Finite Group Databasebeta

← Group #10624322

Character table — Group #10624322

Order 720.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size136682612121626121216515303040136682612121626121216515303040136682612121626121216515303040
order12243510102015510102015222463661231530306015153030601566612636612315303060151530306015666126
χ1111111111111111111111111111111111111111111111111111111111111
χ211-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-1111-1-11
χ32200-12200-12200-12200-12200-12200-12200-12200-12200-12200-12200-12200-1
χ43-11-103-11-103-11-103-11-103-11-103-11-103-11-103-11-103-11-103-11-103-11-103-11-10
χ53-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-1103-1-110
χ6111111111111111-1-1-1-1-1111111111111111-1-1-1-1-1111111111111111-1-1-1-1-1
χ711-1-1111-1-1111-1-11-1-111-111-1-1111-1-1111-1-11-1-111-111-1-1111-1-1111-1-11-1-111-1
χ82200-12200-12200-1-2-20012200-12200-12200-1-2-20012200-12200-12200-1-2-2001
χ93-11-103-11-103-11-10-31-1103-11-103-11-103-11-10-31-1103-11-103-11-103-11-10-31-110
χ103-1-1103-1-1103-1-110-311-103-1-1103-1-1103-1-110-311-103-1-1103-1-1103-1-110-311-10
χ1122222−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−520000022222−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−520000022222−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−5200000
χ1222-2-22−1+52−1+521−521−52−1+52−1−52−1−521+521+52−1−520000022-2-22−1+52−1+521−521−52−1+52−1−52−1−521+521+52−1−520000022-2-22−1+52−1+521−521−52−1+52−1−52−1−521+521+52−1−5200000
χ134400-2−1+5−1+5001−52−1−5−1−5001+52000004400-2−1+5−1+5001−52−1−5−1−5001+52000004400-2−1+5−1+5001−52−1−5−1−5001+5200000
χ146-22-20−3+3521−52−1+521−520−3−3521+52−1−521+520000006-22-20−3+3521−52−1+521−520−3−3521+52−1−521+520000006-22-20−3+3521−52−1+521−520−3−3521+52−1−521+52000000
χ156-2-220−3+3521−521−52−1+520−3−3521+521+52−1−520000006-2-220−3+3521−521−52−1+520−3−3521+521+52−1−520000006-2-220−3+3521−521−52−1+520−3−3521+521+52−1−52000000
χ1622222−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+520000022222−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+520000022222−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+5200000
χ1722-2-22−1−52−1−521+521+52−1−52−1+52−1+521−521−52−1+520000022-2-22−1−52−1−521+521+52−1−52−1+52−1+521−521−52−1+520000022-2-22−1−52−1−521+521+52−1−52−1+52−1+521−521−52−1+5200000
χ184400-2−1−5−1−5001+52−1+5−1+5001−52000004400-2−1−5−1−5001+52−1+5−1+5001−52000004400-2−1−5−1−5001+52−1+5−1+5001−5200000
χ196-22-20−3−3521+52−1−521+520−3+3521−52−1+521−520000006-22-20−3−3521+52−1−521+520−3+3521−52−1+521−520000006-22-20−3−3521+52−1−521+520−3+3521−52−1+521−52000000
χ206-2-220−3−3521+521+52−1−520−3+3521−521−52−1+520000006-2-220−3−3521+521+52−1−520−3+3521−521−52−1+520000006-2-220−3−3521+521+52−1−520−3+3521−521−52−1+52000000
χ2111111111111111111111−1+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+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ2211-1-1111-1-1111-1-1111-1-11−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ232200-12200-12200-12200-1−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32
χ243-11-103-11-103-11-103-11-10−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320
χ253-1-1103-1-1103-1-1103-1-110−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320
χ26111111111111111-1-1-1-1-1−1+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+i321−i321−i321−i321−i321−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−i32−1−i321+i321+i321+i321+i321+i32
