Finite Group Databasebeta

← Group #13141145

Character table — Group #13141145

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11222222244666666661212121212121212121212123636363636363636363636363636363636361122222224466666666121212121212121212121212363636363636363636363636363636363636
order1222236666633666666366666666666244444661212121212121212121222222666666666666666666666666662444446612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-11111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1
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
χ5111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1i−ii−i11ii−i−i-1-1ii−i−i111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1i−ii−i11ii−i−i-1-1ii−i−i
χ6111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1−ii−ii11−i−iii-1-1−i−iii111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1−ii−ii11−i−iii-1-1−i−iii
χ7111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11i−i−ii-1-1ii−i−i11−i−iii111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11i−i−ii-1-1ii−i−i11−i−iii
χ8111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11−iii−i-1-1−i−iii11ii−i−i111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11−iii−i-1-1−i−iii11ii−i−i
χ9222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000-1-10000-1-10000222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000-1-10000-1-10000
χ10222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-20000110000110000222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-20000110000110000
χ1122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002200000000-1-1-1-122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002200000000-1-1-1-1
χ1222222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-200000000111122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-2000000001111
χ13222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-111112-20000-1-10000110000222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-111112-20000-1-10000110000
χ14222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-11111-220000110000-1-10000222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-11111-220000110000-1-10000
χ15222-2-222-2-22-2-12-122112-1-11-2-2-1-1-1111100002i−2i00000000−i−iii222-2-222-2-22-2-12-122112-1-11-2-2-1-1-1111100002i−2i00000000−i−iii
χ16222-2-222-2-22-2-12-122112-1-11-2-2-1-1-111110000−2i2i00000000ii−i−i222-2-222-2-22-2-12-122112-1-11-2-2-1-1-111110000−2i2i00000000ii−i−i
χ1722-22-22222-2-2222-2-2-2-222-222-22-2-222-2-200000000000000000022-22-22222-2-2222-2-2-2-222-222-22-2-222-2-2000000000000000000
χ1822-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000−i3i30000−i3i3000022-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000−i3i30000−i3i30000
χ1922-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000i3−i30000i3−i3000022-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000i3−i30000i3−i30000
χ2022-22-22222-2-2-12-1-2-2112-11-12-2-111-1-111000000000000003−33−322-22-22222-2-2-12-1-2-2112-11-12-2-111-1-111000000000000003−33−3
χ2122-22-22222-2-2-12-1-2-2112-11-12-2-111-1-11100000000000000−33−3322-22-22222-2-2-12-1-2-2112-11-12-2-111-1-11100000000000000−33−33
χ2222-2-2222-2-2-22222-2-22222-2-2-222-2-2-2-22200000000000000000022-2-2222-2-2-22222-2-22222-2-2-222-2-2-2-222000000000000000000
