Finite Group Databasebeta

← Group #13167834

Character table — Group #13167834

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222444444444444444444446666666688888888888888812121212121212121212121212121212121218182424242424242424363636363636364848484854547272727272108
order123334666333666812121212122424242424242424246688121236121212122424242424242424242444666121212242424242424242424661212121212122224681261212122466612248
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-111111111111111-1-111-1-111-1-11-1-11-1-1-111-1-1-1-11-1-11-1-1
χ31111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-111-1-111-111-1-1-1-1-1-111-1-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111-1-1-1-111-1-111-111-1-11
χ711111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-1-111111-1-11-11
χ811111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111-1
χ9111111111111111-111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-11-1111111-1-1-1-1-1-1-1-111111-1-1-11-111-1-11-111-11-11111-1-1-1-1
χ10111111111111111-111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-111-11-1-1-111-11-1-11-11-1-11-1-11-11-111
χ11111111111111111-111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11-11-11-1-111-1-1-1-11-1111
χ12111111111111111-111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111-1-1-1111-11-1-1111-11-11-1111-1-111-1-1
χ13111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111111111111-1-1-11-1-1-1111-111-11-1-1-1-1-111-11
χ14111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-111-11-1-1-11-11-11-11-11-1-1111-11-111-1
χ15111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11-1111-11-11-1-11-1-111-1111-11-11-1
χ16111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111111111-1-1-1111-1111-1-11-11-11-11-1-111-1-1-11
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χ33222-12222-12-1-1-1-12-22-1-1-1211-2-2111122-1-1-2-222-1-1-12-1-1-211-2-211112-2002-1-1-1-1-111-2-21111002-100-2100200-2000-110000-100100
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χ8888-4-4-48-4-4-4222222-8-4-422-44444-2-2-2-200000000-1-122-1-14-2-2-2-2111100000000000000000000000000000000000000000000000
χ8988-4-4-4-8-4-4-4222222044-2-2400006i6i−6i−6i00000000-1-1-2-21100000−3i−3i3i3i00000000000000000000000000000000000000000000000
χ9088-4-4-4-8-4-4-4222222044-2-240000−6i−6i6i6i00000000-1-1-2-211000003i3i−3i−3i00000000000000000000000000000000000000000000000
χ918-8-4880-84-8-48-4-8440000000000000000000000-44000000000000000000000000000000000000000000000000000000000000
χ928-8-48-4044-82-4-444-2000000002i6−2i62i6−2i62i6−2i6000000002-20000000−i6i6−i6i6−i6i600000000000000000000000000000000000000000000000
χ938-8-48-4044-82-4-444-200000000−2i62i6−2i62i6−2i62i6000000002-20000000i6−i6i6−i6i6−i600000000000000000000000000000000000000000000000
χ948-8-4-480-844-4-424-2400000026−260026−26−2626000000002-200000−6600−666−600000000000000000000000000000000000000000000000
χ958-8-4-480-844-4-424-24000000−262600−262626−26000000002-2000006−6006−6−6600000000000000000000000000000000000000000000000
χ968-8-4-4-40444222-2-2-20006i−6i026−262i6−2i6−2ζ5+2ζ132ζ5−2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000-1100−3i3i0−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000000000000000000000
χ978-8-4-4-40444222-2-2-20006i−6i0−2626−2i62i62ζ5−2ζ13−2ζ5+2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000-1100−3i3i06−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000000000000000000000
χ988-8-4-4-40444222-2-2-2000−6i6i026−26−2i62i62ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ1300000000-11003i−3i0−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000000000000000000
χ998-8-4-4-40444222-2-2-2000−6i6i0−26262i6−2i6−2ζ7+2ζ232ζ7−2ζ23−2ζ5+2ζ132ζ5−2ζ1300000000-11003i−3i06−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000000000000000000

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