Finite Group Databasebeta

← Group #13135175

Character table — Group #13135175

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1244222344466612121212661212336666661212121212121212366666666666121212121212121212121212444444448888121212121212121212121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-11-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1
χ611111-1-11-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111
χ711111-1-11-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111
χ811111-1-11-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1
χ91111-11-111-1-1-1-1111-1-11-11-1111111-1-1111111-1-11-1-11-1-1-111-1-11-1-11-111-1-111-1-11-11-1i−ii−ii−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-11-111-1-1-1-1111-1-11-11-1111111-1-1111111-1-11-1-11-1-1-111-1-11-1-11-111-1-111-1-11-11-1−ii−ii−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-11-111-1-1-1-1111-1-11-11-1111111-1-1111111-1-11-1-11-1-1-111-1-11-1-11-111-1-111-1-1-11-11i−ii−i−ii−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111-11-111-1-1-1-1111-1-11-11-1111111-1-1111111-1-11-1-11-1-1-111-1-11-1-11-111-1-111-1-1-11-11−ii−iii−ii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-111-11-1-1-1111-1-1-11-111111-1-1111111-1-1111-1-1-11-1-1-1-1111-1-1-1111-1-1-1-111i−i−ii1-1-11−iii−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ141111-1-111-11-1-1-1111-1-1-11-111111-1-1111111-1-1111-1-1-11-1-1-1-1111-1-1-1111-1-1-1-111i−i−ii-111-1i−i−iiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ151111-1-111-11-1-1-1111-1-1-11-111111-1-1111111-1-1111-1-1-11-1-1-1-1111-1-1-1111-1-1-1-111−iii−i1-1-11i−i−ii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ161111-1-111-11-1-1-1111-1-1-11-111111-1-1111111-1-1111-1-1-11-1-1-1-1111-1-1-1111-1-1-1-111−iii−i-111-1−iii−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222222222222222-12-122-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-12-1-12-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-12-122-1-122-1-122-1-1-12-1-12-1-1-1-1-1-1-12-1-12-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ192222222222222222222222-12-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ202222222222222222222222-12-12-1-122-1-122-1-122-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ2122222-2-22-2-222222222-2-2-2-22-12-1-2-21122-1-1-2-211-12-11-2-1-11111-12-11-2-1-1-1-1111100002i2i−2i−2i000000000000−i−i−i−iiiii00000000
χ2222222-2-22-2-222222222-2-2-2-22-12-1-2-21122-1-1-2-211-12-11-2-1-11111-12-11-2-1-1-1-111110000−2i−2i2i2i000000000000iiii−i−i−i−i00000000
χ2322222-2-22-2-222222222-2-2-2-2-12-1211-2-2-1-12211-2-2-1-12-21-1-11111-1-12-21-1-1-1-111112i2i−2i−2i00000000−i−i−i−iiiii0000000000000000
χ2422222-2-22-2-222222222-2-2-2-2-12-1211-2-2-1-12211-2-2-1-12-21-1-11111-1-12-21-1-1-1-11111−2i−2i2i2i00000000iiii−i−i−i−i0000000000000000
χ252222-22-222-2-2-2-2222-2-22-22-22-12-1221122-1-12211-1-21-1-211-1-111-1-21-1-2-1-111-1-11100002i−2i2i−2i000000000000−i−iii−i−iii00000000
χ262222-22-222-2-2-2-2222-2-22-22-22-12-1221122-1-12211-1-21-1-211-1-111-1-21-1-2-1-111-1-1110000−2i2i−2i2i000000000000ii−i−iii−i−i00000000
