Finite Group Databasebeta

← Group #13135163

Character table — Group #13135163

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12222234444666666612121212336666661212121212121212366666666666121212121212121212121212444488888888121212121212121224242424242424242424242424242424
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
χ51111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-11-111-11-111-1-1-11-111-1-111-1-1-1-11111-1-111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1i−ii−i1-11-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101-11-11-111-11-111-1-1-11-111-1-111-1-1-1-11111-1-111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1i−ii−i-11-11−ii−iiii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111-11-11-111-11-111-1-1-11-111-1-111-1-1-1-11111-1-111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−ii−ii1-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121-11-11-111-11-111-1-1-11-111-1-111-1-1-1-11111-1-111-1-1111-1-111-1-1-1-1111-1-11111-1-1-1-1−ii−ii-11-11i−ii−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131-11-11-11-11-1111-1-1-11-1-1-11111-1-1-1-111-1-111-1-111111-1-111-1-1-1-11-1-111-1-1-1-11111i−i−iii−i−ii-111-1ii−i−i−i−iiiii−i−i−i−iii-1-11111-1-1
χ141-11-11-11-11-1111-1-1-11-1-1-11111-1-1-1-111-1-111-1-111111-1-111-1-1-1-11-1-111-1-1-1-11111i−i−ii−iii−i1-1-11ii−i−i−i−iii−i−iiiii−i−i11-1-1-1-111
χ151-11-11-11-11-1111-1-1-11-1-1-11111-1-1-1-111-1-111-1-111111-1-111-1-1-1-11-1-111-1-1-1-11111−iii−ii−i−ii1-1-11−i−iiiii−i−iii−i−i−i−iii11-1-1-1-111
χ161-11-11-11-11-1111-1-1-11-1-1-11111-1-1-1-111-1-111-1-111111-1-111-1-1-1-11-1-111-1-1-1-11111−iii−i−iii−i-111-1−i−iiiii−i−i−i−iiiii−i−i-1-11111-1-1
χ1722222222222222222222222-122-1-12-122-1-1-1-122-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-122-1-12-122-1-1-1-122-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ192222222222222222222222-12-1-122-12-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-122-12-1-12222-1-1-1-12-12-1-1-1-1-1-1-1-12-12-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ212222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-1-21-211111111100002i2i−2i−2i000000000000−i−i−i−iiiii00000000
χ222222222-2-2-2-22222222-2-2-2-22-122-1-12-1-2-21111-2-2-12-12-1-1-1-1-1-1-1-1-21-21111111110000−2i−2i2i2i000000000000iiii−i−i−i−i00000000
χ232222222-2-2-2-22222222-2-2-2-2-12-1-122-1211-2-2-2-211-1-12-12-1-1-1-1-1-1-11-21-211111111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ242222222-2-2-2-22222222-2-2-2-2-12-1-122-1211-2-2-2-211-1-12-12-1-1-1-1-1-1-11-21-21111111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ252222-2-222-2-22-2-22-2-2222-22-22222222222-2-2-2-2222-2-2-2-2-2-222-2-22-22-2222-2-222-2-2000000000000000000000000000000000000
χ262222-2-222-2-22-2-22-2-2222-22-22-122-1-12-122111122-1-21-2111-1-111-1-2-1-2-1-1-111-1-111000000000000000000003−33−33−33−300000000
χ272222-2-222-2-22-2-22-2-2222-22-22-122-1-12-122111122-1-21-2111-1-111-1-2-1-2-1-1-111-1-11100000000000000000000−33−33−33−3300000000
χ282222-2-222-2-22-2-22-2-2222-22-2-12-1-122-12-1-1-2-2-2-2-1-1-11-21-211-1-111-11212-1-111-1-1110000000000000000000000000000−i3i3−i3i3−i3i3−i3i3
χ292222-2-222-2-22-2-22-2-2222-22-2-12-1-122-12-1-1-2-2-2-2-1-1-11-21-211-1-111-11212-1-111-1-1110000000000000000000000000000i3−i3i3−i3i3−i3i3−i3
χ302222-2-22-222-2-2-22-2-222-22-2222222222-2-22222-2-22-2-2-2-2-2-222-2-222-22-2-2-222-2-222000000000000000000000000000000000000
χ312222-2-22-222-2-2-22-2-222-22-222-122-1-12-1-2-2-1-1-1-1-2-2-1-21-2111-1-111-1212111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ322222-2-22-222-2-2-22-2-222-22-222-122-1-12-1-2-2-1-1-1-1-2-2-1-21-2111-1-111-1212111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ332222-2-22-222-2-2-22-2-222-22-22-12-1-122-1211222211-11-21-211-1-111-1-1-2-1-211-1-111-1-100000000000000000000000000003−33−3−33−33
χ342222-2-22-222-2-2-22-2-222-22-22-12-1-122-1211222211-11-21-211-1-111-1-1-2-1-211-1-111-1-10000000000000000000000000000−33−333−33−3
