Finite Group Databasebeta

← Group #5434

Character table — Group #5434

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1344134413441344134413441344134413441344134413441344134413441344
order1233441212226644121244121244121244121244121222664412122266441212441212441212441212441212
χ11111111111111111111111111111111111111111111111111111111111111111
χ211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32
χ311−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32
χ43-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-1003-100
χ51111iiii-1-1-1-1−i−i−i−i1111iiii-1-1-1-1−i−i−i−i1111iiii-1-1-1-1−i−i−i−i1111iiii-1-1-1-1−i−i−i−i
χ611−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ11
χ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ7
χ83-1003i−i00-3100−3ii003-1003i−i00-3100−3ii003-1003i−i00-3100−3ii003-1003i−i00-3100−3ii00
χ91111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1011−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i32
χ1111−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i32
χ123-100-31003-100-31003-100-31003-100-31003-100-31003-100-31003-100-31003-100-3100
χ131111−i−i−i−i-1-1-1-1iiii1111−i−i−i−i-1-1-1-1iiii1111−i−i−i−i-1-1-1-1iiii1111−i−i−i−i-1-1-1-1iiii
χ1411−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ11
χ1511−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ7
χ163-100−3ii00-31003i−i003-100−3ii00-31003i−i003-100−3ii00-31003i−i003-100−3ii00-31003i−i00
χ171111111111111111iiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ1811−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32iiζ7ζ11iiζ7ζ11iiζ7ζ11iiζ7ζ11-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11
χ1911−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32iiζ11ζ7iiζ11ζ7iiζ11ζ7iiζ11ζ7-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7
χ203-1003-1003-1003-1003i−i003i−i003i−i003i−i00-3100-3100-3100-3100−3ii00−3ii00−3ii00−3ii00
χ211111iiii-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i1111-1-1-1-1−i−i−i−i1111iiii−i−i−i−i1111iiii-1-1-1-1
χ2211−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ11iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32
χ2311−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ7iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32
χ243-1003i−i00-3100−3ii003i−i00-3100−3ii003-100-3100−3ii003-1003i−i00−3ii003-1003i−i00-3100
χ251111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ2611−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i32iiζ7ζ11−i−i−ζ7−ζ11iiζ7ζ11−i−i−ζ7−ζ11-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32−i−i−ζ7−ζ11iiζ7ζ11−i−i−ζ7−ζ11iiζ7ζ11
χ2711−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i32iiζ11ζ7−i−i−ζ11−ζ7iiζ11ζ7−i−i−ζ11−ζ7-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32−i−i−ζ11−ζ7iiζ11ζ7−i−i−ζ11−ζ7iiζ11ζ7
χ283-100-31003-100-31003i−i00−3ii003i−i00−3ii00-31003-100-31003-100−3ii003i−i00−3ii003i−i00
χ291111−i−i−i−i-1-1-1-1iiiiiiii1111−i−i−i−i-1-1-1-1-1-1-1-1iiii1111−i−i−i−i−i−i−i−i-1-1-1-1iiii1111
χ3011−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ11iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32
χ3111−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ7iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32
χ323-100−3ii00-31003i−i003i−i003-100−3ii00-3100-31003i−i003-100−3ii00−3ii00-31003i−i003-100
χ331111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3411−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32
χ3511−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32
χ363-1003-1003-1003-100-3100-3100-3100-31003-1003-1003-1003-100-3100-3100-3100-3100
χ371111iiii-1-1-1-1−i−i−i−i-1-1-1-1−i−i−i−i1111iiii1111iiii-1-1-1-1−i−i−i−i-1-1-1-1−i−i−i−i1111iiii
χ3811−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11
χ3911−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7
χ403-1003i−i00-3100−3ii00-3100−3ii003-1003i−i003-1003i−i00-3100−3ii00-3100−3ii003-1003i−i00
χ411111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ4211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32
χ4311−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32
χ443-100-31003-100-3100-31003-100-31003-1003-100-31003-100-3100-31003-100-31003-100
χ451111−i−i−i−i-1-1-1-1iiii-1-1-1-1iiii1111−i−i−i−i1111−i−i−i−i-1-1-1-1iiii-1-1-1-1iiii1111−i−i−i−i
χ4611−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11
χ4711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7
χ483-100−3ii00-31003i−i00-31003i−i003-100−3ii003-100−3ii00-31003i−i00-31003i−i003-100−3ii00
χ491111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiii
χ5011−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11−i−i−ζ7−ζ11-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32-1-11−i321+i32iiζ7ζ11iiζ7ζ11iiζ7ζ11iiζ7ζ11
χ5111−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7−i−i−ζ11−ζ7-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32-1-11+i321−i32iiζ11ζ7iiζ11ζ7iiζ11ζ7iiζ11ζ7
χ523-1003-1003-1003-100−3ii00−3ii00−3ii00−3ii00-3100-3100-3100-31003i−i003i−i003i−i003i−i00
χ531111iiii-1-1-1-1−i−i−i−i−i−i−i−i1111iiii-1-1-1-1-1-1-1-1−i−i−i−i1111iiiiiiii-1-1-1-1−i−i−i−i1111
χ5411−1+i32−1−i32iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ11−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11-1-11−i321+i32-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32iiζ7ζ11iiζ7ζ11-1-11−i321+i32−i−i−ζ7−ζ1111−1+i32−1−i32
χ5511−1−i32−1+i32iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ7−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7-1-11+i321−i32-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32iiζ11ζ7iiζ11ζ7-1-11+i321−i32−i−i−ζ11−ζ711−1−i32−1+i32
χ563-1003i−i00-3100−3ii00−3ii003-1003i−i00-3100-3100−3ii003-1003i−i003i−i00-3100−3ii003-100
χ571111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ5811−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i32−i−i−ζ7−ζ11iiζ7ζ11−i−i−ζ7−ζ11iiζ7ζ11-1-11−i321+i3211−1+i32−1−i32-1-11−i321+i3211−1+i32−1−i32iiζ7ζ11−i−i−ζ7−ζ11iiζ7ζ11−i−i−ζ7−ζ11
χ5911−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i32−i−i−ζ11−ζ7iiζ11ζ7−i−i−ζ11−ζ7iiζ11ζ7-1-11+i321−i3211−1−i32−1+i32-1-11+i321−i3211−1−i32−1+i32iiζ11ζ7−i−i−ζ11−ζ7iiζ11ζ7−i−i−ζ11−ζ7
χ603-100-31003-100-3100−3ii003i−i00−3ii003i−i00-31003-100-31003-1003i−i00−3ii003i−i00−3ii00
χ611111−i−i−i−i-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii1111-1-1-1-1iiii1111−i−i−i−iiiii1111−i−i−i−i-1-1-1-1
χ6211−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ11−i−i−ζ7−ζ11-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32-1-11−i321+i32iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11iiζ7ζ1111−1+i32−1−i32−i−i−ζ7−ζ11-1-11−i321+i32
χ6311−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ7−i−i−ζ11−ζ7-1-11+i321−i32iiζ11ζ711−1−i32−1+i32-1-11+i321−i32iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7iiζ11ζ711−1−i32−1+i32−i−i−ζ11−ζ7-1-11+i321−i32
χ643-100−3ii00-31003i−i00−3ii00-31003i−i003-100-31003i−i003-100−3ii003i−i003-100−3ii00-3100

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