Finite Group Databasebeta

← Group #13162001

Character table — Group #13162001

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818363636363636363636363636363636363636363636727272727272
order1222333446666666663333344666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121244121212122226666668888242424242424242424661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-111
χ511111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-11-1-111
χ811111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111111-111-1-1
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χ102222222-2-22222222222222200222222222222222-2-2-2-20000-2-20000-2-2-2-2-2-2-2-2-2-200000000000000000000-2-2-2-2-2-2200220000000000000000000000
χ11222222-122222-1-122-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222-1-1-1-1-1-1000000000000000000
χ12222222-122222-1-122-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111-2-2-2111111000000000000000000
χ13222222-122222-1-122-122-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-1-1-122-1-1111122-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2-2111111111111111122-1-1-1-12-2-2-1-11111000000000000000000
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χ17222222-1-2-2222-1-122-122-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-2-211i3i3−i3−i3-2-20000-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i322-1-1-1-1-20011i3i3−i3−i3000000000000000000
χ18222222-1-2-2222-1-122-122-1-1-1-10022-1-1-1-1-1-1-1-12-1-1-1-1-2-211i3i3−i3−i3-2-20000-2-2111111110000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-21111200-1-1−i3−i3i3i3000000000000000000
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χ2122222-12222-1-1222-122-12-1-1-1-2-2-1-122-1-1-1-1-1-1-12-1-1-12-122-2-2-2-22-1-2-211-1-122-1-1-1-1-1-11111-2-2111111-2-21111110000000000000002200-1-1-1-10000-201100
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χ232222-12222-12222-122-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-12222222-12-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000220000-1-1-1-10200-1-1
χ242222-12222-12222-122-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-1-12222222-12-1-122-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000-2-2000011110-20011
χ252222-12222-12222-122-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1222-2-2-2-2-1211-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-2111100000000000000000220000-1-1-1-10-20011
χ262222-12222-12222-122-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1-1222-2-2-2-2-1211-2-2-1-1-1-122-1-1-1-1111111-2-2111111-2-2111100000000000000000-2-2000011110200-1-1
χ2722-2-22220022-22-2-2-2-2-222222002-22-22-222-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i2i−2i−2i000000000−i2i22−2−i2−i2i2i222−2−2000000
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χ312-22-22222-2-2-2-2-2-2222-22222200-2-2-2-2-2-2-2-2-2-222222-222-200002-200002-22-22-222-2-20000000000000000000000000002-2002-22-2000000000000000000
χ322-22-22222-2-2-2-2-2-2222-22222200-2-2-2-2-2-2-2-2-2-222222-222-200002-200002-22-22-222-2-2000000000000000000000000000-2200-22-22000000000000000000
χ332-22-2222-22-2-2-2-2-2222-2222222-2-2-2-2-2-2-2-2-2-2-2222222-2-222-22-2-222-22-2-22-22-22-2-22222-2-22-22-222-2-22-22-222-2-2000000000000000000000000000000000
χ342-22-2222-22-2-2-2-2-2222-222222-22-2-2-2-2-2-2-2-2-2-2222222-2-22-22-22-22-22-22-22-22-22-2-222-2-222-22-22-2-222-22-22-2-222000000000000000000000000000000000
