Finite Group Databasebeta

← Group #65504

Character table — Group #65504

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222222222222244444444444444444444444444442020202020202020
order1222224444551010101010101010101010101010222210101010101010101010101010101010202020202020202044448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ51111-1-11-1-11111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111-1-11-1-11111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111-1-11-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111-1-11-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ911-1-11-111-1-111-1-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-111-1-111-1-1i−ii−ii−ii−i
χ1011-1-11-111-1-111-1-1-1-11111-1-1-1-1111-11-11111-1-1-1-11111-1-1-1-111-1-111-1-1−ii−ii−ii−ii
χ1111-1-11-111-1-111-1-1-1-11111-1-1-1-111-11-11-1-1-1-11111-1-1-1-1111111-1-111-1-1i−ii−i−ii−ii
χ1211-1-11-111-1-111-1-1-1-11111-1-1-1-111-11-11-1-1-1-11111-1-1-1-1111111-1-111-1-1−ii−iii−ii−i
χ1311-1-1-111-11-111-1-1-1-1-1-1-1-11111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111i−i−iii−i−ii
χ1411-1-1-111-11-111-1-1-1-1-1-1-1-11111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-111−iii−i−iii−i
χ1511-1-1-111-11-111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111i−i−ii−iii−i
χ1611-1-1-111-11-111-1-1-1-1-1-1-1-1111111-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111−iii−ii−i−ii
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+52−1−52-2-2-2-21−521−521+521+521−521−521+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
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+52-2-2-2-21+521+521−521−521+521+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
χ21222222-2-2-2-2222222222222222200000000000000000000-2-2-2-2-2-2-2-200000000
χ22222222-2-2-2-2−1+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+52−1−520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+521−521+521−521+521−521+5200000000
χ23222222-2-2-2-2−1+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+52−1−520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+521−521+521−521+521−521+5200000000
χ24222222-2-2-2-2−1−52−1+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+520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−521+521−521+521−521+521−5200000000
χ25222222-2-2-2-2−1−52−1+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+520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−521+521−521+521−521+521−5200000000
χ262222-2-22-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521+521−521+5200000000
χ272222-2-22-2-22−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52-2-2221−521−521+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+52−1−521−521+521−521+5200000000
χ282222-2-22-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521−521+521−5200000000
χ292222-2-22-2-22−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52-2-2221+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+521+521−521+521−5200000000
χ302222-2-2-222-2222222-2-2-2-2-2-2-2-22200000000000000000000-2-2-2-2222200000000
χ312222-2-2-222-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+521−521+52−1+52−1−52−1+52−1−5200000000
χ322222-2-2-222-2−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+521−521+52−1+52−1−52−1+52−1−5200000000
χ332222-2-2-222-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−521+521−52−1−52−1+52−1−52−1+5200000000
χ342222-2-2-222-2−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−521+521−52−1−52−1+52−1−52−1+5200000000
χ3522-2-22-222-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−522-22-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−521−521+5200000000
χ3622-2-22-222-2-2−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52-22-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−1+52−1−521−521+5200000000
χ3722-2-22-222-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+522-22-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−52−1−52−1+521+521−5200000000
χ3822-2-22-222-2-2−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52-22-221+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+521+521−52−1−52−1+521+521−5200000000
χ3922-2-22-2-2-22222-2-2-2-22222-2-2-2-22200000000000000000000-2-222-2-22200000000
χ4022-2-22-2-2-222−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+52−1+52−1−521−521+52−1+52−1−5200000000
χ4122-2-22-2-2-222−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+52−1+52−1−521−521+52−1+52−1−5200000000
χ4222-2-22-2-2-222−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−52−1−52−1+521+521−52−1−52−1+5200000000
χ4322-2-22-2-2-222−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−52−1−52−1+521+521−52−1−52−1+5200000000
χ4422-2-2-222-22-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−522-2-22−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1−5200000000
χ4522-2-2-222-22-2−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52-222-21−521−521+521+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+521−521+52−1+52−1−5200000000
χ4622-2-2-222-22-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+522-2-22−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1+5200000000
χ4722-2-2-222-22-2−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52-222-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−521+521−52−1−52−1+5200000000
χ4822-2-2-22-22-2222-2-2-2-2-2-2-2-222222200000000000000000000-2-22222-2-200000000
χ4922-2-2-22-22-22−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−520000ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521+52−1+52−1−52−1+52−1−521−521+5200000000
χ5022-2-2-22-22-22−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−520000−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521+52−1+52−1−52−1+52−1−521−521+5200000000
χ5122-2-2-22-22-22−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+520000−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521−52−1−52−1+52−1−52−1+521+521−5200000000
χ5222-2-2-22-22-22−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+520000ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521−52−1−52−1+52−1−52−1+521+521−5200000000
χ534-44-4000000444-44-400000000-4-4000000000000000000000000000000000000
χ544-44-4000000−1+5−1−5−1+51−5−1−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+5000000000000000000000000000000000000
χ554-44-4000000−1+5−1−5−1+51−5−1−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+5000000000000000000000000000000000000
χ564-44-4000000−1−5−1+5−1−51+5−1+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−5000000000000000000000000000000000000
χ574-44-4000000−1−5−1+5−1−51+5−1+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−5000000000000000000000000000000000000
χ584-4-4400000044-44-4400000000-4-4000000000000000000000000000000000000
χ594-4-44000000−1+5−1−51−5−1+51+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ181−51+5000000000000000000000000000000000000
χ604-4-44000000−1+5−1−51−5−1+51+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ181−51+5000000000000000000000000000000000000
χ614-4-44000000−1−5−1+51+5−1−51−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ141+51−5000000000000000000000000000000000000
χ624-4-44000000−1−5−1+51+5−1−51−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ141+51−5000000000000000000000000000000000000

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