Finite Group Databasebeta

← Group #11789968

Character table — Group #11789968

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order122244448888336666661212121212121212242424242424242422444444444488888888888824446688881212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-111-1-1-1-11111
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-11111-1-1-1-1
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ91111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11iiii−i−i−i−i1ii−i−i1111-1-1-1-111-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11iiii−i−i−i−i1ii−i−i1111-1-1-1-1-1-111-1-1−ii−ii-1-11111−i−iii−i−iii
χ111111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11−i−i−i−iiiii1ii−i−i-1-1-1-111111-11-111i−i−ii-1-111-1-1ii−i−i−i−iii
χ121111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-11−i−i−i−iiiii1ii−i−i-1-1-1-11111-11-11-1-1−iii−i11-1-111−i−iiiii−i−i
χ131111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11iiii−i−i−i−i1−i−iii-1-1-1-111111-11-111−iii−i-1-111-1-1−i−iiiii−i−i
χ141111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11iiii−i−i−i−i1−i−iii-1-1-1-11111-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii
χ151111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11−i−i−i−iiiii1−i−iii1111-1-1-1-111-1-111−ii−ii11-1-1-1-1−i−iii−i−iii
χ161111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1-11−i−i−i−iiiii1−i−iii1111-1-1-1-1-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i
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χ744-44-4−4i4i4i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ131-22-2-1-112−ii−2i2i2i−2ii−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000000000000000000000000000i3−i33−3000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ754-44-4−4i4i4i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-21-1122-2-12i−2ii−i−ii−2i2i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000−i3i300000000−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ764-44-4−4i4i4i−4i−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ13-21-1122-2-12i−2ii−i−ii−2i2i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000i3−i3000000003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ7788-8-88i−8i8i−8i00002-4-44-22-242i−2i−4i4i−4i4i2i−2i00000000000000000000000000000000000000000000000000000000
χ7888-8-88i−8i8i−8i0000-422-24-44-2−4i4i2i−2i2i−2i−4i4i00000000000000000000000000000000000000000000000000000000
χ7988-8-8−8i8i−8i8i00002-4-44-22-24−2i2i4i−4i4i−4i−2i2i00000000000000000000000000000000000000000000000000000000
χ8088-8-8−8i8i−8i8i0000-422-24-44-24i−4i−2i2i−2i2i4i−4i00000000000000000000000000000000000000000000000000000000
χ818-8-8888-8-800002-4442-2-2-42244-4-4-2-200000000000000000000000000000000000000000000000000000000
χ828-8-8888-8-80000-42-2-2-4442-4-4-2-2224400000000000000000000000000000000000000000000000000000000
χ838-8-88-8-88800002-4442-2-2-4-2-2-4-4442200000000000000000000000000000000000000000000000000000000
χ848-8-88-8-8880000-42-2-2-44424422-2-2-4-400000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.