Finite Group Databasebeta

← Group #72220198

Character table — Group #72220198

Order 5184.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size12333336661818181818182424243699999181818545454545454727272612181818181836363610810810810810810814414414461218181818183636361081081081081081081441441448162424242424484848144144144144144144192192192
order13233666662466121299926266666662466121218181826266666662466121218181841241212121212121244121212123636363363366666612661212999
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1111
χ3111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ4111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32
χ5111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ6111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32
χ72222222222000000-1-1-12222222222000000-1-1-12222222222000000-1-1-12222222222000000-1-1-12222222222000000-1-1-1
χ8222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32
χ9222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32
χ1033-133-1-1-1-1-11-111-1-100033-133-1-1-1-1-11-111-1-100033-133-1-1-1-1-11-111-1-100033-133-1-1-1-1-11-111-1-100033-133-1-1-1-1-11-111-1-1000
χ1133-133-1-1-1-1-1-11-1-11100033-133-1-1-1-1-1-11-1-11100033-133-1-1-1-1-1-11-1-11100033-133-1-1-1-1-1-11-1-11100033-133-1-1-1-1-1-11-1-111000
χ1233-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i32000
χ1333-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i32000
χ1433-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i32000
χ1533-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i32000
χ166-360000-3000000000006-360000-3000000000006-360000-3000000000006-360000-3000000000006-360000-300000000000
χ176-3-200441-2-20000000006-3-200441-2-20000000006-3-200441-2-20000000006-3-200441-2-20000000006-3-200441-2-2000000000
χ186-3-200−2+2i3−2−2i311−i31+i30000000006-3-200−2+2i3−2−2i311−i31+i30000000006-3-200−2+2i3−2−2i311−i31+i30000000006-3-200−2+2i3−2−2i311−i31+i30000000006-3-200−2+2i3−2−2i311−i31+i3000000000
χ196-3-200−2−2i3−2+2i311+i31−i30000000006-3-200−2−2i3−2+2i311+i31−i30000000006-3-200−2−2i3−2+2i311+i31−i30000000006-3-200−2−2i3−2+2i311+i31−i30000000006-3-200−2−2i3−2+2i311+i31−i3000000000
χ2011111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111
χ211111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111111-1-1-1-1-1-1111
χ22111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-1-11−i321+i321−i321+i32-11−i321+i32-1-11−i321+i321−i321+i32-11−i321+i32-1-1-11−i321+i321−i321+i32-11−i321+i32-1-11−i321+i321−i321+i32-11−i321+i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32
χ23111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32-1-1-11−i321+i321−i321+i32-11−i321+i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i32-1-1-11−i321+i321−i321+i32-11−i321+i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i32111−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-1-11−i321+i321−i321+i321−1+i32−1−i32
χ24111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-1-11+i321−i321+i321−i32-11+i321−i32-1-11+i321−i321+i321−i32-11+i321−i32-1-1-11+i321−i321+i321−i32-11+i321−i32-1-11+i321−i321+i321−i32-11+i321−i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32
χ25111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32-1-1-11+i321−i321+i321−i32-11+i321−i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i32-1-1-11+i321−i321+i321−i32-11+i321−i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i32111−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-1-11+i321−i321+i321−i321−1−i32−1+i32
χ262222222222000000-1-1-12222222222000000-1-1-1-2-2-2-2-2-2-2-2-2-2000000111-2-2-2-2-2-2-2-2-2-20000001112222222222000000-1-1-1
χ27222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32-2-2-21−i31+i31−i31+i3-21−i31+i30000001−1+i32−1−i32-2-2-21−i31+i31−i31+i3-21−i31+i30000001−1+i32−1−i32222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3000000-11−i321+i32
