Finite Group Databasebeta

← Group #11773908

Character table — Group #11773908

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222222222224444444444444444444444448888888888888888888818181818242424242424242424242424242424242424242424242424363636363636
order12222233444466666634444666666666661212121212121212121212121212121212121212121212121212121244448888888824242424242424242424242424242424224444
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
χ51111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ71111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-111
χ911111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i-1-1-1-111
χ1011111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii-1-1-1-111
χ1111111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii1111-1-1
χ1211111111-1-1-1-1111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i1111-1-1
χ1311111111-1-1-1-11111111-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-1
χ1411111111-1-1-1-11111111-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-1
χ1511111111-1-1-1-11111111-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111
χ1611111111-1-1-1-11111111-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111
χ172222222-122222-12-12-1-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000222200000000-1-1-1-1-1-1-1-1000000
χ182222222-122222-12-12-1-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000000011111111000000
χ192222222-122222-12-12-1-1-2-2-2-222-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-211-2-2111111-1-1-1-111110000000022-2-200000000-1-1-1-11111000000
χ202222222-122222-12-12-1-1-2-2-2-222-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-211-2-2111111-1-1-1-1111100000000-2-222000000001111-1-1-1-1000000
χ212222222-1-2-2-2-22-12-12-1-122-2-222-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-21122-1-111111111-1-1-1-1000000002i−2i2i−2i00000000−i−iii−i−iii000000
χ222222222-1-2-2-2-22-12-12-1-122-2-222-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-21122-1-111111111-1-1-1-100000000−2i2i−2i2i00000000ii−i−iii−i−i000000
χ232222222-1-2-2-2-22-12-12-1-1-2-22222-1-1-1-1-1-1-1-1-1-2-2-2-2111122-1-1-2-211-1-1-1-111111111000000002i−2i−2i2i00000000−i−iiiii−i−i000000
χ242222222-1-2-2-2-22-12-12-1-1-2-22222-1-1-1-1-1-1-1-1-1-2-2-2-2111122-1-1-2-211-1-1-1-11111111100000000−2i2i2i−2i00000000ii−i−i−i−iii000000
χ25222222-122222-12-12-12-12222-1-122-1-1-1-1-1-1-1-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1000022220000-1-1-1-1-1-1-1-100000000000000
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χ27222222-122222-12-12-12-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1222211-2-211-2-21111-1-1-1-11111000022-2-20000-1-1-1-1111100000000000000
χ28222222-122222-12-12-12-1-2-2-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1222211-2-211-2-21111-1-1-1-111110000-2-22200001111-1-1-1-100000000000000
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χ30222222-12-2-2-2-2-12-12-12-122-2-2-1-122-1-1-1-1-1-1-11111-2-2-2-211-2-2-1-12211111111-1-1-1-10000−2i2i−2i2i0000ii−i−iii−i−i00000000000000
χ31222222-12-2-2-2-2-12-12-12-1-2-222-1-122-1-1-1-1-1-1-11111-2-2-2-2-1-12211-2-2-1-1-1-11111111100002i−2i−2i2i0000−i−iiiii−i−i00000000000000
χ32222222-12-2-2-2-2-12-12-12-1-2-222-1-122-1-1-1-1-1-1-11111-2-2-2-2-1-12211-2-2-1-1-1-1111111110000−2i2i2i−2i0000ii−i−i−i−iii00000000000000
χ332222-2-22222-2-222222220000-2-2-2-22-2-2-2-22222-2-222-2-200000000000022-2-2000022-2-2000000000000000000000000002-200
χ342222-2-22222-2-222222220000-2-2-2-22-2-2-2-22222-2-222-2-200000000000022-2-20000-2-22200000000000000000000000000-2200
χ352222-2-222-2-22222222220000-2-2-2-22-2-2-2-222-2-222-2-222000000000000-2-222000022-2-200000000000000000000000000-2200
χ362222-2-222-2-22222222220000-2-2-2-22-2-2-2-222-2-222-2-222000000000000-2-2220000-2-222000000000000000000000000002-200
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χ432-22-2-2222−2i2i2i−2i-2-222-2-222i−2i-22-22-22-2-2-2222-2−2i2i2i−2i−2i2i2i−2i-22-222i−2i2i−2i-2-222−2i2i2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ442-22-2-2222−2i2i2i−2i-2-222-2-22−2i2i2-2-22-22-2-2-2222-2−2i2i2i−2i−2i2i2i−2i2-22-2−2i2i−2i2i22-2-2−2i2i2i−2i−2i−2i2i2i0000000000000000000000000000000000
