Finite Group Databasebeta

← Group #13135172

Character table — Group #13135172

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12222234444666121212126612123366666666661212121236666666661212121212121212121212121212444488888888121212121212121224242424242424242424242424242424
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
χ51111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111-1-1-1-1111-1-1-1-111-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91-11-11-111-11-1-1-1111-1-11-11-11111-1-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-11111-1-1-1-1i−ii−ii−ii−i1-11-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101-11-11-111-11-1-1-1111-1-11-11-11111-1-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-11111-1-1-1-1i−ii−i−ii−ii-11-11ii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111-11-11-111-11-1-1-1111-1-11-11-11111-1-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-11111-1-1-1-1−ii−iii−ii−i-11-11−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121-11-11-111-11-1-1-1111-1-11-11-11111-1-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-11111-1-1-1-1−ii−ii−ii−ii1-11-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131-11-11-11-11-11-1-11-1-1111-1-111111-1-1-1-1-111-111-1-111-111-1-1-1-11-1-1-1111-1-1-1-11111i−i−ii1-1-11−iii−iii−i−i−i−iii11-1-1-1-111−i−iiiii−i−i
χ141-11-11-11-11-11-1-11-1-1111-1-111111-1-1-1-1-111-111-1-111-111-1-1-1-11-1-1-1111-1-1-1-11111i−i−ii-111-1i−i−iiii−i−i−i−iii-1-11111-1-1ii−i−i−i−iii
χ151-11-11-11-11-11-1-11-1-1111-1-111111-1-1-1-1-111-111-1-111-111-1-1-1-11-1-1-1111-1-1-1-11111−iii−i1-1-11i−i−ii−i−iiiii−i−i11-1-1-1-111ii−i−i−i−iii
χ161-11-11-11-11-11-1-11-1-1111-1-111111-1-1-1-1-111-111-1-111-111-1-1-1-11-1-1-1111-1-1-1-11111−iii−i-111-1−iii−i−i−iiiii−i−i-1-11111-1-1−i−iiiii−i−i
χ1722222222222222222222222-122222-1-12-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122222-1-12-12-1-1-1-1-1-1-1-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ192222222222222222222222-12-1-1-1-1-122-12-12222-122-1-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1222200000000-1-1-1-1-1-1-1-10000000000000000
χ202222222222222222222222-12-1-1-1-1-122-12-12222-122-1-1-1-1-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-200000000111111110000000000000000
χ212222222-2-2-2-2222-2-2-2-222-2-22-122222-1-12-121111-1-1-1-1-1-1-1-1-1-1-2-21-2-2111111111000000002i2i−2i−2i0000000000000000−i−i−i−iiiii
χ222222222-2-2-2-2222-2-2-2-222-2-22-122222-1-12-121111-1-1-1-1-1-1-1-1-1-1-2-21-2-211111111100000000−2i−2i2i2i0000000000000000iiii−i−i−i−i
χ232222222-2-2-2-2222-2-2-2-222-2-2-12-1-1-1-1-122-12-1-2-2-2-2-122-1-1-1-1-1-1-111-211-21111111122-2-200000000-1-1-1-111110000000000000000
χ242222222-2-2-2-2222-2-2-2-222-2-2-12-1-1-1-1-122-12-1-2-2-2-2-122-1-1-1-1-1-1-111-211-211111111-2-222000000001111-1-1-1-10000000000000000
χ252222-2-222-2-222222222-2-2-2-222-2-22-2-222222-2-2-2-22-2-2-2-222-2-222-222-2222-2-222-2-2000000000000000000000000000000000000
