Finite Group Databasebeta

← Group #11791199

Character table — Group #11791199

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222444444444444444488888888181818181818181818181818181818181818181818181818242424242424242424242424242424242424242424242424
order1222444488883366666612121212121212122424242424242424224444444444888888888888224466668888121212122424242424242424
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
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-11111
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ91111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11iiii−i−i−i−i1ii−i−i1111-1-1-1-111-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11iiii−i−i−i−i1ii−i−i1111-1-1-1-1-1-111-1-1-1-1−ii−ii1111−i−iii−i−iii
χ111111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11−i−i−i−iiiii1ii−i−i-1-1-1-111111-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ121111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11−i−i−i−iiiii1ii−i−i-1-1-1-11111-111-1-1-111−iii−i11-1-1−i−iiiii−i−i
χ131111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11iiii−i−i−i−i1−i−iii-1-1-1-111111-1-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ141111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11iiii−i−i−i−i1−i−iii-1-1-1-11111-111-1-1-111i−i−ii11-1-1ii−i−i−i−iii
χ151111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11−i−i−i−iiiii1−i−iii1111-1-1-1-111-1-11111−ii−ii-1-1-1-1−i−iii−i−iii
χ161111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11−i−i−i−iiiii1−i−iii1111-1-1-1-1-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i
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χ754-44-4−4i4i4i−4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-212-1-212-12i−i−2ii−2ii2i−i−2ζ5−2ζ13ζ5+ζ132ζ5+2ζ13−ζ5−ζ132ζ7+2ζ23−ζ7−ζ23−2ζ7−2ζ23ζ7+ζ230000000000000000000000000000−i3i3000000−3300ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ764-44-4−4i4i4i−4i4ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23-212-1-212-12i−i−2ii−2ii2i−i−2ζ5−2ζ13ζ5+ζ132ζ5+2ζ13−ζ5−ζ132ζ7+2ζ23−ζ7−ζ23−2ζ7−2ζ23ζ7+ζ230000000000000000000000000000i3−i30000003−300−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ7788-8-88i−8i8i−8i00002-42-4-24-242i−4i−2i4i2i−4i−2i4i00000000000000000000000000000000000000000000000000000000
χ7888-8-88i−8i8i−8i0000-42-424-24-2−4i2i4i−2i−4i2i4i−2i00000000000000000000000000000000000000000000000000000000
χ7988-8-8−8i8i−8i8i00002-42-4-24-24−2i4i2i−4i−2i4i2i−4i00000000000000000000000000000000000000000000000000000000
χ8088-8-8−8i8i−8i8i0000-42-424-24-24i−2i−4i2i4i−2i−4i2i00000000000000000000000000000000000000000000000000000000
χ818-8-8888-8-800002-4-24-242-42-42-4-24-2400000000000000000000000000000000000000000000000000000000
χ828-8-8888-8-80000-424-24-2-42-42-424-24-200000000000000000000000000000000000000000000000000000000
χ838-8-88-8-88800002-4-24-242-4-24-242-42-400000000000000000000000000000000000000000000000000000000
χ848-8-88-8-8880000-424-24-2-424-24-2-42-4200000000000000000000000000000000000000000000000000000000

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