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χ412-22-222-1-22-2-2-21122-1-22-1-1-1-1-22-2-2111111112-1-1-1-12-21-11-11-1-22-22-22-221-11-111-1-1-2-2221-11-111-1-11-11-111-1-100−i3i3−i3i3000i3−i3i3−i3−i3i3000000000000000000
χ422-22-222-1-22-2-2-21122-1-22-1-1-1-1-22-2-2111111112-1-1-1-12-21-11-11-1-22-22-22-221-11-111-1-1-2-2221-11-111-1-11-11-111-1-100i3−i3i3−i3000−i3i3−i3i3i3−i3000000000000000000
χ432-22-22-12-22-211-2-22-12-2-12-1-1-12-211-2-2111111-12-1-1-121-222-22-2-2-12-2-111-1-221-111-1-1-1-1112-2-11-1-1112-2-11-1-1110000000000000000000−i3i3−i3i3000000−i3i300
χ442-22-22-12-22-211-2-22-12-2-12-1-1-12-211-2-2111111-12-1-1-121-222-22-2-2-12-2-111-1-221-111-1-1-1-1112-2-11-1-1112-2-11-1-1110000000000000000000i3−i3i3−i3000000i3−i300
χ452-22-22-12-22-211-2-22-12-2-12-1-1-1-2211-2-2111111-12-1-1-121-22-22-22-2-1-221-11-1-221-111-1-111-1-1-221-111-1-1-221-111-1-10000000000000000000−i3i3−i3i3000000i3−i300
χ462-22-22-12-22-211-2-22-12-2-12-1-1-1-2211-2-2111111-12-1-1-121-22-22-22-2-1-221-11-1-221-111-1-111-1-1-221-111-1-1-221-111-1-10000000000000000000i3−i3i3−i3000000−i3i300
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χ482-22-2-122-221-2-2-2-2-1221-1-12-1-12-21111-2-21111-1-12-1-1-1-2-222-22-212-112-21-11-1-2211-1-1-1-111-112-2-1-111-112-2-1-11100000000000000000000000−33−330000−33
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χ684444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32-4-4111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-22222-2-22222111111−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-1-1-1-1-11−3i321+3i321−3i321+3i32-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000
χ694444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i3200111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i322222−2i3−2i32i32i3220000-1-1-1-1-1-11+3i321−3i321+3i321−3i323-33-3i3i3i3i3−3−i323−i32−3−i323−i32−i3−i3−i3−i3−3+i323+i32−3+i323+i32000000000000000000000000000000000
χ704444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i3200111111−1−3i32−1+3i32−1−3i32−1+3i32111−1−3i32−1+3i3222222i32i3−2i3−2i3220000-1-1-1-1-1-11+3i321−3i321+3i321−3i32-33-33−i3−i3−i3−i33+i32−3+i323+i32−3+i32i3i3i3i33−i32−3−i323−i32−3−i32000000000000000000000000000000000
χ714444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i3200111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i322222−2i3−2i32i32i3220000-1-1-1-1-1-11−3i321+3i321−3i321+3i32-33-33i3i3i3i33−i32−3−i323−i32−3−i32−i3−i3−i3−i33+i32−3+i323+i32−3+i32000000000000000000000000000000000
χ724444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i3200111111−1+3i32−1−3i32−1+3i32−1−3i32111−1+3i32−1−3i3222222i32i3−2i3−2i3220000-1-1-1-1-1-11−3i321+3i321−3i321+3i323-33-3−i3−i3−i3−i3−3+i323+i32−3+i323+i32i3i3i3i3−3−i323−i32−3−i323−i32000000000000000000000000000000000
χ7344-4-444-20044-4-22-4-42-44-2-2-2-2004-4-22-22-2-222-42222000000000000000000000000000000000000000000004i−4i−2i−2i2i2i000000000000000000000000000
χ7444-4-444-20044-4-22-4-42-44-2-2-2-2004-4-22-22-2-222-4222200000000000000000000000000000000000000000000−4i4i2i2i−2i−2i000000000000000000000000000
χ7544-4-44-24004-224-4-42-4-4-24-2-2-200-224-4-22-2-2222-422200000000000000000000000000000000000000000000000000000000000−2i22i200i2i2−i2−i20000000000
χ7644-4-44-24004-224-4-42-4-4-24-2-2-200-224-4-22-2-2222-4222000000000000000000000000000000000000000000000000000000000002i2−2i200−i2−i2i2i20000000000
