Finite Group Databasebeta

← Group #13178698

Character table — Group #13178698

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size111122222222222244444444444444444444444444444888888888888888888888888888888888888363636363636363636363636363636363636363636363636727272727272
order12223336666666662233333466666666666666666661212666666666666666666666666121212121212121212121212444444444444121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1
χ511111111111111111-111111-111-1-1111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-11-1-1-11-111-1-1-1-1-1-111-1-1111-11-1
χ611111111111111111-111111-111-1-1111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-111-1111-1-11111-1-111-1-1-111-1
χ711111111111111111-111111-111-1-1111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-1-1-11-1-111-1-1-1-1-1-11111-11-11
χ811111111111111111-111111-111-1-1111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-111111111-1-1-1-11-1-11
χ91111111111111111-1111111-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-111-1-1-111-1-111-1-1-1-1-1-11-111-11
χ101111111111111111-1111111-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-11-111111-1-1-1-1111111-11-1-1-11
χ111111111111111111-1111111-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-111-1-11111-1-111111-1-1-11-1
χ121111111111111111-1111111-1-1-111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11-1-1-1-111-1-111-1-1-1-1-11111-1
χ131111111111111111-1-1111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-11-1-1-1-11-111111-1-111-1-1111-11-1-1-1
χ141111111111111111-1-1111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-11-11-1-11-11-1111111-1-111-1-1-11-11-1-1
χ151111111111111111-1-1111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1111-111-1-1-1-1-1-1-11111-1-11-1-1111
χ161111111111111111-1-1111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-111-1111-1-11-1-1-1-111-1-1-1-111-111-111
χ17222222-12222-1-122-1222-1-1-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1220000220000-1-1-1-1000000000000-1-1
χ18222222-12222-1-122-1222-1-1-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-1-12-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-20000-2-20000111100000000000011
χ19222222-12222-1-122-12-22-1-1-1-1-222-2-222-1-1-1-1-1-1-1-12-1-1-1-1112-1-2122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-2111111112-200002-20000-1-111000000000000-11
χ20222222-12222-1-122-12-22-1-1-1-1-222-2-222-1-1-1-1-1-1-1-12-1-1-1-1112-1-2122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-211111111-220000-22000011-1-10000000000001-1
χ21222222-12222-1-122-1-222-1-1-1-1-2-2-22222-1-1-1-1-1-1-1-12-1-1-1-111-212-1-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-2111111112-20000-220000-1-1110000000000001-1
χ22222222-12222-1-122-1-222-1-1-1-1-2-2-22222-1-1-1-1-1-1-1-12-1-1-1-111-212-1-2-21111111122-1-1-1-1-1-1-1-1-2-2-2-211111111-2200002-2000011-1-1000000000000-11
χ23222222-12222-1-122-1-2-22-1-1-1-12-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-1-1-1-21-21-2-211111111-2-2111111112222-1-1-1-1-1-1-1-1220000-2-20000-1-1-1-100000000000011
χ24222222-12222-1-122-1-2-22-1-1-1-12-2-2-2-222-1-1-1-1-1-1-1-12-1-1-1-1-1-1-21-21-2-211111111-2-2111111112222-1-1-1-1-1-1-1-1-2-200002200001111000000000000-1-1
χ2522222-1222-1-1222-1222-12-1-1-1222-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-100002200002200000000-1-1-1-100-1-100