χ2322-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000−i3i30000i3−i3000022-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000−i3i30000i3−i30000
χ2422-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000i3−i30000−i3i3000022-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000i3−i30000−i3i30000
χ2522-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000−i3i3i3−i322-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000−i3i3i3−i3
χ2622-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000i3−i3−i3i322-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000i3−i3−i3i3
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
χ28444-4-444-4-44-4-2-2-2-2-222-21-2222111-1-1-1-1000000000000000000444-4-444-4-44-4-2-2-2-2-222-21-2222111-1-1-1-1000000000000000000
χ2944-44-44444-4-4-2-2-22222-212-2-221-1-111-1-100000000000000000044-44-44444-4-4-2-2-22222-212-2-221-1-111-1-1000000000000000000
χ3044-4-4444-4-4-44-2-2-222-2-2-21222-21-1-1-1-11100000000000000000044-4-4444-4-4-44-2-2-222-2-2-21222-21-1-1-1-111000000000000000000
χ314-40004-4000044-40000-440000-40000000000000000000000004-40004-4000044-40000-440000-4000000000000000000000000
χ324-40004-400004-2-4−2i32i3002-200002−2i32i300000000000000000000004-40004-400004-2-4−2i32i3002-200002−2i32i30000000000000000000000
χ334-40004-400004-2-42i3−2i3002-2000022i3−2i300000000000000000000004-40004-400004-2-42i3−2i3002-2000022i3−2i30000000000000000000000
χ344-40004-40000-24200−2i32i3-4-2000020000−2i32i30000000000000000004-40004-40000-24200−2i32i3-4-2000020000−2i32i3000000000000000000
χ354-40004-40000-242002i3−2i3-4-20000200002i3−2i30000000000000000004-40004-40000-242002i3−2i3-4-20000200002i3−2i3000000000000000000
χ364-40004-40000-2-22−2i32i3−2i32i3210000-1i3−i33-3i3−i30000000000000000004-40004-40000-2-22−2i32i3−2i32i3210000-1i3−i33-3i3−i3000000000000000000
χ374-40004-40000-2-22−2i32i32i3−2i3210000-1i3−i3-33−i3i30000000000000000004-40004-40000-2-22−2i32i32i3−2i3210000-1i3−i3-33−i3i3000000000000000000
χ384-40004-40000-2-222i3−2i3−2i32i3210000-1−i3i3-33i3−i30000000000000000004-40004-40000-2-222i3−2i3−2i32i3210000-1−i3i3-33i3−i3000000000000000000
χ394-40004-40000-2-222i3−2i32i3−2i3210000-1−i3i33-3−i3i30000000000000000004-40004-40000-2-222i3−2i32i3−2i3210000-1−i3i33-3−i3i3000000000000000000
χ4066666-3-3-3-3-3-30000000000000000000000220000-1-1-1-100000066666-3-3-3-3-3-30000000000000000000000220000-1-1-1-1000000
χ4166666-3-3-3-3-3-30000000000000000000000-2-20000111100000066666-3-3-3-3-3-30000000000000000000000-2-200001111000000
χ42666-6-6-3-333-3300000000000000000000002i−2i0000−i−iii000000666-6-6-3-333-3300000000000000000000002i−2i0000−i−iii000000
χ43666-6-6-3-333-330000000000000000000000−2i2i0000ii−i−i000000666-6-6-3-333-330000000000000000000000−2i2i0000ii−i−i000000
χ4466-66-6-3-3-3-3330000000000000000000000000000−i3i3−i3i300000066-66-6-3-3-3-3330000000000000000000000000000−i3i3−i3i3000000
χ4566-66-6-3-3-3-3330000000000000000000000000000i3−i3i3−i300000066-66-6-3-3-3-3330000000000000000000000000000i3−i3i3−i3000000
χ4666-6-66-3-3333-300000000000000000000000000003−3−3300000066-6-66-3-3333-300000000000000000000000000003−3−33000000
χ4766-6-66-3-3333-30000000000000000000000000000−333−300000066-6-66-3-3333-30000000000000000000000000000−333−3000000