χ28222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32-2-2-21+i31−i31+i31−i3-21+i31−i30000001−1−i32−1+i32-2-2-21+i31−i31+i31−i3-21+i31−i30000001−1−i32−1+i32222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3000000-11+i321−i32
χ2933-133-1-1-1-1-11-111-1-100033-133-1-1-1-1-11-111-1-1000-3-31-3-311111-11-1-111000-3-31-3-311111-11-1-11100033-133-1-1-1-1-11-111-1-1000
χ3033-133-1-1-1-1-1-11-1-11100033-133-1-1-1-1-1-11-1-111000-3-31-3-3111111-111-1-1000-3-31-3-3111111-111-1-100033-133-1-1-1-1-1-11-1-111000
χ3133-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i32000-3-313−3i323+3i32−1+i32−1−i321−1+i32−1−i32-111−i321+i32−1+i32−1−i32000-3-313−3i323+3i32−1+i32−1−i321−1+i32−1−i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i321-1−1+i32−1−i321−i321+i32000
χ3233-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i32000-3-313−3i323+3i32−1+i32−1−i321−1+i32−1−i321-1−1+i32−1−i321−i321+i32000-3-313−3i323+3i32−1+i32−1−i321−1+i32−1−i321-1−1+i32−1−i321−i321+i3200033-1−3+3i32−3−3i321−i321+i32-11−i321+i32-111−i321+i32−1+i32−1−i32000
χ3333-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i32000-3-313+3i323−3i32−1−i32−1+i321−1−i32−1+i32-111+i321−i32−1−i32−1+i32000-3-313+3i323−3i32−1−i32−1+i321−1−i32−1+i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i321-1−1−i32−1+i321+i321−i32000
χ3433-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i32000-3-313+3i323−3i32−1−i32−1+i321−1−i32−1+i321-1−1−i32−1+i321+i321−i32000-3-313+3i323−3i32−1−i32−1+i321−1−i32−1+i321-1−1−i32−1+i321+i321−i3200033-1−3−3i32−3+3i321+i321−i32-11+i321−i32-111+i321−i32−1−i32−1+i32000
χ356-360000-3000000000006-360000-300000000000-63-60000300000000000-63-600003000000000006-360000-300000000000
χ366-3-200441-2-20000000006-3-200441-2-2000000000-63200-4-4-122000000000-63200-4-4-1220000000006-3-200441-2-2000000000
χ376-3-200−2+2i3−2−2i311−i31+i30000000006-3-200−2+2i3−2−2i311−i31+i3000000000-632002−2i32+2i3-1−1+i3−1−i3000000000-632002−2i32+2i3-1−1+i3−1−i30000000006-3-200−2+2i3−2−2i311−i31+i3000000000
χ386-3-200−2−2i3−2+2i311+i31−i30000000006-3-200−2−2i3−2+2i311+i31−i3000000000-632002+2i32−2i3-1−1−i3−1+i3000000000-632002+2i32−2i3-1−1−i3−1+i30000000006-3-200−2−2i3−2+2i311+i31−i3000000000
χ392222222222222222222222222222222222222200000000000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ402222222222-2-2-2-2-2-22222222222222-2-2-2-2-2-222200000000000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ41222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i322−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i322−1+i3−1−i3−1+i3−1−i32−1+i3−1−i300000000000000000000000000000000000000-1-1-11−i321+i321−i321+i32-11−i321+i32-1-11−i321+i321−i321+i32-11−i321+i32
χ42222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3-2-21−i31+i31−i31+i32−1+i3−1−i3222−1+i3−1−i3−1+i3−1−i32−1+i3−1−i3-2-21−i31+i31−i31+i32−1+i3−1−i300000000000000000000000000000000000000-1-1-11−i321+i321−i321+i32-11−i321+i3211−1+i32−1−i32−1+i32−1−i32-11−i321+i32
χ43222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i322−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i322−1−i3−1+i3−1−i3−1+i32−1−i3−1+i300000000000000000000000000000000000000-1-1-11+i321−i321+i321−i32-11+i321−i32-1-11+i321−i321+i321−i32-11+i321−i32
χ44222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3-2-21+i31−i31+i31−i32−1−i3−1+i3222−1−i3−1+i3−1−i3−1+i32−1−i3−1+i3-2-21+i31−i31+i31−i32−1−i3−1+i300000000000000000000000000000000000000-1-1-11+i321−i321+i321−i32-11+i321−i3211−1−i32−1+i32−1−i32−1+i32-11+i321−i32
χ454444444444000000-2-2-24444444444000000-2-2-200000000000000000000000000000000000000-2-2-2-2-2-2-2-2-2-2000000111
χ46444−2+2i3−2−2i3−2+2i3−2−2i34−2+2i3−2−2i3000000-21−i31+i3444−2+2i3−2−2i3−2+2i3−2−2i34−2+2i3−2−2i3000000-21−i31+i300000000000000000000000000000000000000-2-2-21−i31+i31−i31+i3-21−i31+i30000001−1+i32−1−i32
χ47444−2−2i3−2+2i3−2−2i3−2+2i34−2−2i3−2+2i3000000-21+i31−i3444−2−2i3−2+2i3−2−2i3−2+2i34−2−2i3−2+2i3000000-21+i31−i300000000000000000000000000000000000000-2-2-21+i31−i31+i31−i3-21+i31−i30000001−1−i32−1+i32
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Here i is the imaginary unit (i² = −1).