Finite Group Databasebeta

← Group #11773859

Character table — Group #11773859

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888818181818242424242424242424242424242424242424242424242424363636363636
order122222334444666666223446666666666612121212121212126666666612121212121212121212121222228888888824242424242424242424242424242424224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ5111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ6111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ7111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111
χ8111111111111111111-1-11-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111
χ911111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-1-1-1
χ1011111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-1-1-1
χ1111111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii-1-11111
χ1211111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i-1-11111
χ1311111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii-1-1-1-111
χ1411111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-1-1-111
χ1511111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i1111-1-1
χ1611111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii1111-1-1
χ172222222-122222-122-1-122-12222-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000222200000000-1-1-1-1-1-1-1-1000000
χ182222222-122222-122-1-122-12222-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000000011111111000000
χ192222222-122222-122-1-1-2-2-1-2-222-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2111111-2-211-1-1-1-111110000000022-2-200000000-1-1-1-11111000000
χ202222222-122222-122-1-1-2-2-1-2-222-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2111111-2-211-1-1-1-1111100000000-2-222000000001111-1-1-1-1000000
χ212222222-1-2-2-2-22-122-1-122-1-2-222-1-1-1-1-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-1-2-21111111111000000002i−2i2i−2i00000000−i−iii−i−iii000000
χ222222222-1-2-2-2-22-122-1-122-1-2-222-1-1-1-1-1-1-1-1-1-2-2-2-2111122-1-1-1-1-1-1-2-2111111111100000000−2i2i−2i2i00000000ii−i−iii−i−i000000
χ232222222-1-2-2-2-22-122-1-1-2-2-12222-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-211111122-1-11111-1-1-1-1000000002i−2i−2i2i00000000−i−iiiii−i−i000000
χ242222222-1-2-2-2-22-122-1-1-2-2-12222-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-211111122-1-11111-1-1-1-100000000−2i2i2i−2i00000000ii−i−i−i−iii000000
χ25222222-122222-12-1-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000000000
χ26222222-122222-12-1-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-200001111111100000000000000
χ27222222-122222-12-1-122-2-2-1-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1222211-2-2111111-2-2-1-1-1-11111000022-2-20000-1-1-1-1111100000000000000
χ28222222-122222-12-1-122-2-2-1-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1222211-2-2111111-2-2-1-1-1-111110000-2-22200001111-1-1-1-100000000000000
χ29222222-12-2-2-2-2-12-1-12222-1-2-2-1-122-1-1-1-1-1-1-11111-2-2-2-2-1-122-1-1-1-111-2-21111111100002i−2i2i−2i0000−i−iii−i−iii00000000000000
χ30222222-12-2-2-2-2-12-1-12222-1-2-2-1-122-1-1-1-1-1-1-11111-2-2-2-2-1-122-1-1-1-111-2-2111111110000−2i2i−2i2i0000ii−i−iii−i−i00000000000000
χ31222222-12-2-2-2-2-12-1-122-2-2-122-1-122-1-1-1-1-1-1-11111-2-2-2-211-2-21111-1-1221111-1-1-1-100002i−2i−2i2i0000−i−iiiii−i−i00000000000000
χ32222222-12-2-2-2-2-12-1-122-2-2-122-1-122-1-1-1-1-1-1-11111-2-2-2-211-2-21111-1-1221111-1-1-1-10000−2i2i2i−2i0000ii−i−i−i−iii00000000000000
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χ342222-2-22222-2-222222200200-2-2-2-22-2-2-2-22222-2-222-2-200000000000022-2-20000-2-22200000000000000000000000000-2200
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χ4522-2-2-222-12i−2i−2i2i2-1-2-2112-2-12i−2i-221-1-111-1-1112i−2i−2i2i−iii−i2-2-11-1-1112i−2i−ii−iii−i−i−iii00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
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χ4722-2-2-222-12i−2i−2i2i2-1-2-211-22-1−2i2i-221-1-111-1-1112i−2i−2i2i−iii−i-221-111-1-1−2i2ii−i−iii−iii−i−i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ4822-2-2-222-12i−2i−2i2i2-1-2-211-22-1−2i2i-221-1-111-1-1112i−2i−2i2i−iii−i-221-111-1-1−2i2ii−i−iii−iii−i−i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ4922-2-2-222-1−2i2i2i−2i2-1-2-2112-2-1−2i2i-221-1-111-1-111−2i2i2i−2ii−i−ii2-2-11-1-111−2i2ii−ii−i−iiii−i−i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ5022-2-2-222-1−2i2i2i−2i2-1-2-2112-2-1−2i2i-221-1-111-1-111−2i2i2i−2ii−i−ii2-2-11-1-111−2i2ii−ii−i−iiii−i−i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ5122-2-2-222-1−2i2i2i−2i2-1-2-211-22-12i−2i-221-1-111-1-111−2i2i2i−2ii−i−ii-221-111-1-12i−2i−iii−i−ii−i−iii00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
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χ5322-2-2-22-122i−2i−2i2i-1211-2-22-2-12i−2i1-1-22-111-1-111−iii−i2i−2i−2i2i-112-2-1-111−ii2i−2i−iii−i−i−iii000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ5422-2-2-22-122i−2i−2i2i-1211-2-22-2-12i−2i1-1-22-111-1-111−iii−i2i−2i−2i2i-112-2-1-111−ii2i−2i−iii−i−i−iii000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ5522-2-2-22-122i−2i−2i2i-1211-2-2-22-1−2i2i1-1-22-111-1-111−iii−i2i−2i−2i2i1-1-2211-1-1i−i−2i2i−iii−iii−i−i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
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χ5822-2-2-22-12−2i2i2i−2i-1211-2-22-2-1−2i2i1-1-22-111-1-111i−i−ii−2i2i2i−2i-112-2-1-111i−i−2i2ii−i−iiii−i−i000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
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χ8444-4-4-44-2-2−4i4i4i−4i-2-22222-4414i−4i2-22-21-1-111-1-12i−2i−2i2i2i−2i−2i2i2-22-2-1-111−2i2i−2i2i−iii−iii−i−i0000000000000000000000000000000000
χ854-44-400440000-4-44-44-4004000000-400004-40000000000000000000000000000004-4000000000000000000000000000000
χ864-44-400440000-4-44-44-4004000000-400004-4000000000000000000000000000000-44000000000000000000000000000000
χ874-4-4400440000-4-4-44-44004000000-40000-4400000000000000000000000000004-400000000000000000000000000000000
χ884-4-4400440000-4-4-44-44004000000-40000-440000000000000000000000000000-4400000000000000000000000000000000
χ898-88-8008-40000-848-8-4400-400000040000-4400000000000000000000000000000000000000000000000000000000000000
χ908-88-800-4800004-8-448-800-400000040000-4400000000000000000000000000000000000000000000000000000000000000
χ918-88-800-4-4000044-44-44002000000-26-66-62-200000000000000000000000000000000000000000000000000000000000000
χ928-88-800-4-4000044-44-44002000000-2-66-662-200000000000000000000000000000000000000000000000000000000000000
χ938-8-88008-40000-84-884-400-4000000400004-400000000000000000000000000000000000000000000000000000000000000
χ948-8-8800-4800004-84-4-8800-4000000400004-400000000000000000000000000000000000000000000000000000000000000
χ958-8-8800-4-40000444-44-4002000000-26-6-66-2200000000000000000000000000000000000000000000000000000000000000
χ968-8-8800-4-40000444-44-4002000000-2-666-6-2200000000000000000000000000000000000000000000000000000000000000

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