Finite Group Databasebeta

← Group #13161972

Character table — Group #13161972

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222222444444444444444444444444448888888888888888888888888888888888888363636363636363636363636363636363636727272727272727272
order1222333446666666663333366666666666666612121212121226666666666666666666666666612121212121212121212448888121212122424242424242424444121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-11-1111-1-111
χ811111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-11111-1-1
χ92222222-2-222222222222222222222222222222-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-22-2000022-2-200000000000000000
χ102222222-2-222222222222222222222222222222-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-2-220000-2-22200000000000000000
χ11222222-1222222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000200-1-10000
χ12222222-1222222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000-200110000
χ13222222-1222222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-1220000-1-1-1-100000000-200110000
χ14222222-1222222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-122-1-122-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-1-2-20000111100000000200-1-10000
χ15222222-1-2-22222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000−i3i30000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-2111111112-20000-1-11100000000000−i3i30000
χ16222222-1-2-22222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000−i3i30000−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-2-211111111-22000011-1-100000000000i3−i30000
χ17222222-1-2-22222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i30000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-2111111112-20000-1-11100000000000i3−i30000
χ18222222-1-2-22222-1-122-12-1-1-1-122-1-1-1-1-1-1-1-12-1-1-1-1-2-211-2-200000i3−i30000i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-2-211111111-22000011-1-100000000000−i3i30000
χ1922222-122222-1-1222-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-10020000-1-1
χ2022222-122222-1-1222-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1222-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-2-200000000111100-2000011
χ2122222-122222-1-1222-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1-2-2-211-2-21111-2-2111111-2-2111111-1-122-1-1-1-1-1-100002200000000-1-1-1-100-2000011
χ2222222-122222-1-1222-12-12-1-1-1-1-122-1-1-1-1-1-1-12-1-1-12-1222-1-2-2-211-2-21111-2-2111111-2-2111111-1-122-1-1-1-1-1-10000-2-20000000011110020000-1-1
χ232222-12222-1-12222-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-122-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-1000002000-1-100
χ242222-12222-1-12222-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-122-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2000000111100000-20001100
χ252222-12222-1-12222-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-10022000000-1-1-1-100000-20001100
χ262222-12222-1-12222-122-1-12-1-1-1-1-1-122-1-1-1-1-1-12-1-1-1222-12-211-2-2-2-2111111-2-2111111-2-21111-1-1-1-122-1-1-1-100-2-20000001111000002000-1-100
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χ312-2-222-122-2-2-211-2-22-12-12-1-1-111-2-2111111-12-1-1-1212-2-2-1000−i3i300−i3−i3i3i300−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3-112-2-11-1-11100002-200000000-1-1110000000−i3i3
χ322-2-222-122-2-2-211-2-22-12-12-1-1-111-2-2111111-12-1-1-1212-2-2-1000−i3i300−i3−i3i3i300−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3-112-2-11-1-1110000-220000000011-1-10000000i3−i3
χ332-2-222-122-2-2-211-2-22-12-12-1-1-111-2-2111111-12-1-1-1212-2-2-1000i3−i300i3i3−i3−i300i3−i3i3i3−i3−i300i3−i3i3i3−i3−i3-112-2-11-1-11100002-200000000-1-1110000000i3−i3
χ342-2-222-122-2-2-211-2-22-12-12-1-1-111-2-2111111-12-1-1-1212-2-2-1000i3−i300i3i3−i3−i300i3−i3i3i3−i3−i300i3−i3i3i3−i3−i3-112-2-11-1-1110000-220000000011-1-10000000−i3i3
χ352-2-22-122-2211-2-2-2-2-122-1-12-1-11111-2-21111-1-12-1-112-22-1-20−i3i30000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i31-11-1-2211-1-1002-2000000-1-111000000000−i3i300