χ4812-12000-66−6i36i3000000000000000000000000000000000000000012-12000-66−6i36i30000000000000000000000000000000000000000
χ4912-12000-666i3−6i3000000000000000000000000000000000000000012-12000-666i3−6i30000000000000000000000000000000000000000
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
χ51111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111
χ521111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111
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
χ54111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1i−ii−i11ii−i−i-1-1ii−i−i-1-1-111-1-111-11-1-1-1-1-111-1-1-1111-1-1-11111-11−ii−ii-1-1−i−iii11−i−iii
χ55111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-11-1−ii−ii11−i−iii-1-1−i−iii-1-1-111-1-111-11-1-1-1-1-111-1-1-1111-1-1-11111-11i−ii−i-1-1ii−i−i11ii−i−i
χ56111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11i−i−ii-1-1ii−i−i11−i−iii-1-1-111-1-111-11-1-1-1-1-111-1-1-1111-1-1-111111-1−iii−i11−i−iii-1-1ii−i−i
χ57111-1-111-1-11-111111-1-1111-1-1-1111-1-1-1-1-11−iii−i-1-1−i−iii11ii−i−i-1-1-111-1-111-11-1-1-1-1-111-1-1-1111-1-1-111111-1i−i−ii11ii−i−i-1-1−i−iii
χ58222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1220000-1-10000-1-10000-2-2-2-2-2-2-2-2-2-2-2-21-211-2-211-2-2111111111-2-20000110000110000
χ59222222222222-12-1-122-1-122-1-1-1-1-1-1-1-1-1-2-20000110000110000-2-2-2-2-2-2-2-2-2-2-2-21-211-2-211-2-2111111111220000-1-10000-1-10000
χ6022222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-100002200000000-1-1-1-1-2-2-2-2-2-2-2-2-2-2-21-21-2-211-2111-2-211111110000-2-2000000001111
χ6122222222222-12-122-1-12-1-1-122-1-1-1-1-1-1-10000-2-2000000001111-2-2-2-2-2-2-2-2-2-2-21-21-2-211-2111-2-2111111100002200000000-1-1-1-1
χ62222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-111112-20000-1-10000110000-2-2-222-2-222-22-21-2112211-22-1-1111-1-1-1-1-220000110000-1-10000
χ63222-2-222-2-22-22-12-1-1-2-2-1-12-211-1-1-11111-220000110000-1-10000-2-2-222-2-222-22-21-2112211-22-1-1111-1-1-1-12-20000-1-10000110000
χ64222-2-222-2-22-2-12-122112-1-11-2-2-1-1-1111100002i−2i00000000−i−iii-2-2-222-2-222-221-21-2-2-1-1-211-122111-1-1-1-10000−2i2i00000000ii−i−i
χ65222-2-222-2-22-2-12-122112-1-11-2-2-1-1-111110000−2i2i00000000ii−i−i-2-2-222-2-222-221-21-2-2-1-1-211-122111-1-1-1-100002i−2i00000000−i−iii
χ6622-22-22222-2-2222-2-2-2-222-222-22-2-222-2-2000000000000000000-2-22-22-2-2-2-222-2-2-22222-2-22-2-22-222-2-222000000000000000000
χ6722-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000−i3i30000−i3i30000-2-22-22-2-2-2-222-21-2-1-122112-21-11-1-111-1-1000000i3−i30000i3−i30000
χ6822-22-22222-2-22-1211-2-2-1-1-22-11-111-1-111000000i3−i30000i3−i30000-2-22-22-2-2-2-222-21-2-1-122112-21-11-1-111-1-1000000−i3i30000−i3i30000
χ6922-22-22222-2-2-12-1-2-2112-11-12-2-111-1-111000000000000003−33−3-2-22-22-2-2-2-2221-2122-1-1-21-11-221-1-111-1-100000000000000−33−33
χ7022-22-22222-2-2-12-1-2-2112-11-12-2-111-1-11100000000000000−33−33-2-22-22-2-2-2-2221-2122-1-1-21-11-221-1-111-1-1000000000000003−33−3
χ7122-2-2222-2-2-22222-2-22222-2-2-222-2-2-2-222000000000000000000-2-222-2-2-2222-2-2-2-222-2-2-2-2222-2-22222-2-2000000000000000000
χ7222-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000−i3i30000i3−i30000-2-222-2-2-2222-2-21-2-1-1-2-21122-111-1-1-1-111000000i3−i30000−i3i30000
χ7322-2-2222-2-2-222-121122-1-1-2-21-1-11111-1-1000000i3−i30000−i3i30000-2-222-2-2-2222-2-21-2-1-1-2-21122-111-1-1-1-111000000−i3i30000i3−i30000
