Finite Group Databasebeta

← Group #64249

Character table — Group #64249

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size136681366813668136681366813668136681366813668136681366813668
order12243444412222464444123661231212121212666126121212121236612312121212126661261212121212
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
χ611111iiiii-1-1-1-1-1−i−i−i−i−i11111iiiii-1-1-1-1-1−i−i−i−i−i11111iiiii-1-1-1-1-1−i−i−i−i−i
χ711-1-11ii−i−ii-1-111-1−i−iii−i11-1-11ii−i−ii-1-111-1−i−iii−i11-1-11ii−i−ii-1-111-1−i−iii−i
χ82200-12i2i00−i-2-2001−2i−2i00i2200-12i2i00−i-2-2001−2i−2i00i2200-12i2i00−i-2-2001−2i−2i00i
χ93-11-103i−ii−i0-31-110−3ii−ii03-11-103i−ii−i0-31-110−3ii−ii03-11-103i−ii−i0-31-110−3ii−ii0
χ103-1-1103i−i−ii0-311-10−3iii−i03-1-1103i−i−ii0-311-10−3iii−i03-1-1103i−i−ii0-311-10−3iii−i0
χ1111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-111111-1-1-1-1-1
χ1211-1-11-1-111-111-1-11-1-111-111-1-11-1-111-111-1-11-1-111-111-1-11-1-111-111-1-11-1-111-1
χ132200-1-2-20012200-1-2-20012200-1-2-20012200-1-2-20012200-1-2-20012200-1-2-2001
χ143-11-10-31-1103-11-10-31-1103-11-10-31-1103-11-10-31-1103-11-10-31-1103-11-10-31-110
χ153-1-110-311-103-1-110-311-103-1-110-311-103-1-110-311-103-1-110-311-103-1-110-311-10
χ1611111−i−i−i−i−i-1-1-1-1-1iiiii11111−i−i−i−i−i-1-1-1-1-1iiiii11111−i−i−i−i−i-1-1-1-1-1iiiii
χ1711-1-11−i−iii−i-1-111-1ii−i−ii11-1-11−i−iii−i-1-111-1ii−i−ii11-1-11−i−iii−i-1-111-1ii−i−ii
χ182200-1−2i−2i00i-2-20012i2i00−i2200-1−2i−2i00i-2-20012i2i00−i2200-1−2i−2i00i-2-20012i2i00−i
χ193-11-10−3ii−ii0-31-1103i−ii−i03-11-10−3ii−ii0-31-1103i−ii−i03-11-10−3ii−ii0-31-1103i−ii−i0
χ203-1-110−3iii−i0-311-103i−i−ii03-1-110−3iii−i0-311-103i−i−ii03-1-110−3iii−i0-311-103i−i−ii0
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
χ2611111iiiii-1-1-1-1-1−i−i−i−i−i−1+i32−1+i32−1+i32−1+i32−1+i32ζ7ζ7ζ7ζ7ζ71−i321−i321−i321−i321−i32−ζ7−ζ7−ζ7−ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32ζ11ζ11ζ11ζ11ζ111+i321+i321+i321+i321+i32−ζ11−ζ11−ζ11−ζ11−ζ11
χ2711-1-11ii−i−ii-1-111-1−i−iii−i−1+i32−1+i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7ζ71−i321−i32−1+i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7−1−i32−1−i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11ζ111+i321+i32−1−i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11
χ282200-12i2i00−i-2-2001−2i−2i00i−1+i3−1+i3001−i322ζ72ζ700−ζ71−i31−i300−1+i32−2ζ7−2ζ700ζ7−1−i3−1−i3001+i322ζ112ζ1100−ζ111+i31+i300−1−i32−2ζ11−2ζ1100ζ11
