Finite Group Databasebeta

← Group #13142362

Character table — Group #13142362

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size112222233334444444446666666666668812121212121212121212121212121212121212121212121212161618181818181824242424363636363636363636484848484848727272727272
order123468833661216162424484848489991212181818242424244436363648484848727272727272144144144144144144144144144144144144121224661212121212128161624244848484836363636363624661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111111111111111111111111-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111-1-111-1-1-1-11111111111111-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-11-1-111-1-1-1-1111-1-1-11-111-1-1
χ6111111111111-1-111-1-1-1-11111111111111-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-111-1-11111111-1-1-1-11-1-111
χ7111111111111-1-111-1-1-1-1111111111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111-1-111-1-1-1-1-1-1-1111-11-1-111
χ8111111111111-1-111-1-1-1-1111111111111-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-111-1-11111-1-1-11111-111-1-1
χ91111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ101111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-1-1-11+i321−i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i32
χ111111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-11+i321−i32-1-11+i321−i321+i321−i32
χ121111111−1−i32−1+i32−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1-11+i321−i321+i321+i321−i321−i32-11+i321−i32-11+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ131111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321-1-1−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i32-11+i321−i321-1−1−i32−1+i321+i321−i32
χ141111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321-1-1-11+i321−i321+i321−i32−1−i32−1+i321+i321−i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11+i321−i32-111+i321−i32−1−i32−1+i32
χ151111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1111−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321-1-1−1−i32−1+i321+i321+i321−i321−i32-11+i321−i321−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ161111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-11−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111−1−i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-11-1-11+i321−i321+i321−i321+i321−i32−1−i32−1+i32-1111+i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ171111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ181111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-1-1-11−i321+i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i32
χ191111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-11−i321+i32-1-11−i321+i321−i321+i32
χ201111111−1+i32−1−i32−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i32-11−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ211111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321-1-1−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i32-11−i321+i321-1−1+i32−1−i321−i321+i32
χ221111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321-1-1-11−i321+i321−i321+i32−1+i32−1−i321−i321+i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11−i321+i32-111−i321+i32−1+i32−1−i32
χ231111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1111−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1−i321-1-1−1+i32−1−i321−i321−i321+i321+i32-11−i321+i321−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ241111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-11−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111−1+i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-11-1-11−i321+i321−i321+i321−i321+i32−1+i32−1−i32-1111−i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ2522222222222222222222-1-1-122-1-1-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000002222000000000-1-1-1-1-1-1000000
χ2622222222222222222222-1-1-122-1-1-12222-2-2-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000-2-2-2-2000000000111111000000
χ27222222222222-2-222-2-2-2-2-1-1-122-1-1-122222-2-1-1-1-2-2-2-2-1-1-1-1-1-11111111111112-200000022-2-2000000000-1-1-1111000000
χ28222222222222-2-222-2-2-2-2-1-1-122-1-1-12222-22-1-1-1-2-2-2-2-1-1-1-1-1-1111111111111-22000000-2-222000000000111-1-1-1000000
χ292222222−1−i3−1+i3−1−i3−1+i3222222222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i322-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3222000000−1−i3−1+i3−1−i3−1+i3000000000-11+i321−i32-11+i321−i32000000
χ302222222−1−i3−1+i3−1−i3−1+i3222222222-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-2-2-11+i321−i32−1−i3−1−i3−1+i3−1+i3-1-11+i321+i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-2-20000001+i31−i31+i31−i30000000001−1−i32−1+i321−1−i32−1+i32000000
χ312222222−1−i3−1+i3−1−i3−1+i32-2-222-2-2-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i32-2-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i322-2000000−1−i3−1+i31+i31−i3000000000-11+i321−i321−1−i32−1+i32000000
χ322222222−1−i3−1+i3−1−i3−1+i32-2-222-2-2-2-2-11+i321−i32−1−i3−1+i3-11+i321−i32−1−i3−1−i3−1+i3−1+i3-22-11+i321−i321+i31+i31−i31−i3-1-11+i321+i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-220000001+i31−i3−1−i3−1+i30000000001−1−i32−1+i32-11+i321−i32000000
χ332222222−1+i3−1−i3−1+i3−1−i3222222222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i322-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3222000000−1+i3−1−i3−1+i3−1−i3000000000-11−i321+i32-11−i321+i32000000
χ342222222−1+i3−1−i3−1+i3−1−i3222222222-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-2-2-11−i321+i32−1+i3−1+i3−1−i3−1−i3-1-11−i321−i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-2-20000001−i31+i31−i31+i30000000001−1+i32−1−i321−1+i32−1−i32000000
χ352222222−1+i3−1−i3−1+i3−1−i32-2-222-2-2-2-2-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i32-2-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i322-2000000−1+i3−1−i31−i31+i3000000000-11−i321+i321−1+i32−1−i32000000
χ362222222−1+i3−1−i3−1+i3−1−i32-2-222-2-2-2-2-11−i321+i32−1+i3−1−i3-11−i321+i32−1+i3−1+i3−1−i3−1−i3-22-11−i321+i321−i31−i31+i31+i3-1-11−i321−i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-220000001−i31+i3−1+i3−1−i30000000001−1+i32−1−i32-11−i321+i32000000
χ3722222-2-22222200-2-2000022222222-2-2-2-2002220000-2-2-2-2-2-2000000000000002222220000-200-2-20000000000000000
χ3822222-2-22222200-2-2000022222222-2-2-2-2002220000-2-2-2-2-2-200000000000000-2-2-2-2-2-20000200220000000000000000
χ3922222-2-2−1−i3−1+i3−1−i3−1+i3200-2-200002−1−i3−1+i3−1−i3−1+i32−1−i3−1+i31+i31+i31−i31−i3002−1−i3−1+i30000-2-21+i31+i31−i31−i30000000000000022−1−i3−1+i3−1−i3−1+i30000-2001+i31−i30000000000000000
χ4022222-2-2−1−i3−1+i3−1−i3−1+i3200-2-200002−1−i3−1+i3−1−i3−1+i32−1−i3−1+i31+i31+i31−i31−i3002−1−i3−1+i30000-2-21+i31+i31−i31−i300000000000000-2-21+i31−i31+i31−i30000200−1−i3−1+i30000000000000000
χ4122222-2-2−1+i3−1−i3−1+i3−1−i3200-2-200002−1+i3−1−i3−1+i3−1−i32−1+i3−1−i31−i31−i31+i31+i3002−1+i3−1−i30000-2-21−i31−i31+i31+i30000000000000022−1+i3−1−i3−1+i3−1−i30000-2001−i31+i30000000000000000
χ4222222-2-2−1+i3−1−i3−1+i3−1−i3200-2-200002−1+i3−1−i3−1+i3−1−i32−1+i3−1−i31−i31−i31+i31+i3002−1+i3−1−i30000-2-21−i31−i31+i31+i300000000000000-2-21−i31+i31−i31+i30000200−1+i3−1−i30000000000000000
χ43222-22002222-22−20022−2−2222-2-2222000000-2-2-22−22−200000022−2−222−2−222−2−2002-222-2-2000002−2002−22−2000000000000
χ44222-22002222-22−20022−2−2222-2-2222000000-2-2-22−22−200000022−2−222−2−222−2−200-22-2-22200000−2200−22−22000000000000
χ45222-22002222-2−2200−2−222222-2-2222000000-2-2-2−22−22000000−2−222−2−222−2−222002-222-2-200000−2200−22−22000000000000
χ46222-22002222-2−2200−2−222222-2-2222000000-2-2-2−22−22000000−2−222−2−222−2−22200-22-2-222000002−2002−22−2000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.