−52−1+52−1+521−52−1−52−1+52ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ140000

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