Finite Group Databasebeta

← Group #13154851

Character table — Group #13154851

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222444444444444444444888888888888888812121212121212121212121212121212121218181818181818183636363636363636363636363636108108108108108108
order122222366633666666666666666633666666666666664412121212121212121212121212121212444412121212888812122424242424242424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−i11−i−iii
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−i−iii-1-1−i−i−i−iiiii11ii−i−i
χ91-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-1111-11-11-111-1-111-1-1i−ii−ii−i
χ101-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1-1-111-11-111-1-1-111-1-111i−i−ii−ii
χ111-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1i−i−ii-11ii−i−i−i−iii−ii-111-1
χ121-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1i−iiiiiiiii−i−i−i−i−i−i−i−i-11-1111-1-1−iii−i-11−i−iiiii−i−i−ii1-1-11
χ131-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-1111-11-11-111-1-111-1-1−ii−ii−ii
χ141-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii1-11-1-1-111-11-111-1-1-111-1-111−iii−ii−i
χ151-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1i−i−ii-11ii−i−i−i−iiii−i1-1-11
χ161-11-11-11-1-11111-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−i−i−i−i−i−i−i−iiiiiiiii-11-1111-1-1−iii−i-11−i−iiiii−i−ii−i-111-1
χ17222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000
χ18222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002222-1-1-1-1-2-2-2-2-1-111111111000000
χ19222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-211112i2i−2i−2i11−i−i−i−iiiii000000
χ20222222-1-1-1-122-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-2-2-21111−2i−2i2i2i11iiii−i−i−i−i000000
χ212222-2-2222222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000002-2-22-2-2-2-200002200000000000000
χ222222-2-2222222-2-222-2-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000-222-222220000-2-200000000000000
χ232222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-111110000000000000000002-2-2211110000-1-13−33−33−33−3000000
χ242222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-111110000000000000000002-2-2211110000-1-1−33−33−33−33000000
χ252222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-222-2-1-1-1-1000011−i3i3−i3i3i3−i3i3−i3000000
χ262222-2-2-1-1-1-1221122-2-2-2-222-2-2-2-222-1-1-1-11111-1-1-1-11111000000000000000000-222-2-1-1-1-1000011i3−i3i3−i3−i3i3−i3i3000000
χ272-22-22-2-111-122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000002-22-211-1-12-22-2-11-1-111-1-111000000
χ282-22-22-2-111-122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000002-22-211-1-1-22-22-1111-1-111-1-1000000
χ292-22-22-2-111-122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000-22-22-1-1112i−2i−2i2i1-1−i−iiiii−i−i000000
χ302-22-22-2-111-122-11222222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000-22-22-1-111−2i2i2i−2i1-1ii−i−i−i−iii000000
χ312-22-2-222-2-2222-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2222200000000000000000022-2-222-2-200002-200000000000000
χ322-22-2-222-2-2222-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000-2-222-2-2220000-2200000000000000
χ332-22-2-22-111-1221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-100000000000000000022-2-2-1-1110000-113−3−333−3−33000000
χ342-22-2-22-111-1221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-100000000000000000022-2-2-1-1110000-11−333−3−333−3000000