χ293-11-103i−ii−i0-31-110−3ii−ii0−3+3i321−i32−1+i321−i3203ζ7−ζ7ζ7−ζ703−3i32−1+i321−i32−1+i320−3ζ7ζ7−ζ7ζ70−3−3i321+i32−1−i321+i3203ζ11−ζ11ζ11−ζ1103+3i32−1−i321+i32−1−i320−3ζ11ζ11−ζ11ζ110
χ303-1-1103i−i−ii0-311-10−3iii−i0−3+3i321−i321−i32−1+i3203ζ7−ζ7−ζ7ζ703−3i32−1+i32−1+i321−i320−3ζ7ζ7ζ7−ζ70−3−3i321+i321+i32−1−i3203ζ11−ζ11−ζ11ζ1103+3i32−1−i32−1−i321+i320−3ζ11ζ11ζ11−ζ110
χ3111111-1-1-1-1-111111-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−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−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32
χ3211-1-11-1-111-111-1-11-1-111-1−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32
χ332200-1-2-20012200-1-2-2001−1+i3−1+i3001−i321−i31−i300−1+i32−1+i3−1+i3001−i321−i31−i300−1+i32−1−i3−1−i3001+i321+i31+i300−1−i32−1−i3−1−i3001+i321+i31+i300−1−i32
χ343-11-10-31-1103-11-10-31-110−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320
χ353-1-110-311-103-1-110-311-10−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320
χ3611111−i−i−i−i−i-1-1-1-1-1iiiii−1+i32−1+i32−1+i32−1+i32−1+i32−ζ7−ζ7−ζ7−ζ7−ζ71−i321−i321−i321−i321−i32ζ7ζ7ζ7ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−ζ11−ζ11−ζ11−ζ11−ζ111+i321+i321+i321+i321+i32ζ11ζ11ζ11ζ11ζ11
χ3711-1-11−i−iii−i-1-111-1ii−i−ii−1+i32−1+i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7−ζ71−i321−i32−1+i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7−1−i32−1−i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11−ζ111+i321+i32−1−i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11
χ382200-1−2i−2i00i-2-20012i2i00−i−1+i3−1+i3001−i32−2ζ7−2ζ700ζ71−i31−i300−1+i322ζ72ζ700−ζ7−1−i3−1−i3001+i32−2ζ11−2ζ1100ζ111+i31+i300−1−i322ζ112ζ1100−ζ11
χ393-11-10−3ii−ii0-31-1103i−ii−i0−3+3i321−i32−1+i321−i320−3ζ7ζ7−ζ7ζ703−3i32−1+i321−i32−1+i3203ζ7−ζ7ζ7−ζ70−3−3i321+i32−1−i321+i320−3ζ11ζ11−ζ11ζ1103+3i32−1−i321+i32−1−i3203ζ11−ζ11ζ11−ζ110
χ403-1-110−3iii−i0-311-103i−i−ii0−3+3i321−i321−i32−1+i320−3ζ7ζ7ζ7−ζ703−3i32−1+i32−1+i321−i3203ζ7−ζ7−ζ7ζ70−3−3i321+i321+i32−1−i320−3ζ11ζ11ζ11−ζ1103+3i32−1−i32−1−i321+i3203ζ11−ζ11−ζ11ζ110
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
χ4611111iiiii-1-1-1-1-1−i−i−i−i−i−1−i32−1−i32−1−i32−1−i32−1−i32ζ11ζ11ζ11ζ11ζ111+i321+i321+i321+i321+i32−ζ11−ζ11−ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+i32−1+i32ζ7ζ7ζ7ζ7ζ71−i321−i321−i321−i321−i32−ζ7−ζ7−ζ7−ζ7−ζ7
χ4711-1-11ii−i−ii-1-111-1−i−iii−i−1−i32−1−i321+i321+i32−1−i32ζ11ζ11−ζ11−ζ11ζ111+i321+i32−1−i32−1−i321+i32−ζ11−ζ11ζ11ζ11−ζ11−1+i32−1+i321−i321−i32−1+i32ζ7ζ7−ζ7−ζ7ζ71−i321−i32−1+i32−1+i321−i32−ζ7−ζ7ζ7ζ7−ζ7
