Finite Group Databasebeta

← Group #10602696

Character table — Group #10602696

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11112222222222222244444444444488888888888888888888888888888820202020404040404040
order1222224444551010101010101010101020202020202020204444442020202020202020202020202020202020202020202020204444228888
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ41111111111111111111111111111111-11-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ6111111111111111111111111111111-11-11-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111
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+52−1−52−1−52−1−52−1−522-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+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+52−1−52−1−52−1−52−1−52-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+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+52−1−52−1−52−1−52−1−52-2-2-2-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000000000
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+522-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+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+52-22-22-2-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−520000000000
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+52-2-2-2-2221+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+520000000000
χ17222222-2-2-2-2222222222222-2-2-2-2-2-2-2-200002-2000000000000000022-2-222-2-20000000000
χ18222222-2-2-2-2222222222222-2-2-2-2-2-2-2-20000-220000000000000000-2-222-2-2220000000000
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+5200002-2ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+521−521−52−1−52−1−521+521+520000000000
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+5200002-2−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+521−521−52−1−52−1−521+521+520000000000
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+520000-22ζ6−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+52−1−52−1−520000000000
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+520000-22−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+52−1−52−1−520000000000
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+521−521−521−521−5200002-2−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−521+521+52−1+52−1+521−521−520000000000
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+521−521−521−521−5200002-2ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−521+521+52−1+52−1+521−521−520000000000
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+521−521−521−521−520000-22−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+520000000000
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+521−521−521−521−520000-22ζ2−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+520000000000
χ272222-2-22-22-222222222-2-2-2-222-2-222-2-2020-200000022220000-2-2-2-2000000000000000000
χ282222-2-22-22-222222222-2-2-2-222-2-222-2-20-202000000-2-2-2-200002222000000000000000000
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+52020-200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ180000000000
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+52020-200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ180000000000
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+520-20200ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−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+ζ180000000000
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+520-20200−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−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−ζ180000000000
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+521−521−52020-200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ6+ζ14ζ6−ζ140000000000
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+521−521−52020-200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ6−ζ14−ζ6+ζ140000000000
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+521−521−520-20200−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−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+ζ140000000000
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+521−521−520-20200ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−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−ζ140000000000
χ372222-2-2-22-2222222222-2-2-2-2-2-222-2-22220-200022220000-2-2-2-20000000000000000000000
χ382222-2-2-22-2222222222-2-2-2-2-2-222-2-222-202000-2-2-2-2000022220000000000000000000000
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+52−1−52−1−5220-2000−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−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+52−1−52−1−5220-2000−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−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+52−1−52−1−52-2020001−521−521+521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−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+52−1−52−1−52-2020001−521−521+521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+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+5220-2000−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ141+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−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+5220-2000−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ141+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−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+52-2020001+521+521−521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−1−52−1−52−1+52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ6−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+52-2020001+521+521−521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−1−52−1−52−1+52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ6+ζ140000000000
χ4722-2-22-222-2-22222-2-2-2-22-22-22-22-22-22-200000000000000000000000000000000002-20000
χ4822-2-22-222-2-22222-2-2-2-22-22-22-22-22-22-20000000000000000000000000000000000-220000
χ4922-2-22-2-2-2222222-2-2-2-22-22-2-22-22-22-220000000000000000000000000000002i2i−2i−2i000000
χ5022-2-22-2-2-2222222-2-2-2-22-22-2-22-22-22-22000000000000000000000000000000−2i−2i2i2i000000
χ5122-2-2-222-2-222222-2-2-2-2-22-222-2-222-2-220000000000000000000000000000000000002i−2i00
χ5222-2-2-222-2-222222-2-2-2-2-22-222-2-222-2-22000000000000000000000000000000000000−2i2i00
χ5322-2-2-22-222-22222-2-2-2-2-22-22-222-2-222-2000000000000000000000000000000000000002i−2i
χ5422-2-2-22-222-22222-2-2-2-2-22-22-222-2-222-200000000000000000000000000000000000000−2i2i
χ5544-4-44-444-4-4−1+5−1−5−1+5−1−51−51+51−51+5−1+51−5−1−51+5−1+51−5−1+51−5−1−51+5−1−51+50000000000000000000000000000000000000000
χ5644-4-44-444-4-4−1−5−1+5−1−5−1+51+51−51+51−5−1−51+5−1+51−5−1−51+5−1−51+5−1+51−5−1+51−50000000000000000000000000000000000000000
χ5744-4-44-4-4-444−1+5−1−5−1+5−1−51−51+51−51+5−1+51−5−1−51+51−5−1+51−5−1+51+5−1−51+5−1−50000000000000000000000000000000000000000
χ5844-4-44-4-4-444−1−5−1+5−1−5−1+51+51−51+51−5−1−51+5−1+51−51+5−1−51+5−1−51−5−1+51−5−1+50000000000000000000000000000000000000000
χ5944-4-4-444-4-44−1+5−1−5−1+5−1−51−51+51−51+51−5−1+51+5−1−5−1+51−51−5−1+5−1−51+51+5−1−50000000000000000000000000000000000000000
χ6044-4-4-444-4-44−1−5−1+5−1−5−1+51+51−51+51−51+5−1−51−5−1+5−1−51+51+5−1−5−1+51−51−5−1+50000000000000000000000000000000000000000
χ6144-4-4-44-444-4−1+5−1−5−1+5−1−51−51+51−51+51−5−1+51+5−1−51−5−1+5−1+51−51+5−1−5−1−51+50000000000000000000000000000000000000000
χ6244-4-4-44-444-4−1−5−1+5−1−5−1+51+51−51+51−51+5−1−51−5−1+51+5−1−5−1−51+51−5−1+5−1+51−50000000000000000000000000000000000000000
χ634-44-400000044-4-444-4-40000000000000000000000000000000000000000002i−2i2i−2i000000
χ644-44-400000044-4-444-4-4000000000000000000000000000000000000000000−2i2i−2i2i000000
χ654-4-4400000044-4-4-4-4440000000000000000000000000000000000000000002-2-22000000
χ664-4-4400000044-4-4-4-444000000000000000000000000000000000000000000-222-2000000
χ678-88-8000000−2+25−2−252−252+25−2+25−2−252−252+250000000000000000000000000000000000000000000000000000
χ688-88-8000000−2−25−2+252+252−25−2−25−2+252+252−250000000000000000000000000000000000000000000000000000
χ698-8-88000000−2+25−2−252−252+252−252+25−2+25−2−250000000000000000000000000000000000000000000000000000
χ708-8-88000000−2−25−2+252+252−252+252−25−2−25−2+250000000000000000000000000000000000000000000000000000

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