χ2622222-1222-1-1222-1222-12-1-1-1222-1-1-1-122-1-1-1-1-1-1-12-1-1-122-1222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-12-1-1-122-1-1-1-1-1-10000-2-20000-2-2000000001111001100
χ2722222-1222-1-1222-122-2-12-1-1-1-22211-1-122-1-1-1-1-1-1-12-1-1-1-2-2-12-2-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-211111100002-200002-200000000-1-11100-1100
χ2822222-1222-1-1222-122-2-12-1-1-1-22211-1-122-1-1-1-1-1-1-12-1-1-1-2-2-12-2-2-1-122-1-1-1-1-1-111-2-2111111-2111-2-21111110000-220000-220000000011-1-1001-100
χ2922222-1222-1-1222-12-22-12-1-1-1-2-2-2-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-21-22211-2-2111111-1-122-1-1-1-1-1-1-2111-2-21111110000220000-2-200000000111100-1-100
χ3022222-1222-1-1222-12-22-12-1-1-1-2-2-2-1-1-1-122-1-1-1-1-1-1-12-1-1-1-2-21-22211-2-2111111-1-122-1-1-1-1-1-1-2111-2-21111110000-2-200002200000000-1-1-1-1001100
χ3122222-1222-1-1222-12-2-2-12-1-1-12-2-211-1-122-1-1-1-1-1-1-12-1-1-1221-2-2-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-100002-20000-220000000011-1-100-1100
χ3222222-1222-1-1222-12-2-2-12-1-1-12-2-211-1-122-1-1-1-1-1-1-12-1-1-1221-2-2-211-2-211111111-2-21111112-1-1-122-1-1-1-1-1-10000-2200002-200000000-1-111001-100
χ332222-122-1-12222-12222-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-10022000022000000-1-1-1-10000-1-10000
χ342222-122-1-12222-12222-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-12222-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-12-1-1-1-122-1-1-1-100-2-20000-2-200000011110000110000
χ352222-122-1-12222-1222-2-1-12-1-1-2-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1-2-2221-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-2111100220000-2-200000011110000-1-10000
χ362222-122-1-12222-1222-2-1-12-1-1-2-1-1-2-2-1-1-1-122-1-1-1-1-1-12-1-1-2-2221-2-1-1-1-122-1-1-1-11111-2-211111-21111-2-2111100-2-2000022000000-1-1-1-10000110000
χ372222-122-1-12222-122-22-1-12-1-1-21122-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-21111002-200002-2000000-1-1110000-110000
χ382222-122-1-12222-122-22-1-12-1-1-21122-1-1-1-122-1-1-1-1-1-12-1-1-2-2-2-2-121111-2-21111-1-1-1-122-1-1-1-11-21111-2-2111100-220000-2200000011-1-100001-10000
χ392222-122-1-12222-122-2-2-1-12-1-1211-2-2-1-1-1-122-1-1-1-1-1-12-1-122-2-21-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-1002-20000-2200000011-1-10000-110000
χ402222-122-1-12222-122-2-2-1-12-1-1211-2-2-1-1-1-122-1-1-1-1-1-12-1-122-2-21-21111-2-211111111-2-21111-12-1-1-1-122-1-1-1-100-2200002-2000000-1-11100001-10000
χ4144444-2-244-2-2-2-24-2-244-2-2111444-2-2-2-2-2-2111111-2-2111-2-2-2-24-2-2-2-2-2111111-2-2-2-21111114-2-2-2-2-2111111000000000000000000000000000000
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χ4444444-2-244-2-2-2-24-2-2-4-4-2-21114-4-422-2-2-2-2111111-2-2111-2-222-422222-1-1-1-1-1-12222-1-1-1-1-1-14-2-2-2-2-2111111000000000000000000000000000000
χ454444-24-2-2-244-2-2-24-244-21-2114-2-244-2-211-2-21111-21-211-2-24-2-2-2-2-211-2-21111-2-211-2-21111-24-2-211-2-21111000000000000000000000000000000
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χ474444-24-2-2-244-2-2-24-2-44-21-211-42244-2-211-2-21111-21-21122-42-2-222-1-122-1-1-1-1-2-211-2-211112-422-1-122-1-1-1-1000000000000000000000000000000
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χ494444-2-24-2-2-2-244-2-24441-2-2114-2-2-2-211-2-2-2-211111-2-21144-24-2411-2-2-2-2111111-2-2-2-21111-2-211-2-2-2-21111000000000000000000000000000000
χ504444-2-24-2-2-2-244-2-244-41-2-211-4-2-22211-2-2-2-211111-2-211-4-4-242-411-2-2-2-21111-1-12222-1-1-1-122-1-12222-1-1-1-1000000000000000000000000000000