χ272222-22-222-2-2-2-2222-2-22-22-2-12-12-1-1-2-2-1-122-1-1-2-2-11-22111-1-111-11-221-1-111-1-1112-22-200000000-1-111-1-1110000000000000000
χ282222-22-222-2-2-2-2222-2-22-22-2-12-12-1-1-2-2-1-122-1-1-2-2-11-22111-1-111-11-221-1-111-1-111-22-220000000011-1-111-1-10000000000000000
χ292222-2-222-22-2-2-2222-2-2-22-222-12-1-2-2-1-122-1-1-2-2-1-1-1-21121111-1-1-1-2112-1-11111-1-100002-2-22000000000000-1-11111-1-100000000
χ302222-2-222-22-2-2-2222-2-2-22-222-12-1-2-2-1-122-1-1-2-2-1-1-1-21121111-1-1-1-2112-1-11111-1-10000-222-200000000000011-1-1-1-11100000000
χ312222-2-222-22-2-2-2222-2-2-22-22-12-121122-1-1221122-11-2-2-11111-1-1-11-2-2-1-1-11111-1-12i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ322222-2-222-22-2-2-2222-2-2-22-22-12-121122-1-1221122-11-2-2-11111-1-1-11-2-2-1-1-11111-1-1−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ3322-2-22222-2-2-2222-2-2-2-222-2-222222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ3422-2-22222-2-2-2222-2-2-2-222-2-22-12-122-1-1-2-211-2-211-12-1-12-1-1-1-1-1-1-1-211-21111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ3522-2-22222-2-2-2222-2-2-2-222-2-22-12-122-1-1-2-211-2-211-12-1-12-1-1-1-1-1-1-1-211-21111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ3622-2-22222-2-2-2222-2-2-2-222-2-2-12-12-1-12211-2-211-2-2-1-122-1-1-1-1-1-1-1-11-2-2111111111000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ3722-2-22222-2-2-2222-2-2-2-222-2-2-12-12-1-12211-2-211-2-2-1-122-1-1-1-1-1-1-1-11-2-2111111111000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ3822-2-22-2-2222-2222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222222-2-222-2-2-2-22-2-222-2-2-2-22222000000000000000000000000000000000000
χ3922-2-22-2-2222-2222-2-2-2-2-2-2222-12-1-2-211-2-21122-1-1-12-11-2-1-11111-1-21-121111-1-1-1-1000000000000000000003−33−3−33−3300000000
χ4022-2-22-2-2222-2222-2-2-2-2-2-2222-12-1-2-211-2-21122-1-1-12-11-2-1-11111-1-21-121111-1-1-1-100000000000000000000−33−333−33−300000000
χ4122-2-22-2-2222-2222-2-2-2-2-2-222-12-1211-2-211-2-2-1-122-1-12-21-1-11111-11-22-11111-1-1-1-10000000000003−33−3−33−330000000000000000
χ4222-2-22-2-2222-2222-2-2-2-2-2-222-12-1211-2-211-2-2-1-122-1-12-21-1-11111-11-22-11111-1-1-1-1000000000000−33−333−33−30000000000000000
χ4322-2-2-22-22-222-2-22-2-2222-2-22222222-2-2-2-2-2-2-2-2222-2-22-2-2-222-2-2222-22-2-222-2-222000000000000000000000000000000000000
χ4422-2-2-22-22-222-2-22-2-2222-2-222-12-12211-2-211-2-2-1-1-1-21-1-211-1-111-12-11211-1-111-1-1000000000000000000003−3−333−3−3300000000
χ4522-2-2-22-22-222-2-22-2-2222-2-222-12-12211-2-211-2-2-1-1-1-21-1-211-1-111-12-11211-1-111-1-100000000000000000000−333−3−333−300000000
χ4622-2-2-22-22-222-2-22-2-2222-2-22-12-12-1-1-2-211-2-21122-11-22111-1-111-1-12-2-111-1-111-1-1000000000000−i3i3i3−i3−i3i3i3−i30000000000000000
χ4722-2-2-22-22-222-2-22-2-2222-2-22-12-12-1-1-2-211-2-21122-11-22111-1-111-1-12-2-111-1-111-1-1000000000000i3−i3−i3i3i3−i3−i3i30000000000000000
χ4822-2-2-2-2222-22-2-22-2-222-222-22222-2-222-2-2-2-222-2-22-2-2-22-2-2-2-2222222-2-2-22222-2-2000000000000000000000000000000000000
