Finite Group Databasebeta

← Group #13161952

Character table — Group #13161952

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636363636363636363636363636727272727272
order122233344666666666223333366666666666666666661212121212126666666666666666666666661212121212121212121222666622466668888121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-111
χ5111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-1-1-111111111111111-1-1-1-1-1-1
χ6111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1111111-1-1-1-11111-1-1-1-1-11-1-111
χ8111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11111-1-111-1-1-1-1-1-111111-111-1-1
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χ11222222-122222-1-12-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-10000-1-100000000000000
χ12222222-122222-1-12-122222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-12-1-122222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-21111-2-2-2111100001100000000000000
χ13222222-122222-1-12-122-2-22-1-1-1-1111122-1-1-1-1-1-1-1-12-1-1-1-12-1-1222-2-2-2-2-2-2-2-2111111111111111122-1-1-1-1-1-1-1-122-1-1-1-1-2-2211110000-1-100000000000000
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χ17222222-1-2-2222-1-12-122002-1-1-1-1i3i3−i3−i322-1-1-1-1-1-1-1-12-1-1-1-1-211-2-2-200000000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-21111111122-1-1-1-100-2i3i3−i3−i300001100000000000000
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χ252222-12222-1-1222222-1-2-2-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1222-12-111-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-100000000000000022000000-1-1-1-10-20011
χ262222-12222-1-1222222-1-2-2-1-12-1-1-2-2-2-2-1-1-1-122-1-1-1-1-1-12-1-1222-12-111-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-1000000000000000-2-200000011110200-1-1
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χ332-2-22222-22-2-2-2-2-222-222-2222222-22-2-2-2-2-2-2-2-2-2-2-2222222-22-2-222-22-222-2-22-22-222-2-22-22-222-2-2-22-22-22-2-222000000000000000000000000000000000
χ342-2-22222-22-2-2-2-2-222-22-2222222-22-22-2-2-2-2-2-2-2-2-2-2222222-22-2-22-22-22-2-222-22-22-2-222-22-22-2-222-22-22-22-2-222000000000000000000000000000000000
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χ372-2-2222-12-2-2-2-2112-1-22002-1-1-1-1i3−i3−i3i3-2-2111111112-1-1-1-1-2-1122-200000000i3−i3i3−i3i3i3−i3−i3−i3i3−i3i3−i3−i3i3i32-2-11-11-1-11100−i3i3−i3i3-2201-11-10000−i3i300000000000000
χ382-2-2222-12-2-2-2-2112-1-22002-1-1-1-1i3−i3−i3i3-2-2111111112-1-1-1-1-2-1122-200000000i3−i3i3−i3i3i3−i3−i3−i3i3−i3i3−i3−i3i3i32-2-11-11-1-11100i3−i3i3−i32-20-11-110000i3−i300000000000000
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χ422-2-2222-1-22-2-2-2112-1-22-222-1-1-1-11-11-1-2-2111111112-1-1-1-121-1-2-22-22-22-2-2221-11-111-1-11-11-111-1-1-221-11-111-1-100i3−i3i3−i3000−i3i3i3−i30000−i3i300000000000000
χ432-2-222-12-22-2-21-2-2-12122-2-12-1-1-12-22-211-2-2111111-12-1-1-1-1-22-2122-2-11-1-1112-2-11-1-1112-2-11-1-1111-1-221-111-1-100000000000000000003−33−30000003−300
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χ452-2-222-12-22-2-21-2-2-1212-22-12-1-1-1-22-2211-2-2111111-12-1-1-1-1-22-212-221-111-1-1-221-111-1-1-221-111-1-11-1-221-111-1-100000000000000000003−33−3000000−3300
χ462-2-222-12-22-2-21-2-2-1212-22-12-1-1-1-22-2211-2-2111111-12-1-1-1-1-22-212-221-111-1-1-221-111-1-1-221-111-1-11-1-221-111-1-10000000000000000000−33−330000003−300
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χ674444-2-2-244-2-2-2-2-2-2-2-2-2-4-4111−1−3i32−1+3i322222111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-22222-1-1-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-11−3i321+3i321−3i321+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000
χ684444-2-2-244-2-2-2-2-2-2-2-2-2-4-4111−1+3i32−1−3i322222111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-22222-1-1-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-11+3i321−3i321+3i321−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000
