Finite Group Databasebeta

← Group #10602670

Character table — Group #10602670

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222222222222244444444444488888888888888888888888888888820202020404040404040
order1222224444551010101010101010101020202020202020202244441010101010101010202020202020202020202020202020204444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111-1-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-11-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ6111111111111111111111111111111-11-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ8111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
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+52−1−52−1−52−1−52−1−52222222−1+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+52−1−52−1−520000000000
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+52−1−52−1−52−1−52−1−522-2-2-22-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000
χ112222222222−1+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+52−1−52−1−52−1−52−1−52-22-2-2-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000
χ122222222222−1+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+52−1−52−1−52−1−52−1−52-2-222-2-21−521−521+521+521−521−521+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+520000000000
χ132222222222−1−52−1+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+52222222−1−52−1−52−1+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+520000000000
χ142222222222−1−52−1+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+522-2-2-22-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000
χ152222222222−1−52−1+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+52-22-2-2-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000
χ162222222222−1−52−1+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+52-2-222-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521−521−521+521+521−521−520000000000
χ17222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2002-2000000000022-2-222-2-2000000000000000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200-220000000000-2-222-2-222000000000000000000
χ19222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52002-200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
χ20222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52002-200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+521−521−52−1−52−1−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ21222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200-2200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−52−1+52−1+521+521+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ22222222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200-2200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−52−1+52−1+521+521+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
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+521+521+521+521+521−521−521−521−52002-200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−521+521+52−1+52−1+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
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+521+521+521+521+521−521−521−521−52002-200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−521+521+52−1+52−1+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
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+521+521+521+521+521−521−521−521−5200-2200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+52−1−52−1−521−521−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
χ26222222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200-2200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+52−1−52−1−521−521−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
χ272222-2-22-22-222222222-2-2-2-222-2-222-2-202000-200002222000000000000-2-2-2-20000000000
χ282222-2-22-22-222222222-2-2-2-222-2-222-2-20-200020000-2-2-2-200000000000022220000000000
χ292222-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5202000-2ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+520000000000
χ302222-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+5202000-2−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+520000000000
χ312222-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+520-20002ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−520000000000
χ322222-2-22-22-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+521−521−52−1−52−1−521+521+520-20002−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−520000000000
χ332222-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5202000-2−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−520000000000
χ342222-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−5202000-2ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−520000000000
χ352222-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−520-20002−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+520000000000
χ362222-2-22-22-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−521+521+52−1+52−1+521−521−520-20002ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+520000000000
χ372222-2-2-22-2222222222-2-2-2-2-2-222-2-2222000-202222000000000000-2-2-2-200000000000000
χ382222-2-2-22-2222222222-2-2-2-2-2-222-2-222-200020-2-2-2-2000000000000222200000000000000
χ392222-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+52−1+521+521+52−1−52−1−522000-20−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ402222-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+52−1+521+521+52−1−52−1−522000-20−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
χ412222-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+52−1+521+521+52−1−52−1−52-2000201−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000000000
χ422222-2-2-22-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−52−1+52−1+521+521+52−1−52−1−52-2000201−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000000000
χ432222-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−52−1−521−521−52−1+52−1+522000-20−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
χ442222-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−52−1−521−521−52−1+52−1+522000-20−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
χ452222-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−52−1−521−521−52−1+52−1+52-2000201+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000000000
χ462222-2-2-22-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+52−1−52−1−521−521−52−1+52−1+52-2000201+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000000000
χ472-22-22-22-2-2222-2-2-2-2222-22-22-22-22-22-20000000000000000000000000000000000002i−2i00
χ482-22-22-22-2-2222-2-2-2-2222-22-22-22-22-22-2000000000000000000000000000000000000−2i2i00
χ492-22-22-2-222-222-2-2-2-2222-22-2-22-22-22-22000000000000000000000000000000000000002i−2i
χ502-22-22-2-222-222-2-2-2-2222-22-2-22-22-22-2200000000000000000000000000000000000000−2i2i
χ512-22-2-2222-2-222-2-2-2-222-22-222-2-222-2-2200000000000000000000000000000000002i−2i0000
χ522-22-2-2222-2-222-2-2-2-222-22-222-2-222-2-220000000000000000000000000000000000−2i2i0000
χ532-22-2-22-2-22222-2-2-2-222-22-22-222-2-222-200000000000000000000000000000022-2-2000000
χ542-22-2-22-2-22222-2-2-2-222-22-22-222-2-222-2000000000000000000000000000000-2-222000000
χ5544-4-400000044-4-444-4-40000000000000000000000000000000000000000002i−2i2i−2i000000
χ5644-4-400000044-4-444-4-4000000000000000000000000000000000000000000−2i2i−2i2i000000
χ574-44-44-44-4-44−1+5−1−51−51+51−51+5−1+5−1−5−1+51−5−1−51+5−1+51−5−1+51−5−1−51+5−1−51+50000000000000000000000000000000000000000
χ584-44-44-44-4-44−1−5−1+51+51−51+51−5−1−5−1+5−1−51+5−1+51−5−1−51+5−1−51+5−1+51−5−1+51−50000000000000000000000000000000000000000
χ594-44-44-4-444-4−1+5−1−51−51+51−51+5−1+5−1−5−1+51−5−1−51+51−5−1+51−5−1+51+5−1−51+5−1−50000000000000000000000000000000000000000
χ604-44-44-4-444-4−1−5−1+51+51−51+51−5−1−5−1+5−1−51+5−1+51−51+5−1−51+5−1−51−5−1+51−5−1+50000000000000000000000000000000000000000
χ614-44-4-4444-4-4−1+5−1−51−51+51−51+5−1+5−1−51−5−1+51+5−1−5−1+51−51−5−1+5−1−51+51+5−1−50000000000000000000000000000000000000000
χ624-44-4-4444-4-4−1−5−1+51+51−51+51−5−1−5−1+51+5−1−51−5−1+5−1−51+51+5−1−5−1+51−51−5−1+50000000000000000000000000000000000000000
χ634-44-4-44-4-444−1+5−1−51−51+51−51+5−1+5−1−51−5−1+51+5−1−51−5−1+5−1+51−51+5−1−5−1−51+50000000000000000000000000000000000000000
χ644-44-4-44-4-444−1−5−1+51+51−51+51−5−1−5−1+51+5−1−51−5−1+51+5−1−5−1−51+51−5−1+5−1+51−50000000000000000000000000000000000000000
χ654-4-440000004444-4-4-4-40000000000000000000000000000000000000000002i−2i−2i2i000000
χ664-4-440000004444-4-4-4-4000000000000000000000000000000000000000000−2i2i2i−2i000000
χ6788-8-8000000−2+25−2−252−252+25−2+25−2−252−252+250000000000000000000000000000000000000000000000000000
χ6888-8-8000000−2−25−2+252+252−25−2−25−2+252+252−250000000000000000000000000000000000000000000000000000
χ698-8-88000000−2+25−2−25−2+25−2−252−252+252−252+250000000000000000000000000000000000000000000000000000
χ708-8-88000000−2−25−2+25−2−25−2+252+252−252+252−250000000000000000000000000000000000000000000000000000

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