Finite Group Databasebeta

← Group #72243953

Character table — Group #72243953

Order 2916.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1222224444666699912121212121212121212121212121212181818181818181818181818181827272736363636363636365454545454545454545454548181162162162243243243
order133333333339992333333999999999999333366669999992663399999966618181818181818181866666266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-11111111111-111111111111-1-1-1-1-1-1-1-1
χ3111111111111111−1+i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ4111111111111111−1+i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i321111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i32-11−i321+i32-11−i321+i32
χ5111111111111111−1−i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ6111111111111111−1−i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i321111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i32-11+i321−i32-11+i321−i32
χ711111111111111-11111111111111111111111-1-1-1-11111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1
χ811111111111111-11111111111111111111111-1-1-1-1111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ911111111111111-1−1+i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ1011111111111111-1−1+i32−1−i321111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11−i321+i32-1-1-11−i321−i321−i321+i321+i321+i321−i321+i32-11−i321+i321−1+i32−1−i32
χ1111111111111111-1−1−i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ1211111111111111-1−1−i32−1+i321111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11+i321−i32-1-1-11+i321+i321+i321−i321−i321−i321+i321−i32-11+i321−i321−1−i32−1+i32
χ1322222222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-102222-1-1-1-1-1-1022-1-1-1-1-1-1-1-1-100000000
χ1422222222222-1-1-12−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i322221−i321−i321−i321+i321+i321+i320−1+i3−1−i3−1+i3−1−i31−i321−i321−i321+i321+i321+i320−1+i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i3200000000
χ1522222222222-1-1-12−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i322221+i321+i321+i321−i321−i321−i320−1−i3−1+i3−1−i3−1+i31+i321+i321+i321−i321−i321−i320−1−i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i3200000000
χ1622222222222-1-1-1-2222222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-10-2-222-1-1-1-1-1-10-2-211111111100000000
χ1722222222222-1-1-1-2−1+i3−1−i32222-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3-2-2-2-21−i321−i321−i321+i321+i321+i3201−i31+i3−1+i3−1−i31−i321−i321−i321+i321+i321+i3201−i31+i3111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000
χ1822222222222-1-1-1-2−1−i3−1+i32222-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3-2-2-2-21+i321+i321+i321−i321−i321−i3201+i31−i3−1−i3−1+i31+i321+i321+i321−i321−i321−i3201+i31−i3111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000