χ694444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1−3i32−1+3i32−2i3−2i32i32i3111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i3222222200003-33-3i3i3i3i3−3−i323−i32−3−i323−i32−i3−i3−i3−i3−3+i323+i32−3+i323+i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000
χ704444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1−3i32−1+3i322i32i3−2i3−2i3111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i322222220000-33-33−i3−i3−i3−i33+i32−3+i323+i32−3+i32i3i3i3i33−i32−3−i323−i32−3−i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000
χ714444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1+3i32−1−3i32−2i3−2i32i32i3111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i322222220000-33-33i3i3i3i33−i32−3−i323−i32−3−i32−i3−i3−i3−i33+i32−3+i323+i32−3+i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000
χ724444-2-2-2-4-4-2-2-2-2-2-2-2-2-200111−1+3i32−1−3i322i32i3−2i3−2i3111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i3222222200003-33-3−i3−i3−i3−i3−3+i323+i32−3+i323+i32i3i3i3i3−3−i323−i32−3−i323−i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000000000000
χ7344-4-444-2004-44-22-42-4-4004-2-2-2-200004-4-22-22-2-222-4222200000000000000000000000000000000000000004-4-2-222000000000000000000000000000
χ7444-4-444-2004-44-22-42-4-4004-2-2-2-200004-4-22-22-2-222-422220000000000000000000000000000000000000000-4422-2-2000000000000000000000000000
χ7544-4-44-24004-4-24-42-42-400-24-2-2-20000-224-4-22-2-2222-422200000000000000000000000000000000000000000000000000000−2i22i20000i2i2−i2−i20000000000
χ7644-4-44-24004-4-24-42-42-400-24-2-2-20000-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000000002i2−2i20000−i2−i2i2i20000000000
χ7744-4-4-24400-2244-4-4-4-4200-2-24-2-20000-22-224-4-2-22222-4220000000000000000000000000000000000000000000000000000000−2i22i2000000i2i2−i2−i2000000
χ7844-4-4-24400-2244-4-4-4-4200-2-24-2-20000-22-224-4-2-22222-42200000000000000000000000000000000000000000000000000000002i2−2i2000000−i2−i2i2i2000000
χ794-44-444400-44-4-44-4-44-400444440000-44-44-44-4-444-4-4-4-4-40000000000000000000000000000000000000000000000000000000000000000000000000
χ804-44-444-200-44-42-2-424-4004-2-2-2-20000-442-22-222-2-2-42222000000000000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000
χ814-44-444-200-44-42-2-424-4004-2-2-2-20000-442-22-222-2-2-422220000000000000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ824-44-44-2400-442-442-4-2-400-24-2-2-200002-2-442-222-2-22-422200000000000000000000000000000000000000000000000000000000000i6−i6−i6i60000000000
χ834-44-44-2400-442-442-4-2-400-24-2-2-200002-2-442-222-2-22-422200000000000000000000000000000000000000000000000000000000000−i6i6i6−i60000000000
χ844-44-4-244002-2-4-44-4-44200-2-24-2-200002-22-2-4422-2-222-4220000000000000000000000000000000000000000000000000000000000000006−6−66000000
χ854-44-4-244002-2-4-44-4-44200-2-24-2-200002-22-2-4422-2-222-422000000000000000000000000000000000000000000000000000000000000000−666−6000000
χ864-4-444-244-4-4-42-4-4-242400-24-2-2-2000022-4-4222222-24-2-2-224-44-2-4000000000000000000000000-224-4-22-2-222000000000000000000000000000000000
χ874-4-444-2-24-4-4-4222-2-22400-2-2111−2i32i32i3−2i32222-1-1-1-1-1-1-2-21112-224-2-400000000−2i32i3i3−i3i3i3−i3−i32i3−2i3−i3i3−i3−i3i3i3-22-221-111-1-1000000000000000000000000000000000
χ884-4-444-2-24-4-4-4222-2-22400-2-21112i3−2i3−2i32i32222-1-1-1-1-1-1-2-21112-224-2-4000000002i3−2i3−i3i3−i3−i3i3i3−2i32i3i3−i3i3i3−i3−i3-22-221-111-1-1000000000000000000000000000000000
χ894-4-444-2-2-44-4-4222-2-2244-4-2-2111-22-222222-1-1-1-1-1-1-2-2111-22-2-4244-4-22-2-222-221-111-1-1-221-111-1-12-22-2-11-1-111000000000000000000000000000000000
χ904-4-444-2-2-44-4-4222-2-224-44-2-21112-22-22222-1-1-1-1-1-1-2-2111-22-2-424-442-222-2-22-2-11-1-1112-2-11-1-1112-22-2-11-1-111000000000000000000000000000000000
χ914-4-44-2444-422-4-4-444-4-200-2-24-2-200002222-4-42222-2-24-2-2-44-4-242000000000000000000000000-22-224-4-2-222000000000000000000000000000000000
χ924-4-44-24-24-422-4224-2-4-200-21-211−2i32i32i3−2i322-1-122-1-1-1-1-21-211-4-22-24200000000i3−i3−2i32i3i3i3−i3−i3−i3i32i3−2i3−i3−i3i3i3-221-1-2211-1-1000000000000000000000000000000000