χ2711-1-1111-1-1111-1-11-1-111-1−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32
χ282200-12200-12200-1-2-2001−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i321−i31−i300−1+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i321+i31+i300−1−i32
χ293-11-103-11-103-11-10-31-110−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320
χ303-1-1103-1-1103-1-110-311-10−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320
χ3122222−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−5200000−1+i3−1+i3−1+i3−1+i3−1+i3ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ1400000−1−i3−1−i3−1−i3−1−i3−1−i3ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ400000
χ3222-2-22−1+52−1+521−521−52−1+52−1−52−1−521+521+52−1−5200000−1+i3−1+i31−i31−i3−1+i3ζ2+ζ8ζ2+ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ1400000−1−i3−1−i31+i31+i3−1−i3ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ+ζ4ζ+ζ4−ζ−ζ4−ζ−ζ4ζ+ζ400000
χ334400-2−1+5−1+5001−52−1−5−1−5001+5200000−2+2i3−2+2i3001−i32ζ2+2ζ82ζ2+2ζ800−ζ2−ζ82ζ11+2ζ142ζ11+2ζ1400−ζ11−ζ1400000−2−2i3−2−2i3001+i32ζ7+2ζ132ζ7+2ζ1300−ζ7−ζ132ζ+2ζ42ζ+2ζ400−ζ−ζ400000
χ346-22-20−3+3521−52−1+521−520−3−3521+52−1−521+52000000−3+3i31−i3−1+i31−i303ζ2+3ζ8−ζ2−ζ8ζ2+ζ8−ζ2−ζ803ζ11+3ζ14−ζ11−ζ14ζ11+ζ14−ζ11−ζ14000000−3−3i31+i3−1−i31+i303ζ7+3ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1303ζ+3ζ4−ζ−ζ4ζ+ζ4−ζ−ζ4000000
χ356-2-220−3+3521−521−52−1+520−3−3521+521+52−1−52000000−3+3i31−i31−i3−1+i303ζ2+3ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ803ζ11+3ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ14000000−3−3i31+i31+i3−1−i303ζ7+3ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1303ζ+3ζ4−ζ−ζ4−ζ−ζ4ζ+ζ4000000
χ3622222−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+5200000−1+i3−1+i3−1+i3−1+i3−1+i3ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ800000−1−i3−1−i3−1−i3−1−i3−1−i3ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ1300000
χ3722-2-22−1−52−1−521+521+52−1−52−1+52−1+521−521−52−1+5200000−1+i3−1+i31−i31−i3−1+i3ζ11+ζ14ζ11+ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ800000−1−i3−1−i31+i31+i3−1−i3ζ+ζ4ζ+ζ4−ζ−ζ4−ζ−ζ4ζ+ζ4ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300000
χ384400-2−1−5−1−5001+52−1+5−1+5001−5200000−2+2i3−2+2i3001−i32ζ11+2ζ142ζ11+2ζ1400−ζ11−ζ142ζ2+2ζ82ζ2+2ζ800−ζ2−ζ800000−2−2i3−2−2i3001+i32ζ+2ζ42ζ+2ζ400−ζ−ζ42ζ7+2ζ132ζ7+2ζ1300−ζ7−ζ1300000
χ396-22-20−3−3521+52−1−521+520−3+3521−52−1+521−52000000−3+3i31−i3−1+i31−i303ζ11+3ζ14−ζ11−ζ14ζ11+ζ14−ζ11−ζ1403ζ2+3ζ8−ζ2−ζ8ζ2+ζ8−ζ2−ζ8000000−3−3i31+i3−1−i31+i303ζ+3ζ4−ζ−ζ4ζ+ζ4−ζ−ζ403ζ7+3ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000
χ406-2-220−3−3521+521+52−1−520−3+3521−521−52−1+52000000−3+3i31−i31−i3−1+i303ζ11+3ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ1403ζ2+3ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ8000000−3−3i31+i31+i3−1−i303ζ+3ζ4−ζ−ζ4−ζ−ζ4ζ+ζ403ζ7+3ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000
χ4111111111111111111111−1−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−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4211-1-1111-1-1111-1-1111-1-11−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ432200-12200-12200-12200-1−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32
χ443-11-103-11-103-11-103-11-10−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320
χ453-1-1103-1-1103-1-1103-1-110−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320