χ362-2-22-122-2211-2-2-2-2-122-1-12-1-11111-2-21111-1-12-1-112-22-1-20−i3i30000−i3i3−i3i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i31-11-1-2211-1-100-2200000011-1-1000000000i3−i300
χ372-2-22-122-2211-2-2-2-2-122-1-12-1-11111-2-21111-1-12-1-112-22-1-20i3−i30000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i31-11-1-2211-1-1002-2000000-1-111000000000i3−i300
χ382-2-22-122-2211-2-2-2-2-122-1-12-1-11111-2-21111-1-12-1-112-22-1-20i3−i30000i3−i3i3−i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i31-11-1-2211-1-100-2200000011-1-1000000000−i3i300
χ3944444-24-4-444-2-2444-24-24-2-2-2-2-244-2-2-2-2-2-2-24-2-2-2-42-4-4-4200000000000000000000000000022-4-4222222000000000000000000000000000
χ4044444-2-24444-2-2-2-24-2-2-2-2111-2-2-2-2111111-2-21114-2-2-24-2444-2-2-2-2-2-2-2-2-2-2111111-2-2111111-2-2-2-2111111000000000000000000000000000
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χ4244444-2-2-4-444-2-2-2-24-2-2-2-2111-2-2-2-2111111-2-2111-4222-4200000−2i32i30000−2i3−2i3i3i3i3i3i3i32i32i3−i3−i3−i3−i3−i3−i32222-1-1-1-1-1-1000000000000000000000000000
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χ444444-244-4-4-2-24444-244-2-24-2-2-2-2-2-244-2-2-2-2-2-24-2-22-4-4-42-40000000000000000000000000002222-4-42222000000000000000000000000000
χ454444-24-244-2-244-2-2-24-2-21-211-2-211-2-21111-21-211-24-2-2-244-2-244-2-2-2-2-2-211-2-2111111-2-21111-2-211-2-21111000000000000000000000000000
χ464444-24-244-2-244-2-2-24-2-21-211-2-211-2-21111-21-211-24-2-2-24-422-4-4222222-1-122-1-1-1-1-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000
χ474444-24-2-4-4-2-244-2-2-24-2-21-211-2-211-2-21111-21-2112-4222-400000−2i32i30000i3i3−2i3−2i3i3i3i3i3−i3−i32i32i3−i3−i3−i3−i322-1-122-1-1-1-1000000000000000000000000000
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χ494444-2-2444-2-2-2-244-2-241-2-21111-2-2-2-211111-2-211-2-244-2-24-2-2-2-2441111-2-2-2-21111-2-2-2-2111111-2-2-2-21111000000000000000000000000000
χ504444-2-2444-2-2-2-244-2-241-2-21111-2-2-2-211111-2-211-2-244-2-2-42222-4-4-1-1-1-12222-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000
χ514444-2-24-4-4-2-2-2-244-2-241-2-21111-2-2-2-211111-2-21122-4-42200000003-3-3300003-3-3300003-3-33-1-12222-1-1-1-1000000000000000000000000000
χ524444-2-24-4-4-2-2-2-244-2-241-2-21111-2-2-2-211111-2-21122-4-4220000000-333-30000-333-30000-333-3-1-12222-1-1-1-1000000000000000000000000000
χ534444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-24-2-2-2-2-2-211111111−1−3i32−1+3i32−1+3i32−1−3i321111−1+3i32−1−3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000
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χ554444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-24-2-2-2-2-2-211111111−1+3i32−1−3i32−1−3i32−1+3i321111−1−3i32−1+3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ564444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i32111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-4222222-1-1-1-1-1-1-1-11−3i321+3i321+3i321−3i32-1-1-1-11+3i321−3i321−3i321+3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000
χ574444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i3222222200000−2i32i33-3-33i3i3i3i3−3−i323−i323−i32−3−i32−i3−i3−i3−i3−3+i323+i323+i32−3+i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
χ584444-2-2-2-4-4-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32222222000002i3−2i3-333-3−i3−i3−i3−i33+i32−3+i32−3+i323+i32i3i3i3i33−i32−3−i32−3−i323−i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000
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χ794-4-444-2-24-4-4-422224-2-2-2-21112222-1-1-1-1-1-1-2-211142-22-4-20002i3−2i3002i32i3−2i3−2i300−i3i3−i3−i3i3i300−i3i3−i3−i3i3i3-22-221-111-1-1000000000000000000000000000
χ804-4-444-2-2-44-4-422224-2-2-2-21112222-1-1-1-1-1-1-2-2111-4-22-24200000000000003-333-3-300-33-3-3332-22-2-11-1-111000000000000000000000000000
χ814-4-444-2-2-44-4-422224-2-2-2-21112222-1-1-1-1-1-1-2-2111-4-22-2420000000000000-33-3-333003-333-3-32-22-2-11-1-111000000000000000000000000000
χ824-4-44-2444-422-4-4-4-4-244-2-24-2-22222-4-42222-2-24-2-2-2-44-424000000000000000000000000000-22-224-4-2-222000000000000000000000000000
χ834-4-44-24-24-422-4-422-24-2-21-21122-1-122-1-1-1-1-21-211-2-4-2224000000000003-3003-33-3-3300-33-33-221-1-2211-1-1000000000000000000000000000