χ7422-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000−i3i3i3−i3-2-222-2-2-2222-21-212211-21-1-12-21-1-1-1-11100000000000000i3−i3−i3i3
χ7522-2-2222-2-2-22-12-1-2-2-1-12-111-22-11111-1-100000000000000i3−i3−i3i3-2-222-2-2-2222-21-212211-21-1-12-21-1-1-1-11100000000000000−i3i3i3−i3
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
χ77444-4-444-4-44-4-2-2-2-2-222-21-2222111-1-1-1-1000000000000000000-4-4-444-4-444-4422222-2-22-12-2-2-2-1-1-11111000000000000000000
χ7844-44-44444-4-4-2-2-22222-212-2-221-1-111-1-1000000000000000000-4-44-44-4-4-4-444222-2-2-2-22-1-222-2-111-1-111000000000000000000
χ7944-4-4444-4-4-44-2-2-222-2-2-21222-21-1-1-1-111000000000000000000-4-444-4-4-4444-4222-2-2222-1-2-2-22-11111-1-1000000000000000000
χ804-40004-4000044-40000-440000-4000000000000000000000000-44000-440000-4-4400004-400004000000000000000000000000
χ814-40004-400004-2-4−2i32i3002-200002−2i32i30000000000000000000000-44000-440000-4242i3−2i300-220000-22i3−2i30000000000000000000000
χ824-40004-400004-2-42i3−2i3002-2000022i3−2i30000000000000000000000-44000-440000-424−2i32i300-220000-2−2i32i30000000000000000000000
χ834-40004-40000-24200−2i32i3-4-2000020000−2i32i3000000000000000000-44000-4400002-4-2002i3−2i3420000-200002i3−2i3000000000000000000
χ844-40004-40000-242002i3−2i3-4-20000200002i3−2i3000000000000000000-44000-4400002-4-200−2i32i3420000-20000−2i32i3000000000000000000
χ854-40004-40000-2-22−2i32i3−2i32i3210000-1i3−i33-3i3−i3000000000000000000-44000-44000022-22i3−2i32i3−2i3-2-100001−i3i3-33−i3i3000000000000000000
χ864-40004-40000-2-22−2i32i32i3−2i3210000-1i3−i3-33−i3i3000000000000000000-44000-44000022-22i3−2i3−2i32i3-2-100001−i3i33-3i3−i3000000000000000000
χ874-40004-40000-2-222i3−2i3−2i32i3210000-1−i3i3-33i3−i3000000000000000000-44000-44000022-2−2i32i32i3−2i3-2-100001i3−i33-3−i3i3000000000000000000
χ884-40004-40000-2-222i3−2i32i3−2i3210000-1−i3i33-3−i3i3000000000000000000-44000-44000022-2−2i32i3−2i32i3-2-100001i3−i3-33i3−i3000000000000000000
χ8966666-3-3-3-3-3-30000000000000000000000220000-1-1-1-1000000-6-6-6-6-63333330000000000000000000000-2-200001111000000
χ9066666-3-3-3-3-3-30000000000000000000000-2-200001111000000-6-6-6-6-63333330000000000000000000000220000-1-1-1-1000000
χ91666-6-6-3-333-3300000000000000000000002i−2i0000−i−iii000000-6-6-66633-3-33-30000000000000000000000−2i2i0000ii−i−i000000
χ92666-6-6-3-333-330000000000000000000000−2i2i0000ii−i−i000000-6-6-66633-3-33-300000000000000000000002i−2i0000−i−iii000000
χ9366-66-6-3-3-3-3330000000000000000000000000000−i3i3−i3i3000000-6-66-663333-3-30000000000000000000000000000i3−i3i3−i3000000
χ9466-66-6-3-3-3-3330000000000000000000000000000i3−i3i3−i3000000-6-66-663333-3-30000000000000000000000000000−i3i3−i3i3000000
χ9566-6-66-3-3333-300000000000000000000000000003−3−33000000-6-666-633-3-3-330000000000000000000000000000−333−3000000
χ9666-6-66-3-3333-30000000000000000000000000000−333−3000000-6-666-633-3-3-3300000000000000000000000000003−3−33000000
χ9712-12000-66−6i36i30000000000000000000000000000000000000000-12120006-66i3−6i30000000000000000000000000000000000000000
χ9812-12000-666i3−6i30000000000000000000000000000000000000000-12120006-6−6i36i30000000000000000000000000000000000000000

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