χ7744-4-4-24400-24-44-42-4-42-2-24-2-200-22-224-4-2-22222-422000000000000000000000000000000000000000000000000000000000000022−220000−2−222000000
χ7844-4-4-24400-24-44-42-4-42-2-24-2-200-22-224-4-2-22222-4220000000000000000000000000000000000000000000000000000000000000−2222000022−2−2000000
χ794-44-44-244-4-422-4-44-24-4-24-2-2-20022-4-4222222-24-2-2-2-4-24-40000420000-224-4-22-2-22200000000000000000000000000000000000000000000000000000
χ804-44-44-2-24-4-422224-2-2-4-2-2111002222-1-1-1-1-1-1-2-2111-4-2-22−2i32i32i3−2i3420000-22-221-111-1-10000−2i32i3i3−i3i3i3−i3−i32i3−2i3−i3i3−i3−i3i3i3000000000000000000000000000000000
χ814-44-44-2-24-4-422224-2-2-4-2-2111002222-1-1-1-1-1-1-2-2111-4-2-222i3−2i3−2i32i3420000-22-221-111-1-100002i3−2i3−i3i3−i3−i3i3i3−2i32i3i3−i3i3i3−i3−i3000000000000000000000000000000000
χ824-44-44-2-2-44-422224-2-2-4-2-21114-42222-1-1-1-1-1-1-2-2111422-2-22-22-4-24-4-222-22-2-11-1-111-2-222-221-111-1-1-221-111-1-1000000000000000000000000000000000
χ834-44-44-2-2-44-422224-2-2-4-2-2111-442222-1-1-1-1-1-1-2-2111422-22-22-2-4-2-442-22-22-2-11-1-11122-2-22-2-11-1-1112-2-11-1-111000000000000000000000000000000000
χ844-44-4-2444-42-4-4-4-4-2442-2-24-2-2002222-4-42222-2-24-2-2244-40000-2-40000-22-224-4-2-22200000000000000000000000000000000000000000000000000000
χ854-44-4-24-24-42-4-422-24-22-21-2110022-1-122-1-1-1-1-21-21124-22−2i32i32i3−2i3-2-40000-221-1-2211-1-10000i3−i3−2i32i3i3i3−i3−i3−i3i32i3−2i3−i3−i3i3i3000000000000000000000000000000000
χ864-44-4-24-24-42-4-422-24-22-21-2110022-1-122-1-1-1-1-21-21124-222i3−2i3−2i32i3-2-40000-221-1-2211-1-10000−i3i32i3−2i3−i3−i3i3i3i3−i3−2i32i3i3i3−i3−i3000000000000000000000000000000000
χ874-44-4-24-2-442-4-422-24-22-21-2114-422-1-122-1-1-1-1-21-211-2-42-2-22-2224-224-42-2-112-2-1-111-2-2221-1-2211-1-11-1-2211-1-1000000000000000000000000000000000
χ884-44-4-24-2-442-4-422-24-22-21-211-4422-1-122-1-1-1-1-21-211-2-42-22-22-2242-2-442-2-112-2-1-11122-2-2-112-2-1-111-112-2-1-111000000000000000000000000000000000
χ894-44-4-2-244-4222-4-4-2-2421-2-21100-1-12222-1-1-1-11-2-2112-24-40000-2200001-1-22-2211-1-13-3-3300003-3-3300003-3-33000000000000000000000000000000000
χ904-44-4-2-244-4222-4-4-2-2421-2-21100-1-12222-1-1-1-11-2-2112-24-40000-2200001-1-22-2211-1-1-333-30000-333-30000-333-3000000000000000000000000000000000
χ914-44-4-2-24-44222-4-4-2-2421-2-2114-4-1-12222-1-1-1-11-2-211-22-444-44-42-2-22-22-112-22-2-1-11111-1-1-22-2211-1-1-22-2211-1-1000000000000000000000000000000000
χ924-44-4-2-24-44222-4-4-2-2421-2-211-44-1-12222-1-1-1-11-2-211-22-44-44-442-22-22-2-112-22-2-1-111-1-1112-22-2-1-1112-22-2-1-111000000000000000000000000000000000
χ934-44-4-2-2-24-422222-2-2-22111−1−3i32−1+3i3200-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-2-22−2i32i32i3−2i3-2200001-11-11-1−1−3i32−1+3i321+3i321−3i323-3-33i3−i3i3−i3−3−i323−i323+i32−3+i32−i3i3−i3i3−3+i323+i323−i32−3−i32000000000000000000000000000000000
χ944-44-4-2-2-24-422222-2-2-22111−1−3i32−1+3i3200-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i322-2-222i3−2i3−2i32i3-2200001-11-11-1−1−3i32−1+3i321+3i321−3i32-333-3−i3i3−i3i33+i32−3+i32−3−i323−i32i3−i3i3−i33−i32−3−i32−3+i323+i32000000000000000000000000000000000
χ954-44-4-2-2-24-422222-2-2-22111−1+3i32−1−3i3200-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-2-22−2i32i32i3−2i3-2200001-11-11-1−1+3i32−1−3i321−3i321+3i32-333-3i3−i3i3−i33−i32−3−i32−3+i323+i32−i3i3−i3i33+i32−3+i32−3−i323−i32000000000000000000000000000000000