χ4922-2-2-2-2222-22-2-22-2-222-222-22-12-1-2-2-1-1-2-2112211-1-21121111-1-1-12-1-1-211-1-1-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ5022-2-2-2-2222-22-2-22-2-222-222-22-12-1-2-2-1-1-2-2112211-1-21121111-1-1-12-1-1-211-1-1-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ5122-2-2-2-2222-22-2-22-2-222-222-2-12-12112211-2-2-1-1-2-2-11-2-2-11111-1-1-1-122111-1-1-1-1110000000000003−3−33−333−30000000000000000
χ5222-2-2-2-2222-22-2-22-2-222-222-2-12-12112211-2-2-1-1-2-2-11-2-2-11111-1-1-1-122111-1-1-1-111000000000000−333−33−3−330000000000000000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000
χ5444444-4-44-4-444444444-4-4-4-4-2-2-2-22222-2-2-2-222221-2-22211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ554444-44-444-4-4-4-4444-4-44-44-4-2-2-2-2-2-222-2-2-2-2-2-222122-22-1-111-1-1122-2211-1-111-1-1000000000000000000000000000000000000
χ564444-4-444-44-4-4-4444-4-4-44-44-2-2-2-222-2-2-2-2-2-222-2-21222-2-1-1-1-1111222-211-1-1-1-111000000000000000000000000000000000000
χ5744-4-44444-4-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5844-4-44-4-4444-4444-4-4-4-4-4-444-2-2-2-222222222-2-2-2-21-2-22211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ5944-4-4-44-44-444-4-44-4-4444-4-44-2-2-2-2-2-222222222-2-2122-22-1-111-1-11-2-22-2-1-111-1-111000000000000000000000000000000000000
χ6044-4-4-4-4444-44-4-44-4-444-444-4-2-2-2-222-2-22222-2-2221222-2-1-1-1-1111-2-2-22-1-11111-1-1000000000000000000000000000000000000
χ614-44i−4i000400000-44i−4i00000044-4-400004i−4i4i−4i000040000000000-400004i−4i000000000000000000000000000000000000000000
χ624-44i−4i000400000-44i−4i0000004-2-4200−2i32i34i−4i−2i2i0023−23-200000000−2i32i320000−2i2i000023−23000000000000000000000000000000000000
χ634-44i−4i000400000-44i−4i0000004-2-42002i3−2i34i−4i−2i2i00−2323-2000000002i3−2i320000−2i2i0000−2323000000000000000000000000000000000000
χ644-44i−4i000400000-44i−4i000000-242-4−2i32i300−2i2i4i−4i23−2300-2000000−2i32i30020000−2i2i0023−2300000000000000000000000000000000000000
χ654-44i−4i000400000-44i−4i000000-242-42i3−2i300−2i2i4i−4i−232300-20000002i3−2i30020000−2i2i00−232300000000000000000000000000000000000000
χ664-44i−4i000400000-44i−4i000000-2-222−2i32i3−2i32i3−2i2i−2i2i23−2323−23100003-3i3−i3i3−i3-10000i−i3i−3i−33−33000000000000000000000000000000000000
χ674-44i−4i000400000-44i−4i000000-2-222−2i32i32i3−2i3−2i2i−2i2i23−23−232310000-33i3−i3−i3i3-10000i−i−3i3i−333−3000000000000000000000000000000000000
χ684-44i−4i000400000-44i−4i000000-2-2222i3−2i3−2i32i3−2i2i−2i2i−232323−2310000-33−i3i3i3−i3-10000i−i−3i3i3−3−33000000000000000000000000000000000000
χ694-44i−4i000400000-44i−4i000000-2-2222i3−2i32i3−2i3−2i2i−2i2i−2323−2323100003-3−i3i3−i3i3-10000i−i3i−3i3−33−3000000000000000000000000000000000000
χ704-4−4i4i000400000-4−4i4i00000044-4-40000−4i4i−4i4i000040000000000-40000−4i4i000000000000000000000000000000000000000000
χ714-4−4i4i000400000-4−4i4i0000004-2-4200−2i32i3−4i4i2i−2i00−2323-200000000−2i32i3200002i−2i0000−2323000000000000000000000000000000000000
χ724-4−4i4i000400000-4−4i4i0000004-2-42002i3−2i3−4i4i2i−2i0023−23-2000000002i3−2i3200002i−2i000023−23000000000000000000000000000000000000