χ352-22-2-22-111-1221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-1000000000000000000-2-22211-1-100001-1−i3i3i3−i3i3−i3−i3i3000000
χ362-22-2-22-111-1221-122-2-2-2-2-2-22222-2-2-1-1-1-111111111-1-1-1-1000000000000000000-2-22211-1-100001-1i3−i3−i3i3−i3i3i3−i3000000
χ3744444444441-2441-211-2-21-211-2-21-21-21-211-2-211-2-211-2-2441111-2-2-2-21111-2-2-2-20000000000000000000000000000
χ3844444444441-2441-211-2-21-211-2-21-21-21-211-2-211-2-211-2-2-4-4-1-1-1-12222-1-1-1-122220000000000000000000000000000
χ394444444444-2144-21-2-211-21-2-211-21-21-21-2-211-2-211-2-21144-2-2-2-21111-2-2-2-211110000000000000000000000000000
χ404444444444-2144-21-2-211-21-2-211-21-21-21-2-211-2-211-2-211-4-42222-1-1-1-12222-1-1-1-10000000000000000000000000000
χ414444-4-444441-2-4-41-2-1-1221-2-1-1221-21-21-2-1-12211-2-2-1-1220033-3-3000033-3-300000000000000000000000000000000
χ424444-4-444441-2-4-41-2-1-1221-2-1-1221-21-21-2-1-12211-2-2-1-12200-3-3330000-3-33300000000000000000000000000000000
χ434444-4-44444-21-4-4-2122-1-1-2122-1-1-21-21-2122-1-1-2-21122-1-100000033-3-3000033-3-30000000000000000000000000000
χ444444-4-44444-21-4-4-2122-1-1-2122-1-1-21-21-2122-1-1-2-21122-1-1000000-3-3330000-3-3330000000000000000000000000000
χ4544-4-40044-4-41-200-123-3001-23-300-121-2-123-3001-12-23-300003−33−30023−233−33−30023−230000000000000000000000000000
χ4644-4-40044-4-41-200-123-3001-23-300-121-2-123-3001-12-23-30000−33−3300−2323−33−3300−23230000000000000000000000000000
χ4744-4-40044-4-41-200-12-33001-2-3300-121-2-12-33001-12-2-3300003−3−3323−23003−3−3323−23000000000000000000000000000000
χ4844-4-40044-4-41-200-12-33001-2-3300-121-2-12-33001-12-2-330000−333−3−232300−333−3−2323000000000000000000000000000000
χ4944-4-40044-4-44400-4-40000440000-4-444-4-400004-4-4400000000000000000000000000000000000000000000000000
χ5044-4-40044-4-4-21002-1003-3-21003-32-1-212-1003-3-22-11003-3000023−233−3−330023−233−3−330000000000000000000000000000
χ5144-4-40044-4-4-21002-1003-3-21003-32-1-212-1003-3-22-11003-30000−2323−333−300−2323−333−30000000000000000000000000000
χ5244-4-40044-4-4-21002-100-33-2100-332-1-212-100-33-22-1100-330023−2300−33−3323−2300−33−330000000000000000000000000000
χ5344-4-40044-4-4-21002-100-33-2100-332-1-212-100-33-22-1100-3300−2323003−33−3−2323003−33−30000000000000000000000000000
χ5444-4-400-2-2224400-4-40000440000-4-4-2-2220000-222-20000000000000000000000000023−2323−2300000000000000000000
χ5544-4-400-2-2224400-4-40000440000-4-4-2-2220000-222-200000000000000000000000000−2323−232300000000000000000000
χ564-44-44-44-4-441-24-41-211-2-2-12-1-122-121-21-211-2-2-1-122-1-1224i−4iiiii−2i−2i−2i−2i−i−i−i−i2i2i2i2i0000000000000000000000000000
χ574-44-44-44-4-441-24-41-211-2-2-12-1-122-121-21-211-2-2-1-122-1-122−4i4i−i−i−i−i2i2i2i2iiiii−2i−2i−2i−2i0000000000000000000000000000
χ584-44-44-44-4-44-214-4-21-2-2112-122-1-12-1-21-21-2-21122-1-122-1-14i−4i−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000000000
χ594-44-44-44-4-44-214-4-21-2-2112-122-1-12-1-21-21-2-21122-1-122-1-1−4i4i2i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000000000
χ604-44-4-444-4-441-2-441-2-1-122-1211-2-2-121-21-2-1-122-1-12211-2-2003i3i−3i−3i0000−3i−3i3i3i00000000000000000000000000000000
χ614-44-4-444-4-441-2-441-2-1-122-1211-2-2-121-21-2-1-122-1-12211-2-200−3i−3i3i3i00003i3i−3i−3i00000000000000000000000000000000
χ624-44-4-444-4-44-21-44-2122-1-12-1-2-2112-1-21-2122-1-122-1-1-2-2110000003i3i−3i−3i0000−3i−3i3i3i0000000000000000000000000000