χ46111111111111111-1-1-1-1-1−1−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−i321+i321+i321+i321+i321+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+i32−1+i321−i321−i321−i321−i321−i32
χ4711-1-1111-1-1111-1-11-1-111-1−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32
χ482200-12200-12200-1-2-2001−1−i3−1−i3001+i32−1−i3−1−i3001+i32−1−i3−1−i3001+i321+i31+i300−1−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i32−1+i3−1+i3001−i321−i31−i300−1+i32
χ493-11-103-11-103-11-10-31-110−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i320−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i320−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320
χ503-1-1103-1-1103-1-110-311-10−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i320−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i320−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320
χ5122222−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−5200000−1−i3−1−i3−1−i3−1−i3−1−i3ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ400000−1+i3−1+i3−1+i3−1+i3−1+i3ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ1400000
χ5222-2-22−1+52−1+521−521−52−1+52−1−52−1−521+521+52−1−5200000−1−i3−1−i31+i31+i3−1−i3ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ+ζ4ζ+ζ4−ζ−ζ4−ζ−ζ4ζ+ζ400000−1+i3−1+i31−i31−i3−1+i3ζ2+ζ8ζ2+ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ8ζ11+ζ14ζ11+ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ1400000
χ534400-2−1+5−1+5001−52−1−5−1−5001+5200000−2−2i3−2−2i3001+i32ζ7+2ζ132ζ7+2ζ1300−ζ7−ζ132ζ+2ζ42ζ+2ζ400−ζ−ζ400000−2+2i3−2+2i3001−i32ζ2+2ζ82ζ2+2ζ800−ζ2−ζ82ζ11+2ζ142ζ11+2ζ1400−ζ11−ζ1400000
χ546-22-20−3+3521−52−1+521−520−3−3521+52−1−521+52000000−3−3i31+i3−1−i31+i303ζ7+3ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1303ζ+3ζ4−ζ−ζ4ζ+ζ4−ζ−ζ4000000−3+3i31−i3−1+i31−i303ζ2+3ζ8−ζ2−ζ8ζ2+ζ8−ζ2−ζ803ζ11+3ζ14−ζ11−ζ14ζ11+ζ14−ζ11−ζ14000000
χ556-2-220−3+3521−521−52−1+520−3−3521+521+52−1−52000000−3−3i31+i31+i3−1−i303ζ7+3ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1303ζ+3ζ4−ζ−ζ4−ζ−ζ4ζ+ζ4000000−3+3i31−i31−i3−1+i303ζ2+3ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ803ζ11+3ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ14000000
χ5622222−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+5200000−1−i3−1−i3−1−i3−1−i3−1−i3ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ+ζ4ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ1300000−1+i3−1+i3−1+i3−1+i3−1+i3ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ8ζ2+ζ800000
χ5722-2-22−1−52−1−521+521+52−1−52−1+52−1+521−521−52−1+5200000−1−i3−1−i31+i31+i3−1−i3ζ+ζ4ζ+ζ4−ζ−ζ4−ζ−ζ4ζ+ζ4ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ1300000−1+i3−1+i31−i31−i3−1+i3ζ11+ζ14ζ11+ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ14ζ2+ζ8ζ2+ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ800000
χ584400-2−1−5−1−5001+52−1+5−1+5001−5200000−2−2i3−2−2i3001+i32ζ+2ζ42ζ+2ζ400−ζ−ζ42ζ7+2ζ132ζ7+2ζ1300−ζ7−ζ1300000−2+2i3−2+2i3001−i32ζ11+2ζ142ζ11+2ζ1400−ζ11−ζ142ζ2+2ζ82ζ2+2ζ800−ζ2−ζ800000
χ596-22-20−3−3521+52−1−521+520−3+3521−52−1+521−52000000−3−3i31+i3−1−i31+i303ζ+3ζ4−ζ−ζ4ζ+ζ4−ζ−ζ403ζ7+3ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000−3+3i31−i3−1+i31−i303ζ11+3ζ14−ζ11−ζ14ζ11+ζ14−ζ11−ζ1403ζ2+3ζ8−ζ2−ζ8ζ2+ζ8−ζ2−ζ8000000
χ606-2-220−3−3521+521+52−1−520−3+3521−521−52−1+52000000−3−3i31+i31+i3−1−i303ζ+3ζ4−ζ−ζ4−ζ−ζ4ζ+ζ403ζ7+3ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13000000−3+3i31−i31−i3−1+i303ζ11+3ζ14−ζ11−ζ14−ζ11−ζ14ζ11+ζ1403ζ2+3ζ8−ζ2−ζ8−ζ2−ζ8ζ2+ζ8000000

Here ζ is a primitive root of unity of order 15 (ζ15 = 1); i = ζ3.