Finite Group Databasebeta

← Group #72243897

Character table — Group #72243897

Order 8748.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size12666666669991218181818181818181818181818181818183636363636363654545454545454545454545454545454545454548181108108108108108108108108108108108162162162162162162162162243243243243243243486486486486486486
order133399999923333333336999999918181839999993333666699991818181818181818663339999999966181818181818226666666666
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111−1+i32−1−i3211111−1+i32−1−i32111111−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ411111111111−1+i32−1−i3211111−1+i32−1−i32111111−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i3211111111−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321+i321−i321+i32
χ511111111111−1−i32−1+i3211111−1−i32−1+i32111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ611111111111−1−i32−1+i3211111−1−i32−1+i32111111−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i3211111111−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321−i321+i321−i32
χ71111111111-1111111111-11111111-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-11-11-11-111-1-1
χ81111111111-1111111111-11111111-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-11-11-11-1-111
χ91111111111-1−1+i32−1−i3211111−1+i32−1−i32-111111−1+i32−1−i32-1-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321+i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i321-1−1+i32−1−i321−i321+i32
χ101111111111-1−1+i32−1−i3211111−1+i32−1−i32-111111−1+i32−1−i32-1-1-111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11−i321+i321−1+i32−1−i3211−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i32-111−i321+i32−1+i32−1−i32
χ111111111111-1−1−i32−1+i3211111−1−i32−1+i32-111111−1−i32−1+i32-1-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321−i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i321-1−1−i32−1+i321+i321−i32
χ121111111111-1−1−i32−1+i3211111−1−i32−1+i32-111111−1−i32−1+i32-1-1-111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11+i321−i321−1−i32−1+i3211−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i32-111+i321−i32−1−i32−1+i32
χ1322222222220222222-12202222222000-12-1-1-12222-1-1000022220000000000-1-1-1-1-1-1-1-1-1-1-1000000000202020-100-1-1
χ1422222222220222222-12202222222000-12-1-1-12222-1-1000022220000000000-1-1-1-1-1-1-1-1-1-1-1000000000-20-20-2010011
χ1522222222220−1+i3−1−i32222-1−1+i3−1−i3022222−1+i3−1−i3000-12-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i320000−1+i3−1+i3−1−i3−1−i30000000000-11−i321+i32-1-11−i321−i321−i321+i321+i321+i3200000000020−1+i30−1−i30-1001−i321+i32
χ1622222222220−1+i3−1−i32222-1−1+i3−1−i3022222−1+i3−1−i3000-12-1-1-1−1+i3−1−i3−1+i3−1−i31−i321+i320000−1+i3−1+i3−1−i3−1−i30000000000-11−i321+i32-1-11−i321−i321−i321+i321+i321+i32000000000-201−i301+i30100−1+i32−1−i32
χ1722222222220−1−i3−1+i32222-1−1−i3−1+i3022222−1−i3−1+i3000-12-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i320000−1−i3−1−i3−1+i3−1+i30000000000-11+i321−i32-1-11+i321+i321+i321−i321−i321−i3200000000020−1−i30−1+i30-1001+i321−i32
χ1822222222220−1−i3−1+i32222-1−1−i3−1+i3022222−1−i3−1+i3000-12-1-1-1−1−i3−1+i3−1−i3−1+i31+i321−i320000−1−i3−1−i3−1+i3−1+i30000000000-11+i321−i32-1-11+i321+i321+i321−i321−i321−i32000000000-201+i301−i30100−1−i32−1+i32
χ192222222-1-1-12222-1-1-1222222-1-1-1-1-12222-1222-1-1-1-1222-1-1-12-12-1-1-1-122-1-1-122-1-1-1-1-12-1-12-1-1-1-1-1-12-12-1000000000000