χ634-44-4-444-4-44-21-44-2122-1-12-1-2-2112-1-21-2122-1-122-1-1-2-211000000−3i−3i3i3i00003i3i−3i−3i0000000000000000000000000000
χ644-4-44004-44-41-200-123-300-12-33001-21-2-123-300-11-22-330000−i3i3−i3i300−2i32i3i3−i3i3−i3002i3−2i30000000000000000000000000000
χ654-4-44004-44-41-200-123-300-12-33001-21-2-123-300-11-22-330000i3−i3i3−i3002i3−2i3−i3i3−i3i300−2i32i30000000000000000000000000000
χ664-4-44004-44-41-200-12-3300-123-3001-21-2-12-3300-11-223-30000−i3i3i3−i3−2i32i300i3−i3−i3i32i3−2i3000000000000000000000000000000
χ674-4-44004-44-41-200-12-3300-123-3001-21-2-12-3300-11-223-30000i3−i3−i3i32i3−2i300−i3i3i3−i3−2i32i3000000000000000000000000000000
χ684-4-44004-44-44400-4-40000-4-400004444-4-40000-444-400000000000000000000000000000000000000000000000000
χ694-4-44004-44-4-21002-1003-32-100-33-21-212-1003-32-21-100-330000−2i32i3−i3i3i3−i3002i3−2i3i3−i3−i3i30000000000000000000000000000
χ704-4-44004-44-4-21002-1003-32-100-33-21-212-1003-32-21-100-3300002i3−2i3i3−i3−i3i300−2i32i3−i3i3i3−i30000000000000000000000000000
χ714-4-44004-44-4-21002-100-332-1003-3-21-212-100-332-21-1003-300−2i32i300i3−i3i3−i32i3−2i300−i3i3−i3i30000000000000000000000000000
χ724-4-44004-44-4-21002-100-332-1003-3-21-212-100-332-21-1003-3002i3−2i300−i3i3−i3i3−2i32i300i3−i3i3−i30000000000000000000000000000
χ734-4-4400-22-224400-4-40000-4-4000044-2-22200002-2-220000000000000000000000000023−23−232300000000000000000000
χ744-4-4400-22-224400-4-40000-4-4000044-2-22200002-2-2200000000000000000000000000−232323−2300000000000000000000
χ75888888-4-4-4-42-4-4-42-422-4-42-422-4-42-4-12-12-1-122-1-122-1-1220000000000000000000000000000000000000000000000
χ76888888-4-4-4-4-42-4-4-42-4-422-42-4-422-422-12-122-1-122-1-122-1-10000000000000000000000000000000000000000000000
χ778888-8-8-4-4-4-42-4442-4-2-2442-4-2-2442-4-12-1211-2-2-1-12211-2-20000000000000000000000000000000000000000000000
χ788888-8-8-4-4-4-4-4244-4244-2-2-4244-2-2-422-12-1-2-21122-1-1-2-2110000000000000000000000000000000000000000000000
χ7988-8-800-4-4442-400-246-6002-46-600-24-121-2-3300-11-22-33000000000000000000000000000000000000000000000000
χ8088-8-800-4-4442-400-24-66002-4-6600-24-121-23-300-11-223-3000000000000000000000000000000000000000000000000
χ8188-8-800-4-444-42004-2006-6-42006-64-22-1-2100-332-21-100-330000000000000000000000000000000000000000000000
χ8288-8-800-4-444-42004-200-66-4200-664-22-1-21003-32-21-1003-30000000000000000000000000000000000000000000000
χ838-88-88-8-444-42-4-442-422-4-4-24-2-244-24-12-12-1-12211-2-211-2-20000000000000000000000000000000000000000000000
χ848-88-88-8-444-4-42-44-42-4-4224-244-2-24-22-12-122-1-1-2-211-2-2110000000000000000000000000000000000000000000000
χ858-88-8-88-444-42-44-42-4-2-244-2422-4-4-24-12-1211-2-211-2-2-1-1220000000000000000000000000000000000000000000000
χ868-88-8-88-444-4-424-4-4244-2-24-2-4-4224-22-12-1-2-211-2-21122-1-10000000000000000000000000000000000000000000000
χ878-8-8800-44-442-400-246-600-24-66002-4-121-2-33001-12-23-3000000000000000000000000000000000000000000000000
χ888-8-8800-44-442-400-24-6600-246-6002-4-121-23-3001-12-2-33000000000000000000000000000000000000000000000000
χ898-8-8800-44-44-42004-2006-64-200-66-422-1-2100-33-22-11003-30000000000000000000000000000000000000000000000
χ908-8-8800-44-44-42004-200-664-2006-6-422-1-21003-3-22-1100-330000000000000000000000000000000000000000000000

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