χ482200-12i2i00−i-2-2001−2i−2i00i−1−i3−1−i3001+i322ζ112ζ1100−ζ111+i31+i300−1−i32−2ζ11−2ζ1100ζ11−1+i3−1+i3001−i322ζ72ζ700−ζ71−i31−i300−1+i32−2ζ7−2ζ700ζ7
χ493-11-103i−ii−i0-31-110−3ii−ii0−3−3i321+i32−1−i321+i3203ζ11−ζ11ζ11−ζ1103+3i32−1−i321+i32−1−i320−3ζ11ζ11−ζ11ζ110−3+3i321−i32−1+i321−i3203ζ7−ζ7ζ7−ζ703−3i32−1+i321−i32−1+i320−3ζ7ζ7−ζ7ζ70
χ503-1-1103i−i−ii0-311-10−3iii−i0−3−3i321+i321+i32−1−i3203ζ11−ζ11−ζ11ζ1103+3i32−1−i32−1−i321+i320−3ζ11ζ11ζ11−ζ110−3+3i321−i321−i32−1+i3203ζ7−ζ7−ζ7ζ703−3i32−1+i32−1+i321−i320−3ζ7ζ7ζ7−ζ70
χ5111111-1-1-1-1-111111-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+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+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32
χ5211-1-11-1-111-111-1-11-1-111-1−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32
χ532200-1-2-20012200-1-2-2001−1−i3−1−i3001+i321+i31+i300−1−i32−1−i3−1−i3001+i321+i31+i300−1−i32−1+i3−1+i3001−i321−i31−i300−1+i32−1+i3−1+i3001−i321−i31−i300−1+i32
χ543-11-10-31-1103-11-10-31-110−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320−3−3i321+i32−1−i321+i3203+3i32−1−i321+i32−1−i320−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320−3+3i321−i32−1+i321−i3203−3i32−1+i321−i32−1+i320
χ553-1-110-311-103-1-110-311-10−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320−3−3i321+i321+i32−1−i3203+3i32−1−i32−1−i321+i320−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320−3+3i321−i321−i32−1+i3203−3i32−1+i32−1+i321−i320
χ5611111−i−i−i−i−i-1-1-1-1-1iiiii−1−i32−1−i32−1−i32−1−i32−1−i32−ζ11−ζ11−ζ11−ζ11−ζ111+i321+i321+i321+i321+i32ζ11ζ11ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+i32−1+i32−ζ7−ζ7−ζ7−ζ7−ζ71−i321−i321−i321−i321−i32ζ7ζ7ζ7ζ7ζ7
χ5711-1-11−i−iii−i-1-111-1ii−i−ii−1−i32−1−i321+i321+i32−1−i32−ζ11−ζ11ζ11ζ11−ζ111+i321+i32−1−i32−1−i321+i32ζ11ζ11−ζ11−ζ11ζ11−1+i32−1+i321−i321−i32−1+i32−ζ7−ζ7ζ7ζ7−ζ71−i321−i32−1+i32−1+i321−i32ζ7ζ7−ζ7−ζ7ζ7
χ582200-1−2i−2i00i-2-20012i2i00−i−1−i3−1−i3001+i32−2ζ11−2ζ1100ζ111+i31+i300−1−i322ζ112ζ1100−ζ11−1+i3−1+i3001−i32−2ζ7−2ζ700ζ71−i31−i300−1+i322ζ72ζ700−ζ7
χ593-11-10−3ii−ii0-31-1103i−ii−i0−3−3i321+i32−1−i321+i320−3ζ11ζ11−ζ11ζ1103+3i32−1−i321+i32−1−i3203ζ11−ζ11ζ11−ζ110−3+3i321−i32−1+i321−i320−3ζ7ζ7−ζ7ζ703−3i32−1+i321−i32−1+i3203ζ7−ζ7ζ7−ζ70
χ603-1-110−3iii−i0-311-103i−i−ii0−3−3i321+i321+i32−1−i320−3ζ11ζ11ζ11−ζ1103+3i32−1−i32−1−i321+i3203ζ11−ζ11−ζ11ζ110−3+3i321−i321−i32−1+i320−3ζ7ζ7ζ7−ζ703−3i32−1+i32−1+i321−i3203ζ7−ζ7−ζ7ζ70

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.