χ202222222-1-1-12−1+i3−1−i32-1-1-12−1+i3−1−i3222-1-1-11−i321+i322222-12221−i321+i321−i321+i32−1+i3−1−i32-1-1-1−1+i31−i32−1−i31+i32-1-1-122-1-1-1−1+i3−1−i3-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i321−i321+i321−i321+i32−1+i31−i32−1−i31+i32000000000000
χ212222222-1-1-12−1−i3−1+i32-1-1-12−1−i3−1+i3222-1-1-11+i321−i322222-12221+i321−i321+i321−i32−1−i3−1+i32-1-1-1−1−i31+i32−1+i31−i32-1-1-122-1-1-1−1−i3−1+i3-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i321+i321−i321+i321−i32−1−i31+i32−1+i31−i32000000000000
χ222222222-1-1-1-2222-1-1-1222-222-1-1-1-1-1-2-2-22-1222-1-1-1-122-21112-12-1111-2-2111-2-2-1-1-1-1-12-1-12-1-11111-21-21000000000000
χ232222222-1-1-1-2−1+i3−1−i32-1-1-12−1+i3−1−i3-222-1-1-11−i321+i32-2-2-22-12221−i321+i321−i321+i32−1+i3−1−i3-2111−1+i31−i32−1−i31+i32111-2-21111−i31+i3-11−i321+i32-1-1−1+i31−i321−i32−1−i31+i321+i32−1+i32−1−i32−1+i32−1−i321−i3−1+i321+i3−1−i32000000000000
χ242222222-1-1-1-2−1−i3−1+i32-1-1-12−1−i3−1+i3-222-1-1-11+i321−i32-2-2-22-12221+i321−i321+i321−i32−1−i3−1+i3-2111−1−i31+i32−1+i31−i32111-2-21111+i31−i3-11+i321−i32-1-1−1−i31+i321+i32−1+i31−i321−i32−1−i32−1+i32−1−i32−1+i321+i3−1−i321−i3−1+i32000000000000
χ252222-1-1-12222222-1-1-12222-1-1-1-1-122-1-1-122-1-1-122-1-1222-1-1-1-1-1-1-1222-1-1-1-1-122-1-1-12-1-12-1-12-1-1-122-1-1-1-1000000000000
χ262222-1-1-12222−1+i3−1−i32-1-1-12−1+i3−1−i32-1-1-1-1-1−1+i3−1−i3-1-1-122-1-1-1−1+i3−1−i31−i321+i32−1+i3−1−i32-1-1-11−i321−i321+i321+i32222-1-1-1-1-1−1+i3−1−i3-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32000000000000
χ272222-1-1-12222−1−i3−1+i32-1-1-12−1−i3−1+i32-1-1-1-1-1−1−i3−1+i3-1-1-122-1-1-1−1−i3−1+i31+i321−i32−1−i3−1+i32-1-1-11+i321+i321−i321−i32222-1-1-1-1-1−1−i3−1+i3-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32000000000000
χ282222-1-1-1222-2222-1-1-1222-2-1-1-1-1-12211122-1-1-122-1-122-2111-1-1-1-1-2-2-211111-2-2-1-1-12-1-12-1-12-111-2-21111000000000000
χ292222-1-1-1222-2−1+i3−1−i32-1-1-12−1+i3−1−i3-2-1-1-1-1-1−1+i3−1−i311122-1-1-1−1+i3−1−i31−i321+i32−1+i3−1−i3-21111−i321−i321+i321+i32-2-2-2111111−i31+i3-11−i321+i322-11−i32−1+i31−i321+i32−1−i31+i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i32000000000000
χ302222-1-1-1222-2−1−i3−1+i32-1-1-12−1−i3−1+i3-2-1-1-1-1-1−1−i3−1+i311122-1-1-1−1−i3−1+i31+i321−i32−1−i3−1+i3-21111+i321+i321−i321−i32-2-2-2111111+i31−i3-11+i321−i322-11+i32−1−i31+i321−i32−1+i31−i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i32000000000000
χ312222-1-1-1-1-1-122222222222-1-1-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1222222-12-12-1-1-1-1-1-1-1-122-122-12-1-1-1-1-1-1-1-1-1-1-12-12000000000000
χ322222-1-1-1-1-1-12222-1-1-12222-1-1222-1-1-1-1-12-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-12-1-1222-1-1-1-1-1-1000000000000
χ332222-1-1-1-1-1-12−1+i3−1−i322222−1+i3−1−i32-1-1-1-1-11−i321+i32-1-1-12-1-1-1-11−i321+i321−i321+i32−1+i3−1−i322221−i32−1+i31+i32−1−i3-1-1-1-1-1-1-1-1−1+i3−1−i3-1−1+i3−1−i3-121−i321−i321−i321+i321+i321+i321−i321+i321−i321+i321−i32−1+i31+i32−1−i3000000000000
χ342222-1-1-1-1-1-12−1+i3−1−i32-1-1-12−1+i3−1−i32-1-12221−i321+i32-1-1-12-1-1-1-11−i321+i32−1+i3−1−i3−1+i3−1−i32-1-1-11−i321−i321+i321+i32-1-1-1-1-1222−1+i3−1−i321−i321+i32-1-11−i321−i32−1+i31+i321+i32−1−i3−1+i3−1−i31−i321+i321−i321−i321+i321+i32000000000000
χ352222-1-1-1-1-1-12−1−i3−1+i322222−1−i3−1+i32-1-1-1-1-11+i321−i32-1-1-12-1-1-1-11+i321−i321+i321−i32−1−i3−1+i322221+i32−1−i31−i32−1+i3-1-1-1-1-1-1-1-1−1−i3−1+i3-1−1−i3−1+i3-121+i321+i321+i321−i321−i321−i321+i321−i321+i321−i321+i32−1−i31−i32−1+i3000000000000