χ192222222222-1222022-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-10000222222200-1-1-1-1-1-1-1-120000000000022-1-1-1000
χ202222222222-1222022-1-1-1-1222-1-1-1-1-1-1-1-1-122-1-10000222222-200-1-1-1-1-1-1-1-1-200000000000-2-2111000
χ212222222222-12220−1+i3−1−i3-1-1-1-1222-1-1-1-1-1-1-1-1-1−1+i3−1−i31−i321+i320000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i32001−i321+i321−i321−i321−i321+i321+i321+i32200000000000−1+i3−1−i3-11−i321+i32000
χ222222222222-12220−1+i3−1−i3-1-1-1-1222-1-1-1-1-1-1-1-1-1−1+i3−1−i31−i321+i320000−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-2001−i321+i321−i321−i321−i321+i321+i321+i32-2000000000001−i31+i31−1+i32−1−i32000
χ232222222222-12220−1−i3−1+i3-1-1-1-1222-1-1-1-1-1-1-1-1-1−1−i3−1+i31+i321−i320000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i32001+i321−i321+i321+i321+i321−i321−i321−i32200000000000−1−i3−1+i3-11+i321−i32000
χ242222222222-12220−1−i3−1+i3-1-1-1-1222-1-1-1-1-1-1-1-1-1−1−i3−1+i31+i321−i320000−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-2001+i321−i321+i321+i321+i321−i321−i321−i32-2000000000001+i31−i31−1−i32−1+i32000
χ252-1-1-1222-1-1-122-1-12222-1-1-12-1-1222-1-1-1-1-1-1-1-122-1-1-122-1-12-1-1022-1-12-1-12-1-10-1-12-1-12-1-12-1-100000000
χ262-1-1-1222-1-1-122-1-12−1+i3−1−i32-1-1-12-1-1222-1-1-1-1-1-11−i321+i32−1+i3−1−i3-1-1-12−1+i31−i321−i32−1−i31+i321+i320−1+i3−1−i31−i321+i32−1+i31−i321−i32−1−i31+i321+i3201−i321+i322-1-1−1+i31−i321−i32−1−i31+i321+i3200000000
χ272-1-1-1222-1-1-122-1-12−1−i3−1+i32-1-1-12-1-1222-1-1-1-1-1-11+i321−i32−1−i3−1+i3-1-1-12−1−i31+i321+i32−1+i31−i321−i320−1−i3−1+i31+i321−i32−1−i31+i321+i32−1+i31−i321−i3201+i321−i322-1-1−1−i31+i321+i32−1+i31−i321−i3200000000
χ282-1-1-1222-1-1-122-1-1-2222-1-1-12-1-1222-1-1-1-1-1-1-1-122111-22-1-12-1-10-2-2-1-12-1-12-1-1011-211-211-21100000000
χ292-1-1-1222-1-1-122-1-1-2−1+i3−1−i32-1-1-12-1-1222-1-1-1-1-1-11−i321+i32−1+i3−1−i3111-2−1+i31−i321−i32−1−i31+i321+i3201−i31+i31−i321+i32−1+i31−i321−i32−1−i31+i321+i320−1+i32−1−i32-2111−i3−1+i32−1+i321+i3−1−i32−1−i3200000000
χ302-1-1-1222-1-1-122-1-1-2−1−i3−1+i32-1-1-12-1-1222-1-1-1-1-1-11+i321−i32−1−i3−1+i3111-2−1−i31+i321+i32−1+i31−i321−i3201+i31−i31+i321−i32−1−i31+i321+i32−1+i31−i321−i320−1−i32−1+i32-2111+i3−1−i32−1−i321−i3−1+i32−1+i3200000000
χ312-1-1-1222-1-1-12-12-12222-1-1-1-12-1-1-1-1222-1-1-1-1-122-1-1-12-12-1-12-1022-1-1-12-1-12-10-1-1-12-1-12-1-12-100000000
χ322-1-1-1222-1-1-12-12-12−1+i3−1−i32-1-1-1-12-1-1-1-1222-1-1-11−i321+i32−1+i3−1−i3-1-1-121−i32−1+i31−i321+i32−1−i31+i320−1+i3−1−i31−i321+i321−i32−1+i31−i321+i32−1−i31+i3201−i321+i32-12-11−i32−1+i31−i321+i32−1−i31+i3200000000
χ332-1-1-1222-1-1-12-12-12−1−i3−1+i32-1-1-1-12-1-1-1-1222-1-1-11+i321−i32−1−i3−1+i3-1-1-121+i32−1−i31+i321−i32−1+i31−i320−1−i3−1+i31+i321−i321+i32−1−i31+i321−i32−1+i31−i3201+i321−i32-12-11+i32−1−i31+i321−i32−1+i31−i3200000000
χ342-1-1-1222-1-1-12-12-1-2222-1-1-1-12-1-1-1-1222-1-1-1-1-122111-2-12-1-12-10-2-2-1-1-12-1-12-10111-211-211-2100000000