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χ524444-2-24-2-2-2-244-2-24-4-41-2-2114222211-2-2-2-211111-2-211442-42-4-1-12222-1-1-1-1-1-12222-1-1-1-1-2-211-2-2-2-21111000000000000000000000000000000
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χ554444-2-2-2-2-2-2-2-2-2-2-2-24-4111−1−3i32−1+3i32-4-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i3222-2-222111111−1−3i32−1−3i32−1+3i32−1+3i32-1-1-1-1-1-11+3i321+3i321−3i321−3i3222-1-1-1-1-1-11+3i321+3i321−3i321−3i32000000000000000000000000000000
χ564444-2-2-2-2-2-2-2-2-2-2-2-24-4111−1+3i32−1−3i32-4-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i3222-2-222111111−1+3i32−1+3i32−1−3i32−1−3i32-1-1-1-1-1-11−3i321−3i321+3i321+3i3222-1-1-1-1-1-11−3i321−3i321+3i321+3i32000000000000000000000000000000
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χ784-4-444-24-4-422-4-44-2400-24-2-2-2000−2i32i322-4-4222222-24-2-2-20000000000000000−2i32i300−2i32i3−2i32i3−2i32i3000000000000000000000000000000000000000000
χ794-4-444-24-4-422-4-44-2400-24-2-2-20002i3−2i322-4-4222222-24-2-2-200000000000000002i3−2i3002i3−2i32i3−2i32i3−2i3000000000000000000000000000000000000000000
χ804-4-444-2-2-4-422224-2-200-2-2111000−2i32i32222-1-1-1-1-1-1-2-2111−2i32i3000000003-33-33-3−2i32i300i3−i3i3−i3i3−i30000−2i32i3i3−i3i3−i3i3−i3000000000000000000000000000000
χ814-4-444-2-2-4-422224-2-200-2-2111000−2i32i32222-1-1-1-1-1-1-2-21112i3−2i300000000-33-33-33−2i32i300i3−i3i3−i3i3−i300002i3−2i3−i3i3−i3i3−i3i3000000000000000000000000000000
χ824-4-444-2-2-4-422224-2-200-2-21110002i3−2i32222-1-1-1-1-1-1-2-2111−2i32i300000000-33-33-332i3−2i300−i3i3−i3i3−i3i30000−2i32i3i3−i3i3−i3i3−i3000000000000000000000000000000
χ834-4-444-2-2-4-422224-2-200-2-21110002i3−2i32222-1-1-1-1-1-1-2-21112i3−2i3000000003-33-33-32i3−2i300−i3i3−i3i3−i3i300002i3−2i3−i3i3−i3i3−i3i3000000000000000000000000000000
χ844-4-44-24422-4-4-4-4-24400-2-24-2-20−2i32i3002222-4-42222-2-24-2-2000000−2i32i3−2i32i300−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ854-4-44-24422-4-4-4-4-24400-2-24-2-202i3−2i3002222-4-42222-2-24-2-20000002i3−2i32i3−2i3002i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ864-4-44-24-222-4-422-24-200-21-2110−2i32i30022-1-122-1-1-1-1-21-211−2i32i30000−2i32i3i3−i300i3−i3−i3i3003-3003-3-330000i3−i3−2i32i3i3−i3i3−i3000000000000000000000000000000
χ874-4-44-24-222-4-422-24-200-21-2110−2i32i30022-1-122-1-1-1-1-21-2112i3−2i30000−2i32i3i3−i300i3−i3−i3i300-3300-333-30000−i3i32i3−2i3−i3i3−i3i3000000000000000000000000000000
χ884-4-44-24-222-4-422-24-200-21-21102i3−2i30022-1-122-1-1-1-1-21-211−2i32i300002i3−2i3−i3i300−i3i3i3−i300-3300-333-30000i3−i3−2i32i3i3−i3i3−i3000000000000000000000000000000
χ894-4-44-24-222-4-422-24-200-21-21102i3−2i30022-1-122-1-1-1-1-21-2112i3−2i300002i3−2i3−i3i300−i3i3i3−i3003-3003-3-330000−i3i32i3−2i3−i3i3−i3i3000000000000000000000000000000
χ904-4-44-2-242222-4-4-2-24001-2-2110−2i32i3−2i32i3-1-12222-1-1-1-11-2-211000000i3−i3−2i32i300i3−i3−i3i3i3−i300−2i32i3i3−i3i3−i3003-300003-3-33000000000000000000000000000000
χ914-4-44-2-242222-4-4-2-24001-2-2110−2i32i32i3−2i3-1-12222-1-1-1-11-2-211000000i3−i3−2i32i300i3−i3−i3i3−i3i3002i3−2i3−i3i3−i3i300-330000-333-3000000000000000000000000000000
χ924-4-44-2-242222-4-4-2-24001-2-21102i3−2i3−2i32i3-1-12222-1-1-1-11-2-211000000−i3i32i3−2i300−i3i3i3−i3i3−i300−2i32i3i3−i3i3−i300-330000-333-3000000000000000000000000000000