χ362222-1-1-1-1-1-12−1−i3−1+i32-1-1-12−1−i3−1+i32-1-12221+i321−i32-1-1-12-1-1-1-11+i321−i32−1−i3−1+i3−1−i3−1+i32-1-1-11+i321+i321−i321−i32-1-1-1-1-1222−1−i3−1+i321+i321−i32-1-11+i321+i32−1−i31−i321−i32−1+i3−1−i3−1+i31+i321−i321+i321+i321−i321−i32000000000000
χ372222-1-1-1-1-1-1-2222222222-2-1-1-1-1-1-1-11112-1-1-1-1-1-1-1-122-2-2-2-2-12-1211111111-2-2-122-12-1-1-1-1-1-111111-21-2000000000000
χ382222-1-1-1-1-1-1-2222-1-1-1222-2-1-1222-1-11112-1-1-1-1-1-12222-2111-1-1-1-111111-2-2-2-2-22-1-1-1-1-1-12-1-12-2-2111111000000000000
χ392222-1-1-1-1-1-1-2−1+i3−1−i322222−1+i3−1−i3-2-1-1-1-1-11−i321+i321112-1-1-1-11−i321+i321−i321+i32−1+i3−1−i3-2-2-2-21−i32−1+i31+i32−1−i3111111111−i31+i3-1−1+i3−1−i3-121−i321−i321−i321+i321+i321+i32−1+i32−1−i32−1+i32−1−i32−1+i321−i3−1−i321+i3000000000000
χ402222-1-1-1-1-1-1-2−1+i3−1−i32-1-1-12−1+i3−1−i3-2-1-12221−i321+i321112-1-1-1-11−i321+i32−1+i3−1−i3−1+i3−1−i3-21111−i321−i321+i321+i3211111-2-2-21−i31+i321−i321+i32-1-11−i321−i32−1+i31+i321+i32−1−i31−i31+i3−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32000000000000
χ412222-1-1-1-1-1-1-2−1−i3−1+i322222−1−i3−1+i3-2-1-1-1-1-11+i321−i321112-1-1-1-11+i321−i321+i321−i32−1−i3−1+i3-2-2-2-21+i32−1−i31−i32−1+i3111111111+i31−i3-1−1−i3−1+i3-121+i321+i321+i321−i321−i321−i32−1−i32−1+i32−1−i32−1+i32−1−i321+i3−1+i321−i3000000000000
χ422222-1-1-1-1-1-1-2−1−i3−1+i32-1-1-12−1−i3−1+i3-2-1-12221+i321−i321112-1-1-1-11+i321−i32−1−i3−1+i3−1−i3−1+i3-21111+i321+i321−i321−i3211111-2-2-21+i31−i321+i321−i32-1-11+i321+i32−1−i31−i321−i32−1+i31+i31−i3−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000000000
χ434444444-2-2-20444-2-2-2-244044-2-2-2-2-2000-2-2-2-2-2-2-2-2-2-2-200004-24-2000000000011111-211-21100000000000000000000
χ444444444-2-2-20−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i3044-2-2-21−i31+i3000-2-2-2-2-21−i31+i31−i31+i31−i31+i30000−2+2i31−i3−2−2i31+i300000000001−1+i32−1−i32111−i3−1+i32−1+i321+i3−1−i32−1−i3200000000000000000000
χ454444444-2-2-20−2−2i3−2+2i34-2-2-2-2−2−2i3−2+2i3044-2-2-21+i31−i3000-2-2-2-2-21+i31−i31+i31−i31+i31−i30000−2−2i31+i3−2+2i31−i300000000001−1−i32−1+i32111+i3−1−i32−1−i321−i3−1+i32−1+i3200000000000000000000
χ464444-2-2-24440444-2-2-2-2440-2-2-2-2-244000-2411144-2-2-2-20000-2-2-2-20000000000111-211-211-2100000000000000000000
χ474444-2-2-24440−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i30-2-2-2-2-2−2+2i3−2−2i3000-24111−2+2i3−2−2i31−i31+i31−i31+i300001−i31−i31+i31+i300000000001−1+i32−1−i32-21−1+i321−i3−1+i32−1−i321+i3−1−i3200000000000000000000
χ484444-2-2-24440−2−2i3−2+2i34-2-2-2-2−2−2i3−2+2i30-2-2-2-2-2−2−2i3−2+2i3000-24111−2−2i3−2+2i31+i31−i31+i31−i300001+i31+i31−i31−i300000000001−1−i32−1+i32-21−1−i321+i3−1−i32−1+i321−i3−1+i3200000000000000000000
χ494444-2-2-2-2-2-20444444-2440-2-2-2-2-2-2-2000-2-2111-2-2-2-2-2-20000-24-2400000000001-2-21-211111100000000000000000000
χ504444-2-2-2-2-2-20444-2-2-2-2440-2-2444-2-2000-2-2111-2-244-2-20000-2-2-2-20000000000-2111111-211-200000000000000000000
χ514444-2-2-2-2-2-20−2+2i3−2−2i34444-2−2+2i3−2−2i30-2-2-2-2-21−i31+i3000-2-21111−i31+i31−i31+i31−i31+i300001−i3−2+2i31+i3−2−2i3000000000011−i31+i31-2−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000
χ524444-2-2-2-2-2-20−2+2i3−2−2i34-2-2-2-2−2+2i3−2−2i30-2-24441−i31+i3000-2-21111−i31+i3−2+2i3−2−2i31−i31+i300001−i31−i31+i31+i30000000000-2−1+i32−1−i3211−1+i32−1+i321−i3−1−i32−1−i321+i300000000000000000000
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Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.