χ352-1-1-1222-1-1-12-12-1-2−1+i3−1−i32-1-1-1-12-1-1-1-1222-1-1-11−i321+i32−1+i3−1−i3111-21−i32−1+i31−i321+i32−1−i31+i3201−i31+i31−i321+i321−i32−1+i31−i321+i32−1−i31+i320−1+i32−1−i321-21−1+i321−i3−1+i32−1−i321+i3−1−i3200000000
χ362-1-1-1222-1-1-12-12-1-2−1−i3−1+i32-1-1-1-12-1-1-1-1222-1-1-11+i321−i32−1−i3−1+i3111-21+i32−1−i31+i321−i32−1+i31−i3201+i31−i31+i321−i321+i32−1−i31+i321−i32−1+i31−i320−1−i32−1+i321-21−1−i321+i3−1−i32−1+i321−i3−1+i3200000000
χ372-1-1-1222-1-1-12-1-122222-1-1-1-1-12-1-1-1-1-1-1222-1-122-1-1-12-1-12-1-12022-1-1-1-12-1-120-1-1-1-12-1-12-1-1200000000
χ382-1-1-1222-1-1-12-1-122−1+i3−1−i32-1-1-1-1-12-1-1-1-1-1-12221−i321+i32−1+i3−1−i3-1-1-121−i321−i32−1+i31+i321+i32−1−i30−1+i3−1−i31−i321+i321−i321−i32−1+i31+i321+i32−1−i301−i321+i32-1-121−i321−i32−1+i31+i321+i32−1−i300000000
χ392-1-1-1222-1-1-12-1-122−1−i3−1+i32-1-1-1-1-12-1-1-1-1-1-12221+i321−i32−1−i3−1+i3-1-1-121+i321+i32−1−i31−i321−i32−1+i30−1−i3−1+i31+i321−i321+i321+i32−1−i31−i321−i32−1+i301+i321−i32-1-121+i321+i32−1−i31−i321−i32−1+i300000000
χ402-1-1-1222-1-1-12-1-12-2222-1-1-1-1-12-1-1-1-1-1-1222-1-122111-2-1-12-1-120-2-2-1-1-1-12-1-1201111-211-211-200000000
χ412-1-1-1222-1-1-12-1-12-2−1+i3−1−i32-1-1-1-1-12-1-1-1-1-1-12221−i321+i32−1+i3−1−i3111-21−i321−i32−1+i31+i321+i32−1−i301−i31+i31−i321+i321−i321−i32−1+i31+i321+i32−1−i30−1+i32−1−i3211-2−1+i32−1+i321−i3−1−i32−1−i321+i300000000
χ422-1-1-1222-1-1-12-1-12-2−1−i3−1+i32-1-1-1-1-12-1-1-1-1-1-12221+i321−i32−1−i3−1+i3111-21+i321+i32−1−i31−i321−i32−1+i301+i31−i31+i321−i321+i321+i32−1−i31−i321−i32−1+i30−1−i32−1+i3211-2−1−i32−1−i321+i3−1+i32−1+i321−i300000000
χ434444444444-2-2-2-2044-2-2-2-2-2-2-211111111144-2-20000-2-2-2-2-2-2000-2-211111100000000000000000000
χ444444444444-2-2-2-20−2+2i3−2−2i3-2-2-2-2-2-2-2111111111−2+2i3−2−2i31−i31+i300001−i31−i31−i31+i31+i31+i30001−i31+i3−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3200000000000000000000
χ454444444444-2-2-2-20−2−2i3−2+2i3-2-2-2-2-2-2-2111111111−2−2i3−2+2i31+i31−i300001+i31+i31+i31−i31−i31−i30001+i31−i3−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3200000000000000000000
χ464-2-2-2444-2-2-2-24-2-2044-21114-2-2-2-2-2111111-2-2-2-200004-2-24-2-200011-211-21100000000000000000000
χ474-2-2-2444-2-2-2-24-2-20−2+2i3−2−2i3-21114-2-2-2-2-21111111−i31+i31−i31+i30000−2+2i31−i31−i3−2−2i31+i31+i3000−1+i32−1−i321−i3−1+i32−1+i321+i3−1−i32−1−i3200000000000000000000
χ484-2-2-2444-2-2-2-24-2-20−2−2i3−2+2i3-21114-2-2-2-2-21111111+i31−i31+i31−i30000−2−2i31+i31+i3−2+2i31−i31−i3000−1−i32−1+i321+i3−1−i32−1−i321−i3−1+i32−1+i3200000000000000000000
χ494-2-2-2444-2-2-2-2-24-2044-2111-24-2111-2-2-2111-2-2-2-20000-24-2-24-2000111-211-2100000000000000000000
χ504-2-2-2444-2-2-2-2-24-20−2+2i3−2−2i3-2111-24-2111-2-2-21111−i31+i31−i31+i300001−i3−2+2i31−i31+i3−2−2i31+i3000−1+i32−1−i32−1+i321−i3−1+i32−1−i321+i3−1−i3200000000000000000000