χ352-22-22-222-22-222-2-2-22-222-2-22-1-2-2112-12211-1-1-2-2-12-1-21-1-11111-12-1-21-1-1-1-1111100002-22-2000000000000-1-111-1-11100000000
χ362-22-22-222-22-222-2-2-22-222-2-22-1-2-2112-12211-1-1-2-2-12-1-21-1-11111-12-1-21-1-1-1-111110000-22-2200000000000011-1-111-1-100000000
χ372-22-22-222-22-222-2-2-22-222-2-2-1211-2-2-12-1-1-2-22211-1-121-2-1-11111-1-121-2-1-1-1-11111000000002i−2i2i−2i0000000000000000−i−iii−i−iii
χ382-22-22-222-22-222-2-2-22-222-2-2-1211-2-2-12-1-1-2-22211-1-121-2-1-11111-1-121-2-1-1-1-1111100000000−2i2i−2i2i0000000000000000ii−i−iii−i−i
χ392-22-22-22-22-2222-2-2-22-2-2-2222-1-2-2112-1-2-2-1-11122-12-1-21-1-11111-1-212-11111-1-1-1-100002i−2i−2i2i000000000000−i−iiiii−i−i00000000
χ402-22-22-22-22-2222-2-2-22-2-2-2222-1-2-2112-1-2-2-1-11122-12-1-21-1-11111-1-212-11111-1-1-1-10000−2i2i2i−2i000000000000ii−i−i−i−iii00000000
χ412-22-22-22-22-2222-2-2-22-2-2-222-1211-2-2-121122-2-2-1-1-1-121-2-1-11111-11-2-121111-1-1-1-1000000002-2-220000000000000000-1-11111-1-1
χ422-22-22-22-22-2222-2-2-22-2-2-222-1211-2-2-121122-2-2-1-1-1-121-2-1-11111-11-2-121111-1-1-1-100000000-222-2000000000000000011-1-1-1-111
χ432-22-2-22222-2-2-2-2-2222-22-2-2222-2-2-2-2222222-2-2-2-22-2-222-2-2-2-2222-222-222-2-2-2-222000000000000000000000000000000000000
χ442-22-2-22222-2-2-2-2-2222-22-2-222-1-2-2112-122-1-111-2-2-1-212-11111-1-1-1-2-121-1-11111-1-1000000000000000000003−3−333−3−3300000000
χ452-22-2-22222-2-2-2-2-2222-22-2-222-1-2-2112-122-1-111-2-2-1-212-11111-1-1-1-2-121-1-11111-1-100000000000000000000−333−3−333−300000000
χ462-22-2-22222-2-2-2-2-2222-22-2-22-1211-2-2-12-1-122-2-211-11-2-121111-1-1-112-1-2-1-11111-1-100000000000000000000000000003−3−333−3−33
χ472-22-2-22222-2-2-2-2-2222-22-2-22-1211-2-2-12-1-122-2-211-11-2-121111-1-1-112-1-2-1-11111-1-10000000000000000000000000000−333−3−333−3
χ482-22-2-222-2-222-2-2-2222-2-222-222-2-2-2-222-2-2-2-222222-2-222-2-2-2-22222-2-22-2-22222-2-2000000000000000000000000000000000000
χ492-22-2-222-2-222-2-2-2222-2-222-22-1-2-2112-1-2-211-1-122-1-212-11111-1-1-121-2-111-1-1-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ502-22-2-222-2-222-2-2-2222-2-222-22-1-2-2112-1-2-211-1-122-1-212-11111-1-1-121-2-111-1-1-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ512-22-2-222-2-222-2-2-2222-2-222-2-1211-2-2-1211-2-222-1-1-11-2-121111-1-1-1-1-21211-1-1-1-1110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ522-22-2-222-2-222-2-2-2222-2-222-2-1211-2-2-1211-2-222-1-1-11-2-121111-1-1-1-1-21211-1-1-1-1110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
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
χ544444444-4-4-4-44444444-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-444-4-44-4-44-4-4444-44-4-2-2-2-2-2-2-2-2-2-22222-2-212222-1-111-1-112-22-211-1-111-1-1000000000000000000000000000000000000
χ564444-4-44-444-4-4-44-4-444-44-44-2-2-2-2-2-2-2-222-2-2-2-22212222-1-111-1-11-22-22-1-111-1-111000000000000000000000000000000000000
χ5744-4-4004000000400-4-40000444-44-4-4-40000000040000004-400-4000000000000000000000000000000000000000000000000
χ5844-4-4004000000400-4-400004-24-4-22-420023−2323−2300-2000000-2200200000023−230023−23000000000000000000000000000000000000
χ5944-4-4004000000400-4-400004-24-4-22-4200−2323−232300-2000000-22002000000−232300−2323000000000000000000000000000000000000
χ6044-4-4004000000400-4-40000-24-224-42-423−23000023−23-2000000-22002000023−230023−2300000000000000000000000000000000000000
χ6144-4-4004000000400-4-40000-24-224-42-4−23230000−2323-2000000-220020000−232300−232300000000000000000000000000000000000000
χ6244-4-4004000000400-4-40000-2-2-22-222223−2323−2323−2323−23100003-31-13-3-10000−33−33−33−33000000000000000000000000000000000000
χ6344-4-4004000000400-4-40000-2-2-22-222223−23−2323−232323−2310000-331-1-33-10000−333−3−333−3000000000000000000000000000000000000
χ6444-4-4004000000400-4-40000-2-2-22-2222−232323−2323−23−232310000-331-1-33-100003−3−333−3−33000000000000000000000000000000000000
