Finite Group Databasebeta

← Group #13141149

Character table — Group #13141149

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11222222244666666661212121212121212121212123636363636363636363636363636363636361122222224466666666121212121212121212121212363636363636363636363636363636363636
order1222236666633666666366666666666244444661212121212121212121222222666666666666666666666666662444446612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i
χ6111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii
χ7111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii
χ8111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i
χ9222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-100002200000000-1-1-1-1222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-100002200000000-1-1-1-1
χ10222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-10000-2-2000000001111222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-10000-2-2000000001111
χ1122222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-10022000000-1-1-1-1000022222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-10022000000-1-1-1-10000
χ1222222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-100-2-20000001111000022222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-100-2-200000011110000
χ13222-2-22222-2-22-12-1-2-211-12-1-21-1-1-1111100002i−2i00000000−i−iii222-2-22222-2-22-12-1-2-211-12-1-21-1-1-1111100002i−2i00000000−i−iii
χ14222-2-22222-2-22-12-1-2-211-12-1-21-1-1-111110000−2i2i00000000ii−i−i222-2-22222-2-22-12-1-2-211-12-1-21-1-1-111110000−2i2i00000000ii−i−i
χ15222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-11111002i−2i000000−i−iii0000222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-11111002i−2i000000−i−iii0000
χ16222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-1111100−2i2i000000ii−i−i0000222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-1111100−2i2i000000ii−i−i0000
χ1722-22-22-2-222-2222222-2-22-2-2-222-2-222-2-200000000000000000022-22-22-2-222-2222222-2-22-2-2-222-2-222-2-2000000000000000000
χ1822-22-22-2-222-22-12-12211-1-21-2-1-111-1-111000000000000003−33−322-22-22-2-222-22-12-12211-1-21-2-1-111-1-111000000000000003−33−3
χ1922-22-22-2-222-22-12-12211-1-21-2-1-111-1-11100000000000000−33−3322-22-22-2-222-22-12-12211-1-21-2-1-111-1-11100000000000000−33−33
χ2022-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000−i3i3−i3i3000022-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000−i3i3−i3i30000
χ2122-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000i3−i3i3−i3000022-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000i3−i3i3−i30000
χ2222-2-222-2-22-222222-2-2222-2-22-22-2-2-2-22200000000000000000022-2-222-2-22-222222-2-2222-2-22-22-2-2-2-222000000000000000000
χ2322-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000−i3i3i3−i322-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000−i3i3i3−i3
χ2422-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000i3−i3−i3i322-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000i3−i3−i3i3
χ2522-2-222-2-22-22-12-121122-11-2-1-2-11111-1-100000000003−3−33000022-2-222-2-22-22-12-121122-11-2-1-2-11111-1-100000000003−3−330000