χ514-2-2-2444-2-2-2-2-24-20−2−2i3−2+2i3-2111-24-2111-2-2-21111+i31−i31+i31−i300001+i3−2−2i31+i31−i3−2+2i31−i3000−1−i32−1+i32−1−i321+i3−1−i32−1+i321−i3−1+i3200000000000000000000
χ524-2-2-2444-2-2-2-2-2-24044-2111-2-24111111-2-2-2-2-2-2-20000-2-24-2-240001111-211-200000000000000000000
χ534-2-2-2444-2-2-2-2-2-240−2+2i3−2−2i3-2111-2-24111111-2-2-21−i31+i31−i31+i300001−i31−i3−2+2i31+i31+i3−2−2i3000−1+i32−1−i32−1+i32−1+i321−i3−1−i32−1−i321+i300000000000000000000
χ544-2-2-2444-2-2-2-2-2-240−2−2i3−2+2i3-2111-2-24111111-2-2-21+i31−i31+i31−i300001+i31+i3−2−2i31−i31−i3−2+2i3000−1−i32−1+i32−1−i32−1−i321+i3−1+i32−1+i321−i300000000000000000000
χ556666-36-3-3-3-306660000000-3-3-30000000000000000000000060000000000-30000000000000000000
χ566666-36-3-3-3-306660000000-3-3-300000000000000000000000-6000000000030000000000000000000
χ5766-3-36-3-36-3-36000600-36-3-300000000000000006-3-3-30000000000000000000000000000000000000
χ5866-3-36-3-36-3-36000-600-36-3-30000000000000000-63330000000000000000000000000000000000000
χ596-36-36-3-3-36-36000600-3-36-30000000000000000-36-3-30000000000000000000000000000000000000
χ606-36-36-3-3-36-36000-600-3-36-300000000000000003-6330000000000000000000000000000000000000
χ616-3-366-3-3-3-366000600-3-3-360000000000000000-3-36-30000000000000000000000000000000000000
χ626-3-366-3-3-3-366000-600-3-3-36000000000000000033-630000000000000000000000000000000000000
χ6312121212-612-6-6-6-60-6-6-60000000333000000000000000000000000000000000000000000000000000000
χ641212-6-612-6-612-6-6-60000003-633000000000000000000000000000000000000000000000000000000000
χ651212-6-6-6-63-633000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000
χ661212-6-6-6-63-633000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ671212-6-6-6-63-633000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ6812-612-612-6-6-612-6-600000033-63000000000000000000000000000000000000000000000000000000000
χ6912-612-6-6-633-63000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ7012-612-6-6-633-63000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000
χ7112-612-6-6-633-63000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ7212-6-61212-6-6-6-612-6000000333-6000000000000000000000000000000000000000000000000000000000
χ7312-6-612-6-6333-6000000000000003ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ2+3ζ73ζ4+3ζ53ζ+3ζ8000000000000000000000000000000000000000000000
χ7412-6-612-6-6333-6000000000000003ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ+3ζ83ζ2+3ζ73ζ4+3ζ53ζ4+3ζ53ζ+3ζ83ζ2+3ζ7000000000000000000000000000000000000000000000
χ7512-6-612-6-6333-6000000000000003ζ4+3ζ53ζ+3ζ83ζ2+3ζ73ζ2+3ζ73ζ4+3ζ53ζ+3ζ83ζ+3ζ83ζ2+3ζ73ζ4+3ζ5000000000000000000000000000000000000000000000
χ7612-6-6-6-612-6333012-6-60000000-633000000000000000000000000000000000000000000000000000000
χ7712-6-6-6-612-63330-612-600000003-63000000000000000000000000000000000000000000000000000000
χ7812-6-6-6-612-63330-6-612000000033-6000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 9 (ζ9 = 1); i = ζ2.