χ6544-4-4004000000400-4-40000-2-2-22-2222−2323−2323−2323−2323100003-31-13-3-100003−33−33−33−3000000000000000000000000000000000000
χ664-44-44-444-44-444-4-4-44-444-4-4-2-22222-2-2-2-222-2-2221-2-22211-1-1-1-11-2-2221111-1-1-1-1000000000000000000000000000000000000
χ674-44-44-44-44-4444-4-4-44-4-4-444-2-22222-2-222-2-222-2-21-2-22211-1-1-1-1122-2-2-1-1-1-11111000000000000000000000000000000000000
χ684-44-4-44444-4-4-4-4-4444-44-4-44-2-22222-2-2-2-2-2-22222122-2-2-1-1-1-11112-2-2211-1-1-1-111000000000000000000000000000000000000
χ694-44-4-444-4-444-4-4-4444-4-444-4-2-22222-2-22222-2-2-2-2122-2-2-1-1-1-1111-222-2-1-11111-1-1000000000000000000000000000000000000
χ704-4-44004000000-400-44000044-44-44-4-4000000004000000-4400-4000000000000000000000000000000000000000000000000
χ714-4-44004000000-400-4400004-2-442-2-420023−23−232300-20000002-2002000000−23230023−23000000000000000000000000000000000000
χ724-4-44004000000-400-4400004-2-442-2-4200−232323−2300-20000002-200200000023−2300−2323000000000000000000000000000000000000
χ734-4-44004000000-400-440000-242-2-442-423−230000−2323-20000002-2002000023−2300−232300000000000000000000000000000000000000
χ744-4-44004000000-400-440000-242-2-442-4−2323000023−23-20000002-20020000−23230023−2300000000000000000000000000000000000000
χ754-4-44004000000-400-440000-2-22-22-22223−2323−23−2323−232310000-33-113-3-10000−333−33−3−33000000000000000000000000000000000000
χ764-4-44004000000-400-440000-2-22-22-22223−23−232323−23−2323100003-3-11-33-10000−33−333−33−3000000000000000000000000000000000000
χ774-4-44004000000-400-440000-2-22-22-222−232323−23−232323−23100003-3-11-33-100003−33−3−33−33000000000000000000000000000000000000
χ784-4-44004000000-400-440000-2-22-22-222−2323−232323−2323−2310000-33-113-3-100003−3−33−333−3000000000000000000000000000000000000
χ79666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-10000000000000000
χ80666666-36666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-2-2-2-200000000111111110000000000000000
χ81666666-3-6-6-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000022-2-200000000-1-1-1-111110000000000000000
χ82666666-3-6-6-6-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000-2-222000000001111-1-1-1-10000000000000000
χ836666-6-6-36-6-6633-333-3-3-33-330000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ846666-6-6-36-6-6633-333-3-3-33-330000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ856666-6-6-3-666-633-333-3-33-33-30000000000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ866666-6-6-3-666-633-333-3-33-33-30000000000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ876-66-66-6-36-66-6-3-3333-33-3-33300000000000000000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii0000000000000000
χ886-66-66-6-36-66-6-3-3333-33-3-3330000000000000000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000000000
χ896-66-66-6-3-66-66-3-3333-3333-3-300000000000000000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ906-66-66-6-3-66-66-3-3333-3333-3-30000000000000000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ916-66-6-66-366-6-6333-3-3-33-333-300000000000000000000000000000000000000000000000000003−3−333−3−330000000000000000
χ926-66-6-66-366-6-6333-3-3-33-333-30000000000000000000000000000000000000000000000000000−333−3−333−30000000000000000
χ936-66-6-66-3-6-666333-3-3-333-3-3300000000000000000000000000000000000000000000000000003−3−33−333−30000000000000000
χ946-66-6-66-3-6-666333-3-3-333-3-330000000000000000000000000000000000000000000000000000−333−33−3−330000000000000000
χ951212-12-1200-60000−6i36i3-6−6i36i36600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-1200-600006i3−6i3-66i3−6i36600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121200-60000−6i36i366i3−6i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121200-600006i3−6i36−6i36i36-600000000000000000000000000000000000000000000000000000000000000000000000000000000

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