χ2622-2-222-2-22-22-12-121122-11-2-1-2-11111-1-10000000000−333−3000022-2-222-2-22-22-12-121122-11-2-1-2-11111-1-10000000000−333−30000
χ2744444444444-2-2-2-2-2-2-2-21-2-2-2-2111111100000000000000000044444444444-2-2-2-2-2-2-2-21-2-2-2-21111111000000000000000000
χ28444-4-44444-4-4-2-2-2-222221-2-222111-1-1-1-1000000000000000000444-4-44444-4-4-2-2-2-222221-2-222111-1-1-1-1000000000000000000
χ2944-44-44-4-444-4-2-2-2-2-2-2221222-21-1-111-1-100000000000000000044-44-44-4-444-4-2-2-2-2-2-2221222-21-1-111-1-1000000000000000000
χ3044-4-444-4-44-44-2-2-2-222-2-2122-221-1-1-1-11100000000000000000044-4-444-4-44-44-2-2-2-222-2-2122-221-1-1-1-111000000000000000000
χ314-4000400-40044-4-4000040000-40000000000000000000000004-4000400-40044-4-4000040000-4000000000000000000000000
χ324-4000400-4004-2-4200−2i32i3-2000020000−2i32i30000000000000000004-4000400-4004-2-4200−2i32i3-2000020000−2i32i3000000000000000000
χ334-4000400-4004-2-42002i3−2i3-20000200002i3−2i30000000000000000004-4000400-4004-2-42002i3−2i3-20000200002i3−2i3000000000000000000
χ344-4000400-400-242-4−2i32i300-20000200−2i32i3000000000000000000004-4000400-400-242-4−2i32i300-20000200−2i32i300000000000000000000
χ354-4000400-400-242-42i3−2i300-200002002i3−2i3000000000000000000004-4000400-400-242-42i3−2i300-200002002i3−2i300000000000000000000
χ364-4000400-400-2-222−2i32i3−2i32i310000-13-3i3−i3i3−i30000000000000000004-4000400-400-2-222−2i32i3−2i32i310000-13-3i3−i3i3−i3000000000000000000
χ374-4000400-400-2-222−2i32i32i3−2i310000-1-33i3−i3−i3i30000000000000000004-4000400-400-2-222−2i32i32i3−2i310000-1-33i3−i3−i3i3000000000000000000
χ384-4000400-400-2-2222i3−2i3−2i32i310000-1-33−i3i3i3−i30000000000000000004-4000400-400-2-2222i3−2i3−2i32i310000-1-33−i3i3i3−i3000000000000000000
χ394-4000400-400-2-2222i3−2i32i3−2i310000-13-3−i3i3−i3i30000000000000000004-4000400-400-2-2222i3−2i32i3−2i310000-13-3−i3i3−i3i3000000000000000000
χ4066666-3-3-3-3-3-300000000000000000000220000-1-1-1-10000000066666-3-3-3-3-3-300000000000000000000220000-1-1-1-100000000
χ4166666-3-3-3-3-3-300000000000000000000-2-2000011110000000066666-3-3-3-3-3-300000000000000000000-2-20000111100000000
χ42666-6-6-3-3-3-333000000000000000000002-20000-1-11100000000666-6-6-3-3-3-333000000000000000000002-20000-1-11100000000
χ43666-6-6-3-3-3-33300000000000000000000-22000011-1-100000000666-6-6-3-3-3-33300000000000000000000-22000011-1-100000000
χ4466-66-6-333-3-3300000000000000000000000000−i3i3−i3i30000000066-66-6-333-3-3300000000000000000000000000−i3i3−i3i300000000
χ4566-66-6-333-3-3300000000000000000000000000i3−i3i3−i30000000066-66-6-333-3-3300000000000000000000000000i3−i3i3−i300000000
χ4666-6-66-333-33-300000000000000000000000000−i3i3i3−i30000000066-6-66-333-33-300000000000000000000000000−i3i3i3−i300000000
χ4766-6-66-333-33-300000000000000000000000000i3−i3−i3i30000000066-6-66-333-33-300000000000000000000000000i3−i3−i3i300000000
χ4812-12000-6−6i36i36000000000000000000000000000000000000000012-12000-6−6i36i360000000000000000000000000000000000000000
χ4912-12000-66i3−6i36000000000000000000000000000000000000000012-12000-66i3−6i360000000000000000000000000000000000000000