χ734-4−4i4i000400000-4−4i4i000000-242-4−2i32i3002i−2i−4i4i−232300-2000000−2i32i300200002i−2i00−232300000000000000000000000000000000000000
χ744-4−4i4i000400000-4−4i4i000000-242-42i3−2i3002i−2i−4i4i23−2300-20000002i3−2i300200002i−2i0023−2300000000000000000000000000000000000000
χ754-4−4i4i000400000-4−4i4i000000-2-222−2i32i3−2i32i32i−2i2i−2i−2323−2323100003-3i3−i3i3−i3-10000−ii−3i3i3−33−3000000000000000000000000000000000000
χ764-4−4i4i000400000-4−4i4i000000-2-222−2i32i32i3−2i32i−2i2i−2i−232323−2310000-33i3−i3−i3i3-10000−ii3i−3i3−3−33000000000000000000000000000000000000
χ774-4−4i4i000400000-4−4i4i000000-2-2222i3−2i3−2i32i32i−2i2i−2i23−23−232310000-33−i3i3i3−i3-10000−ii3i−3i−333−3000000000000000000000000000000000000
χ784-4−4i4i000400000-4−4i4i000000-2-2222i3−2i32i3−2i32i−2i2i−2i23−2323−23100003-3−i3i3−i3i3-10000−ii−3i3i−33−33000000000000000000000000000000000000
χ796666666-3666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000000022220000000000000000-1-1-1-1-1-1-1-1
χ806666666-3666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000000000-2-2-2-2000000000000000011111111
χ8166666-6-6-3-6-66-3-3-3-3-3-3-3333300000000000000000000000000000000000000000000000022-2-20000000000000000-1-1-1-11111
χ8266666-6-6-3-6-66-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000000-2-22200000000000000001111-1-1-1-1
χ836666-66-6-36-6-633-3-3-333-33-330000000000000000000000000000000000000000000000002i−2i2i−2i0000000000000000−i−iii−i−iii
χ846666-66-6-36-6-633-3-3-333-33-33000000000000000000000000000000000000000000000000−2i2i−2i2i0000000000000000ii−i−iii−i−i
χ856666-6-66-3-66-633-3-3-3333-33-30000000000000000000000000000000000000000000000002i−2i−2i2i0000000000000000−i−iiiii−i−i
χ866666-6-66-3-66-633-3-3-3333-33-3000000000000000000000000000000000000000000000000−2i2i2i−2i0000000000000000ii−i−i−i−iii
χ8766-6-6666-3-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000000000000000000000000000000003−33−33−33−3
χ8866-6-6666-3-6-6-6-3-3-33333-3-33300000000000000000000000000000000000000000000000000000000000000000000−33−33−33−33
χ8966-6-66-6-6-366-6-3-3-3333333-3-3000000000000000000000000000000000000000000000000000000000000000000003−33−3−33−33
χ9066-6-66-6-6-366-6-3-3-3333333-3-300000000000000000000000000000000000000000000000000000000000000000000−33−333−33−3
χ9166-6-6-66-6-3-66633-333-3-3-333-300000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3−i3i3i3−i3
χ9266-6-6-66-6-3-66633-333-3-3-333-300000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3i3−i3−i3i3
χ9366-6-6-6-66-36-6633-333-3-33-3-3300000000000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ9466-6-6-6-66-36-6633-333-3-33-3-3300000000000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ9512-1212i−12i000-6000−6i36i36−6i6i63−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212i−12i000-60006i3−6i36−6i6i−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12−12i12i000-6000−6i36i366i−6i−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12−12i12i000-60006i3−6i366i−6i63−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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