χ844-4-44-24-24-422-4-422-24-2-21-21122-1-122-1-1-1-1-21-211-2-4-222400000000000-3300-33-333-3003-33-3-221-1-2211-1-1000000000000000000000000000
χ854-4-44-24-2-4422-4-422-24-2-21-21122-1-122-1-1-1-1-21-211242-2-2-40−2i32i30000−2i32i3−2i32i3i3−i300i3−i3i3−i3i3−i300i3−i3i3−i32-2-112-2-1-111000000000000000000000000000
χ864-4-44-24-2-4422-4-422-24-2-21-21122-1-122-1-1-1-1-21-211242-2-2-402i3−2i300002i3−2i32i3−2i3−i3i300−i3i3−i3i3−i3i300−i3i3−i3i32-2-112-2-1-111000000000000000000000000000
χ874-4-44-2-244-42222-4-4-2-241-2-211-1-12222-1-1-1-11-2-211-224-42-2000−2i32i300i3i3−i3−i300−2i32i3i3i3−i3−i300−2i32i3i3i3−i3−i31-1-22-2211-1-1000000000000000000000000000
χ884-4-44-2-244-42222-4-4-2-241-2-211-1-12222-1-1-1-11-2-211-224-42-20002i3−2i300−i3−i3i3i3002i3−2i3−i3−i3i3i3002i3−2i3−i3−i3i3i31-1-22-2211-1-1000000000000000000000000000
χ894-4-44-2-24-442222-4-4-2-241-2-211-1-12222-1-1-1-11-2-2112-2-44-220−2i32i30000i3−i3i3−i3−2i32i300i3−i3i3−i3−2i32i300i3−i3i3−i3-112-22-2-1-111000000000000000000000000000
χ904-4-44-2-24-442222-4-4-2-241-2-211-1-12222-1-1-1-11-2-2112-2-44-2202i3−2i30000−i3i3−i3i32i3−2i300−i3i3−i3i32i3−2i300−i3i3−i3i3-112-22-2-1-111000000000000000000000000000
χ914-4-44-2-2-24-4222222-2-2-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-22-222-2000−2i32i300i3i3−i3−i33-3i3−i3−3−i323−i32−3+i323+i32-33i3−i33−i32−3−i323+i32−3+i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000
χ924-4-44-2-2-24-4222222-2-2-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32-22-222-20002i3−2i300−i3−i3i3i3-33−i3i33+i32−3+i323−i32−3−i323-3−i3i3−3+i323+i32−3−i323−i321-11-11-1−1−3i32−1+3i321+3i321−3i32000000000000000000000000000
χ934-4-44-2-2-24-4222222-2-2-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-22-222-2000−2i32i300i3i3−i3−i3-33i3−i33−i32−3−i323+i32−3+i323-3i3−i3−3−i323−i32−3+i323+i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000
χ944-4-44-2-2-24-4222222-2-2-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32-22-222-20002i3−2i300−i3−i3i3i33-3−i3i3−3+i323+i32−3−i323−i32-33−i3i33+i32−3+i323−i32−3−i321-11-11-1−1+3i32−1−3i321−3i321+3i32000000000000000000000000000
χ954-4-44-2-2-2-44222222-2-2-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322-22-2-220−2i32i30000i3−i3i3−i3i3−i33-3−3−i32−3+i323−i323+i32i3−i3-333−i323+i32−3−i32−3+i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000
χ964-4-44-2-2-2-44222222-2-2-2111−1−3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322-22-2-2202i3−2i30000−i3i3−i3i3−i3i3-333+i323−i32−3+i32−3−i32−i3i33-3−3+i32−3−i323+i323−i32-11-11-111+3i321−3i32−1−3i32−1+3i32000000000000000000000000000
χ974-4-44-2-2-2-44222222-2-2-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322-22-2-220−2i32i30000i3−i3i3−i3i3−i3-333−i323+i32−3−i32−3+i32i3−i33-3−3−i32−3+i323−i323+i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000
χ984-4-44-2-2-2-44222222-2-2-2111−1+3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322-22-2-2202i3−2i30000−i3i3−i3i3−i3i33-3−3+i32−3−i323+i323−i32−i3i3-333+i323−i32−3+i32−3−i32-11-11-111−3i321+3i32−1+3i32−1−3i32000000000000000000000000000
χ9988-8-88-4-4008-8-44-44-844-4-4222-44-442-22-22-244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-400-448-8-444-84-42-422-442-2-442-22-24-24-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4800-44-448-844-82-4-4222-2-44-442-22-2-244-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-400-44-44-44444222−1−3i3−1+3i32-22-22-2−1−3i31+3i3−1+3i31−3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-400-44-44-44444222−1+3i3−1−3i32-22-22-2−1+3i31−3i3−1−3i31+3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-88-4-400-884-44-4-844-4-42224-44-4-22-22-2244-2-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-4004-4-884-44-84-42-4224-4-224-4-22-224-24-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48004-44-4-8844-82-4-422-224-44-4-22-22-244-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4004-44-44-4444222−1−3i3−1+3i3-22-22-221+3i3−1−3i31−3i3−1+3i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004-44-44-4444222−1+3i3−1−3i3-22-22-221−3i3−1+3i31+3i3−1−3i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000000

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