χ964-44-4-2-2-24-422222-2-2-22111−1+3i32−1−3i3200-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i322-2-222i3−2i3−2i32i3-2200001-11-11-1−1+3i32−1−3i321−3i321+3i323-3-33−i3i3−i3i3−3+i323+i323−i32−3−i32i3−i3i3−i3−3−i323−i323+i32−3+i32000000000000000000000000000000000
χ974-44-4-2-2-2-4422222-2-2-22111−1−3i32−1+3i324-4-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-222-2-22-222-2-22-22-11-11-111+3i321−3i32−1−3i32−1+3i3211-1-11-11-1−1−3i32−1+3i321+3i321−3i321-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000000000
χ984-44-4-2-2-2-4422222-2-2-22111−1−3i32−1+3i32-44-1-1-1-1-1-11+3i321−3i321+3i321−3i32111−1−3i32−1+3i32-222-22-22-22-22-22-2-11-11-111+3i321−3i32−1−3i32−1+3i32-1-111-11-111+3i321−3i32−1−3i32−1+3i32-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000000000
χ994-44-4-2-2-2-4422222-2-2-22111−1+3i32−1−3i324-4-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-222-2-22-222-2-22-22-11-11-111−3i321+3i32−1+3i32−1−3i3211-1-11-11-1−1+3i32−1−3i321−3i321+3i321-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000000000
χ1004-44-4-2-2-2-4422222-2-2-22111−1+3i32−1−3i32-44-1-1-1-1-1-11−3i321+3i321−3i321+3i32111−1+3i32−1−3i32-222-22-22-22-22-22-2-11-11-111−3i321+3i32−1+3i32−1−3i32-1-111-11-111−3i321+3i32−1+3i32−1−3i32-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000000000
χ1014-4-4444400-4-44-44-4-4-444444400-44-44-44-4-444-4-4-4-4-400000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-4444-200-4-442-2-4-4244-2-2-2-200-442-22-222-2-2-42222000000000000000000000000000000000000000000000023−23−2323000000000000000000000000000
χ1034-4-4444-200-4-442-2-4-4244-2-2-2-200-442-22-222-2-2-422220000000000000000000000000000000000000000000000−232323−23000000000000000000000000000
χ1044-4-444-2400-42-2-44-42-44-24-2-2-2002-2-442-222-2-22-42220000000000000000000000000000000000000000000000000000000000000006−6−660000000000
χ1054-4-444-2400-42-2-44-42-44-24-2-2-2002-2-442-222-2-22-4222000000000000000000000000000000000000000000000000000000000000000−666−60000000000
χ1064-4-44-244002-44-442-4-4-2-2-24-2-2002-22-2-4422-2-222-42200000000000000000000000000000000000000000000000000000000000000000006−6−66000000
χ1074-4-44-244002-44-442-4-4-2-2-24-2-2002-22-2-4422-2-222-4220000000000000000000000000000000000000000000000000000000000000000000−666−6000000
χ10888-8-88-4-4008-44-44-844-8-4-422200-44-442-222-2-244-2-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-48-400-48-8-444-844-42-42200-442-2-4422-2-24-24-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4800-4-448-844-842-4-422002-2-44-4422-2-2-244-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-400-4-44-444444222−1−3i3−1+3i3002-22-22-2−1−3i3−1+3i31+3i31−3i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000000000000000
χ11288-8-8-4-4-400-4-44-444444222−1+3i3−1−3i3002-22-22-2−1+3i3−1−3i31−3i31+3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-888-4-400-84-44-4-8448-4-4222004-44-4-22-2-22244-2-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-4004-884-44-84-4-42-422004-4-224-4-2-2224-24-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-480044-4-8844-8-42-4-42200-224-44-4-2-222-244-2-200000000000000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044-44-4444-4222−1−3i3−1+3i300-22-22-221+3i31−3i3−1−3i3−1+3i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044-44-4444-4222−1+3i3−1−3i300-22-22-221−3i31+3i3−1+3i3−1−3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000000000000

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