χ934-4-44-2-242222-4-4-2-24001-2-21102i3−2i32i3−2i3-1-12222-1-1-1-11-2-211000000−i3i32i3−2i300−i3i3i3−i3−i3i3002i3−2i3−i3i3−i3i3003-300003-3-33000000000000000000000000000000
χ944-4-44-2-2-2222222-2-2-200111−1−3i32−1+3i320−2i32i3−2i32i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32−2i32i30000i3−i3i3−i33-3−3−i323+i32−3+i323−i32i3−i33-3i3−i3−3−i323+i323−i32−3+i32003-3i3−i3i3−i3−3−i323+i323−i32−3+i32000000000000000000000000000000
χ954-4-44-2-2-2222222-2-2-200111−1−3i32−1+3i320−2i32i32i3−2i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322i3−2i30000i3−i3i3−i33-3−3−i323+i32−3+i323−i32−i3i3-33−i3i33+i32−3−i32−3+i323−i3200-33−i3i3−i3i33+i32−3−i32−3+i323−i32000000000000000000000000000000
χ964-4-44-2-2-2222222-2-2-200111−1−3i32−1+3i3202i3−2i3−2i32i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i322i3−2i30000−i3i3−i3i3-333+i32−3−i323−i32−3+i32i3−i33-3i3−i3−3−i323+i323−i32−3+i3200-33−i3i3−i3i33+i32−3−i32−3+i323−i32000000000000000000000000000000
χ974-4-44-2-2-2222222-2-2-200111−1−3i32−1+3i3202i3−2i32i3−2i3-1-1-1-1-1-11+3i321+3i321−3i321−3i32111−1−3i32−1+3i32−2i32i30000−i3i3−i3i3-333+i32−3−i323−i32−3+i32−i3i3-33−i3i33+i32−3−i32−3+i323−i32003-3i3−i3i3−i3−3−i323+i323−i32−3+i32000000000000000000000000000000
χ984-4-44-2-2-2222222-2-2-200111−1+3i32−1−3i320−2i32i3−2i32i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322i3−2i30000i3−i3i3−i3-333−i32−3+i323+i32−3−i32i3−i3-33i3−i33−i32−3+i32−3−i323+i32003-3−i3i3−i3i3−3+i323−i323+i32−3−i32000000000000000000000000000000
χ994-4-44-2-2-2222222-2-2-200111−1+3i32−1−3i320−2i32i32i3−2i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32−2i32i30000i3−i3i3−i3-333−i32−3+i323+i32−3−i32−i3i33-3−i3i3−3+i323−i323+i32−3−i3200-33i3−i3i3−i33−i32−3+i32−3−i323+i32000000000000000000000000000000
χ1004-4-44-2-2-2222222-2-2-200111−1+3i32−1−3i3202i3−2i3−2i32i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i32−2i32i30000−i3i3−i3i33-3−3+i323−i32−3−i323+i32i3−i3-33i3−i33−i32−3+i32−3−i323+i3200-33i3−i3i3−i33−i32−3+i32−3−i323+i32000000000000000000000000000000
χ1014-4-44-2-2-2222222-2-2-200111−1+3i32−1−3i3202i3−2i32i3−2i3-1-1-1-1-1-11−3i321−3i321+3i321+3i32111−1+3i32−1−3i322i3−2i30000−i3i3−i3i33-3−3+i323−i32−3−i323+i32−i3i33-3−i3i3−3+i323−i323+i32−3−i32003-3−i3i3−i3i3−3+i323−i323+i32−3−i32000000000000000000000000000000
χ10288-8-88-4-48-8-44-44-84400-4-422200000-44-442-22-22-244-2-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-4-448-8-444-8400-42-42200000-442-2-442-22-24-24-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-48-44-448-844-8002-4-422000002-2-44-442-22-2-244-2-200000000000000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-4-44-44-4444400222−1−3i3−1+3i3000002-22-22-2−1−3i31+3i3−1+3i31−3i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-44-44-4444400222−1+3i3−1−3i3000002-22-22-2−1+3i31−3i3−1−3i31+3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-4-884-44-4-84400-4-4222000004-44-4-22-22-2244-2-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-44-4-884-44-8400-42-422000004-4-224-4-22-224-24-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-484-44-4-8844-8002-4-42200000-224-44-4-22-22-244-2-200000000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-44-44-444400222−1−3i3−1+3i300000-22-22-221+3i3−1−3i31−3i3−1+3i3-2-2-21+3i31−3i300000000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-44-44-444400222−1+3i3−1−3i300000-22-22-221−3i3−1+3i31+3i3−1−3i3-2-2-21−3i31+3i300000000000000000000000000000000000000000000000000000000000000000000

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