χ452-22-2-222-12i−2i−2i2i-212-1-21-12i−2i2-2-221-1111-1-1-112i−2i−2i2i−iii−i2-2-112i−2i−ii-1-111−iii−i−i−iii00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ462-22-2-222-12i−2i−2i2i-212-1-21-12i−2i2-2-221-1111-1-1-112i−2i−2i2i−iii−i2-2-112i−2i−ii-1-111−iii−i−i−iii00000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ472-22-2-222-12i−2i−2i2i-212-1-21-1−2i2i-22-221-1111-1-1-112i−2i−2i2i−iii−i-221-1−2i2ii−i11-1-1−iii−iii−i−i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000
χ482-22-2-222-12i−2i−2i2i-212-1-21-1−2i2i-22-221-1111-1-1-112i−2i−2i2i−iii−i-221-1−2i2ii−i11-1-1−iii−iii−i−i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000
χ492-22-2-222-1−2i2i2i−2i-212-1-21-12i−2i-22-221-1111-1-1-11−2i2i2i−2ii−i−ii-221-12i−2i−ii11-1-1i−i−ii−i−iii00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ502-22-2-222-1−2i2i2i−2i-212-1-21-12i−2i-22-221-1111-1-1-11−2i2i2i−2ii−i−ii-221-12i−2i−ii11-1-1i−i−ii−i−iii00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ512-22-2-222-1−2i2i2i−2i-212-1-21-1−2i2i2-2-221-1111-1-1-11−2i2i2i−2ii−i−ii2-2-11−2i2ii−i-1-111i−i−iiii−i−i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000
χ522-22-2-222-1−2i2i2i−2i-212-1-21-1−2i2i2-2-221-1111-1-1-11−2i2i2i−2ii−i−ii2-2-11−2i2ii−i-1-111i−i−iiii−i−i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000
χ532-22-2-22-122i−2i−2i2i1-2-121-2-12i−2i2-21-1-22111-1-1-11−iii−i2i−2i−2i2i-112-2−ii2i−2i-1-111−iii−i−i−iii000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ542-22-2-22-122i−2i−2i2i1-2-121-2-12i−2i2-21-1-22111-1-1-11−iii−i2i−2i−2i2i-112-2−ii2i−2i-1-111−iii−i−i−iii000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ552-22-2-22-122i−2i−2i2i1-2-121-2-1−2i2i-221-1-22111-1-1-11−iii−i2i−2i−2i2i1-1-22i−i−2i2i11-1-1−iii−iii−i−i000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000
χ562-22-2-22-122i−2i−2i2i1-2-121-2-1−2i2i-221-1-22111-1-1-11−iii−i2i−2i−2i2i1-1-22i−i−2i2i11-1-1−iii−iii−i−i000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000
χ572-22-2-22-12−2i2i2i−2i1-2-121-2-12i−2i-221-1-22111-1-1-11i−i−ii−2i2i2i−2i1-1-22−ii2i−2i11-1-1i−i−ii−i−iii000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000
χ582-22-2-22-12−2i2i2i−2i1-2-121-2-12i−2i-221-1-22111-1-1-11i−i−ii−2i2i2i−2i1-1-22−ii2i−2i11-1-1i−i−ii−i−iii000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
χ592-22-2-22-12−2i2i2i−2i1-2-121-2-1−2i2i2-21-1-22111-1-1-11i−i−ii−2i2i2i−2i-112-2i−i−2i2i-1-111i−i−iiii−i−i000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000
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χ814-44-44-4-2-2−4i4i−4i4i22-2-22210000-22-22-111-1-11-12i−2i2i−2i2i−2i2i−2i000000003-3-33−ii−ii−3i3i3i−3i0000000000000000000000000000000000
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χ854-44-4-44-2-2−4i4i4i−4i22-2-22214i−4i-442-22-2-1-1-1111-12i−2i−2i2i2i−2i−2i2i2-22-2−2i2i−2i2i-1-111−iii−iii−i−i0000000000000000000000000000000000
χ864-44-4-44-2-2−4i4i4i−4i22-2-2221−4i4i4-42-22-2-1-1-1111-12i−2i−2i2i2i−2i−2i2i-22-222i−2i2i−2i11-1-1−iii−i−i−iii0000000000000000000000000000000000
χ874-4-440044000044-4-4-4-440000000040000-4-400000000000000000000000000004i−4i00000000000000000000000000000000
χ884-4-440044000044-4-4-4-440000000040000-4-40000000000000000000000000000−4i4i00000000000000000000000000000000
χ8988-8-8008-40000-84-848-4-400000000400004-400000000000000000000000000000000000000000000000000000000000000
χ9088-8-800-4800004-84-8-48-400000000400004-400000000000000000000000000000000000000000000000000000000000000
χ9188-8-800-4-400004444-4-4200000000-26-66-6-2200000000000000000000000000000000000000000000000000000000000000
χ9288-8-800-4-400004444-4-4200000000-2-66-66-2200000000000000000000000000000000000000000000000000000000000000
χ938-8-88008-400008-4-84-84-400000000-400004400000000000000000000000000000000000000000000000000000000000000
χ948-8-8800-480000-484-84-8-400000000-400004400000000000000000000000000000000000000000000000000000000000000
χ958-8-8800-4-40000-4-4444420000000026-6-66-2-200000000000000000000000000000000000000000000000000000000000000
χ968-8-8800-4-40000-4-444442000000002-666-6-2-200000000000000000000000000000000000000000000000000000000000000

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