χ501111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ521111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ531111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ54111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-11−ii−ii-1-111−i−iii−i−iii
χ55111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-11i−ii−i-1-111ii−i−iii−i−i
χ56111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-111111-1−iii−i11-1-1−i−iiiii−i−i
χ57111-1-11111-1-11111-1-1-1-1111-1-1111-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-111111-1i−i−ii11-1-1ii−i−i−i−iii
χ58222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-100002200000000-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-21-21-2-2111-21-2111111110000-2-2000000001111
χ59222222222222-12-122-1-1-12-12-1-1-1-1-1-1-1-10000-2-2000000001111-2-2-2-2-2-2-2-2-2-2-2-21-21-2-2111-21-21111111100002200000000-1-1-1-1
χ6022222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-10022000000-1-1-1-10000-2-2-2-2-2-2-2-2-2-2-21-21-211-2-211-21-2111111100-2-200000011110000
χ6122222222222-12-12-1-122-1-12-12-1-1-1-1-1-1-100-2-200000011110000-2-2-2-2-2-2-2-2-2-2-21-21-211-2-211-21-211111110022000000-1-1-1-10000
χ62222-2-22222-2-22-12-1-2-211-12-1-21-1-1-1111100002i−2i00000000−i−iii-2-2-222-2-2-2-222-21-2122-1-11-212-1111-1-1-1-10000−2i2i00000000ii−i−i
χ63222-2-22222-2-22-12-1-2-211-12-1-21-1-1-111110000−2i2i00000000ii−i−i-2-2-222-2-2-2-222-21-2122-1-11-212-1111-1-1-1-100002i−2i00000000−i−iii
χ64222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-11111002i−2i000000−i−iii0000-2-2-222-2-2-2-2221-21-2-1-12211-2-12111-1-1-1-100−2i2i000000ii−i−i0000
χ65222-2-22222-2-2-12-1211-2-2-1-121-2-1-1-1111100−2i2i000000ii−i−i0000-2-2-222-2-2-2-2221-21-2-1-12211-2-12111-1-1-1-1002i−2i000000−i−iii0000
χ6622-22-22-2-222-2222222-2-22-2-2-222-2-222-2-2000000000000000000-2-22-22-222-2-22-2-2-2-2-2-222-2222-2-222-2-222000000000000000000
χ6722-22-22-2-222-22-12-12211-1-21-2-1-111-1-111000000000000003−33−3-2-22-22-222-2-22-21-21-2-2-1-112-1211-1-111-1-100000000000000−33−33
χ6822-22-22-2-222-22-12-12211-1-21-2-1-111-1-11100000000000000−33−33-2-22-22-222-2-22-21-21-2-2-1-112-1211-1-111-1-1000000000000003−33−3
χ6922-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000−i3i3−i3i30000-2-22-22-222-2-221-21-211221-12-1-21-1-111-1-10000000000i3−i3i3−i30000
χ7022-22-22-2-222-2-12-12-1-1-2-2-11-212-111-1-1110000000000i3−i3i3−i30000-2-22-22-222-2-221-21-211221-12-1-21-1-111-1-10000000000−i3i3−i3i30000
χ7122-2-222-2-22-222222-2-2222-2-22-22-2-2-2-222000000000000000000-2-222-2-222-22-2-2-2-2-222-2-2-222-22-22222-2-2000000000000000000
χ7222-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000−i3i3i3−i3-2-222-2-222-22-2-21-21221112-1-2-11-1-1-1-11100000000000000i3−i3−i3i3
χ7322-2-222-2-22-222-12-1-2-2-1-1-1-2121-11111-1-100000000000000i3−i3−i3i3-2-222-2-222-22-2-21-21221112-1-2-11-1-1-1-11100000000000000−i3i3i3−i3
χ7422-2-222-2-22-22-12-121122-11-2-1-2-11111-1-100000000003−3−330000-2-222-2-222-22-21-21-2-1-1-2-21-12121-1-1-1-1110000000000−333−30000