χ934-4-44-24-24-422-4224-2-4-200-21-2112i3−2i3−2i32i322-1-122-1-1-1-1-21-211-4-22-24200000000−i3i32i3−2i3−i3−i3i3i3i3−i3−2i32i3i3i3−i3−i3-221-1-2211-1-1000000000000000000000000000000000
χ944-4-44-24-2-4422-4224-2-4-24-4-21-211-22-2222-1-122-1-1-1-1-21-21142-22-4-2-224-4-2-2221-1-2211-1-11-1-2211-1-12-2-112-2-1-111000000000000000000000000000000000
χ954-4-44-24-2-4422-4224-2-4-2-44-21-2112-22-222-1-122-1-1-1-1-21-21142-22-4-22-2-4422-2-2-112-2-1-111-112-2-1-1112-2-112-2-1-111000000000000000000000000000000000
χ964-4-44-2-244-4222-4-4-242-2001-2-2110000-1-12222-1-1-1-11-2-21124-4-2-2200003-3-3300003-3-3300003-3-331-1-22-2211-1-1000000000000000000000000000000000
χ974-4-44-2-244-4222-4-4-242-2001-2-2110000-1-12222-1-1-1-11-2-21124-4-2-220000-333-30000-333-30000-333-31-1-22-2211-1-1000000000000000000000000000000000
χ984-4-44-2-24-44222-4-4-242-24-41-2-2114-44-4-1-12222-1-1-1-11-2-211-2-4422-2-22-2211-1-1-22-2211-1-1-22-2211-1-1-112-22-2-1-111000000000000000000000000000000000
χ994-4-44-2-24-44222-4-4-242-2-441-2-211-44-44-1-12222-1-1-1-11-2-211-2-4422-22-22-2-1-1112-22-2-1-1112-22-2-1-111-112-22-2-1-111000000000000000000000000000000000
χ1004-4-44-2-2-24-422222-2-22-200111−1−3i32−1+3i32−2i32i32i3−2i3-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-2200003-3-33i3−i3i3−i3−3−i323−i323+i32−3+i32−i3i3−i3i3−3+i323+i323−i32−3−i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000000
χ1014-4-44-2-2-24-422222-2-22-200111−1−3i32−1+3i322i3−2i3−2i32i3-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-22-2-220000-333-3−i3i3−i3i33+i32−3+i32−3−i323−i32i3−i3i3−i33−i32−3−i32−3+i323+i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000000
χ1024-4-44-2-2-24-422222-2-22-200111−1+3i32−1−3i32−2i32i32i3−2i3-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-220000-333-3i3−i3i3−i33−i32−3−i32−3+i323+i32−i3i3−i3i33+i32−3+i32−3−i323−i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000
χ1034-4-44-2-2-24-422222-2-22-200111−1+3i32−1−3i322i3−2i3−2i32i3-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-22-2-2200003-3-33−i3i3−i3i3−3+i323+i323−i32−3−i32i3−i3i3−i3−3−i323−i323+i32−3+i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000
χ1044-4-44-2-2-2-4422222-2-22-24-4111−1−3i32−1+3i32-22-22-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-2-22-2211-1-11-11-1−1−3i32−1+3i321+3i321−3i321-11-1−1+3i32−1−3i321−3i321+3i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ1054-4-44-2-2-2-4422222-2-22-24-4111−1+3i32−1−3i32-22-22-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-22-222-2-22-2211-1-11-11-1−1+3i32−1−3i321−3i321+3i321-11-1−1−3i32−1+3i321+3i321−3i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ1064-4-44-2-2-2-4422222-2-22-2-44111−1−3i32−1+3i322-22-2-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-22-222-22-22-2-1-111-11-111+3i321−3i32−1−3i32−1+3i32-11-111−3i321+3i32−1+3i32−1−3i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ1074-4-44-2-2-2-4422222-2-22-2-44111−1+3i32−1−3i322-22-2-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-22-222-22-22-2-1-111-11-111−3i321+3i32−1+3i32−1−3i32-11-111+3i321−3i32−1−3i32−1+3i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ10888-8-88-4-4008-8-4-44444-800-4-42220000-44-442-222-2-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-48-400-448-44-84-8400-42-4220000-442-2-4422-2-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4800-44-48-84-844002-4-42200002-2-44-4422-2-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-44-4-44444400222−1−3i3−1+3i300002-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ11288-8-8-4-4-400-44-4-44444400222−1+3i3−1−3i300002-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-88-4-400-8844-444-4-800-4-422200004-44-4-22-2-22244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-48-4004-4-84-4-848400-42-42200004-4-224-4-2-2224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-48004-44-884-8-44002-4-4220000-224-44-4-2-222-244-2-20000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-88-8-4-4-4004-444-444-4400222−1−3i3−1+3i30000-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-88-8-4-4-4004-444-444-4400222−1+3i3−1−3i30000-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).