χ7522-2-222-2-22-22-12-121122-11-2-1-2-11111-1-10000000000−333−30000-2-222-2-222-22-21-21-2-1-1-2-21-12121-1-1-1-11100000000003−3−330000
χ7644444444444-2-2-2-2-2-2-2-21-2-2-2-21111111000000000000000000-4-4-4-4-4-4-4-4-4-4-422222222-12222-1-1-1-1-1-1-1000000000000000000
χ77444-4-44444-4-4-2-2-2-222221-2-222111-1-1-1-1000000000000000000-4-4-444-4-4-4-4442222-2-2-2-2-122-2-2-1-1-11111000000000000000000
χ7844-44-44-4-444-4-2-2-2-2-2-2221222-21-1-111-1-1000000000000000000-4-44-44-444-4-44222222-2-2-1-2-2-22-111-1-111000000000000000000
χ7944-4-444-4-44-44-2-2-2-222-2-2122-221-1-1-1-111000000000000000000-4-444-4-444-44-42222-2-222-1-2-22-2-11111-1-1000000000000000000
χ804-4000400-40044-4-4000040000-4000000000000000000000000-44000-400400-4-4440000-400004000000000000000000000000
χ814-4000400-4004-2-4200−2i32i3-2000020000−2i32i3000000000000000000-44000-400400-424-2002i3−2i320000-200002i3−2i3000000000000000000
χ824-4000400-4004-2-42002i3−2i3-20000200002i3−2i3000000000000000000-44000-400400-424-200−2i32i320000-20000−2i32i3000000000000000000
χ834-4000400-400-242-4−2i32i300-20000200−2i32i300000000000000000000-44000-4004002-4-242i3−2i30020000-2002i3−2i300000000000000000000
χ844-4000400-400-242-42i3−2i300-200002002i3−2i300000000000000000000-44000-4004002-4-24−2i32i30020000-200−2i32i300000000000000000000
χ854-4000400-400-2-222−2i32i3−2i32i310000-13-3i3−i3i3−i3000000000000000000-44000-40040022-2-22i3−2i32i3−2i3-100001-33−i3i3−i3i3000000000000000000
χ864-4000400-400-2-222−2i32i32i3−2i310000-1-33i3−i3−i3i3000000000000000000-44000-40040022-2-22i3−2i3−2i32i3-1000013-3−i3i3i3−i3000000000000000000
χ874-4000400-400-2-2222i3−2i3−2i32i310000-1-33−i3i3i3−i3000000000000000000-44000-40040022-2-2−2i32i32i3−2i3-1000013-3i3−i3−i3i3000000000000000000
χ884-4000400-400-2-2222i3−2i32i3−2i310000-13-3−i3i3−i3i3000000000000000000-44000-40040022-2-2−2i32i3−2i32i3-100001-33i3−i3i3−i3000000000000000000
χ8966666-3-3-3-3-3-300000000000000000000220000-1-1-1-100000000-6-6-6-6-633333300000000000000000000-2-20000111100000000
χ9066666-3-3-3-3-3-300000000000000000000-2-20000111100000000-6-6-6-6-633333300000000000000000000220000-1-1-1-100000000
χ91666-6-6-3-3-3-333000000000000000000002-20000-1-11100000000-6-6-6663333-3-300000000000000000000-22000011-1-100000000
χ92666-6-6-3-3-3-33300000000000000000000-22000011-1-100000000-6-6-6663333-3-3000000000000000000002-20000-1-11100000000
χ9366-66-6-333-3-3300000000000000000000000000−i3i3−i3i300000000-6-66-663-3-333-300000000000000000000000000i3−i3i3−i300000000
χ9466-66-6-333-3-3300000000000000000000000000i3−i3i3−i300000000-6-66-663-3-333-300000000000000000000000000−i3i3−i3i300000000
χ9566-6-66-333-33-300000000000000000000000000−i3i3i3−i300000000-6-666-63-3-33-3300000000000000000000000000i3−i3−i3i300000000
χ9666-6-66-333-33-300000000000000000000000000i3−i3−i3i300000000-6-666-63-3-33-3300000000000000000000000000−i3i3i3−i300000000
χ9712-12000-6−6i36i360000000000000000000000000000000000000000-121200066i3−6i3-60000000000000000000000000000000000000000
χ9812-12000-66i3−6i360000000000000000000000000000000000000000-12120006−6i36i3-60000000000000000000000000000000000000000

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