χ262222-2-222-2-222222222-2-2-2-22-1-2-22-2-2-1-12-121111-11111-1-111-12-2-12-2-1-1-111-1-11100000000000000000000000000003−33−33−33−3
χ272222-2-222-2-222222222-2-2-2-22-1-2-22-2-2-1-12-121111-11111-1-111-12-2-12-2-1-1-111-1-1110000000000000000000000000000−33−33−33−33
χ282222-2-222-2-222222222-2-2-2-2-1211-11122-12-1-2-2-2-2-1-2-211-1-111-1-112-112-1-111-1-111000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ292222-2-222-2-222222222-2-2-2-2-1211-11122-12-1-2-2-2-2-1-2-211-1-111-1-112-112-1-111-1-111000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ302222-2-22-222-2222-2-2-2-2-2-22222-2-22-2-22222222222-2-2-2-222-2-22-22-2-22-2-2-222-2-222000000000000000000000000000000000000
χ312222-2-22-222-2222-2-2-2-2-2-2222-1-2-22-2-2-1-12-12-1-1-1-1-11111-1-111-1-221-22111-1-111-1-10000000000000000000000000000−i3i3−i3i3i3−i3i3−i3
χ322222-2-22-222-2222-2-2-2-2-2-2222-1-2-22-2-2-1-12-12-1-1-1-1-11111-1-111-1-221-22111-1-111-1-10000000000000000000000000000i3−i3i3−i3−i3i3−i3i3
χ332222-2-22-222-2222-2-2-2-2-2-222-1211-11122-12-12222-1-2-211-1-111-11-1-21-1-211-1-111-1-1000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ342222-2-22-222-2222-2-2-2-2-2-222-1211-11122-12-12222-1-2-211-1-111-11-1-21-1-211-1-111-1-1000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ352-22-22-222-22-2-2-2222-2-22-22-22-122-2-2-2112-1-211-1-1-1-11-1-11111-122-1-2-21-1-1-1-11111000000002-22-20000000000000000-1-111-1-111
χ362-22-22-222-22-2-2-2222-2-22-22-22-122-2-2-2112-1-211-1-1-1-11-1-11111-122-1-2-21-1-1-1-1111100000000-22-22000000000000000011-1-111-1-1
χ372-22-22-222-22-2-2-2222-2-22-22-2-12-1-1111-2-2-121-2-222-12-2-1-11111-1-1-1211-2-1-1-1-111112i−2i2i−2i00000000−i−iii−i−iii0000000000000000
χ382-22-22-222-22-2-2-2222-2-22-22-2-12-1-1111-2-2-121-2-222-12-2-1-11111-1-1-1211-2-1-1-1-11111−2i2i−2i2i00000000ii−i−iii−i−i0000000000000000
χ392-22-22-22-22-22-2-22-2-2222-2-222-122-2-2-2112-1-2-1-111-1-11-1-11111-1-2-2122-11111-1-1-1-1000000002i−2i−2i2i0000000000000000−i−iiiii−i−i
χ402-22-22-22-22-22-2-22-2-2222-2-222-122-2-2-2112-1-2-1-111-1-11-1-11111-1-2-2122-11111-1-1-1-100000000−2i2i2i−2i0000000000000000ii−i−i−i−iii
χ412-22-22-22-22-22-2-22-2-2222-2-22-12-1-1111-2-2-12122-2-2-12-2-1-11111-111-2-1-121111-1-1-1-12i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ422-22-22-22-22-22-2-22-2-2222-2-22-12-1-1111-2-2-12122-2-2-12-2-1-11111-111-2-1-121111-1-1-1-1−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ432-22-2-22222-2-2-2-2222-2-2-22-2222-2-2-222-2-222-222-2-22-22-2-2-2-22222-22-22-222-2-2-2-222000000000000000000000000000000000000
χ442-22-2-22222-2-2-2-2222-2-2-22-222-1-2-2-222112-1-2-1-111-11-11111-1-1-12-2-1-221-1-11111-1-100000000000000000000000000003−3−333−3−33
χ452-22-2-22222-2-2-2-2222-2-2-22-222-1-2-2-222112-1-2-1-111-11-11111-1-1-12-2-1-221-1-11111-1-10000000000000000000000000000−333−3−333−3
χ462-22-2-22222-2-2-2-2222-2-2-22-22-12111-1-1-2-2-12122-2-2-1-221111-1-1-1-1121-1-2-1-11111-1-10000000000003−3−333−3−330000000000000000
χ472-22-2-22222-2-2-2-2222-2-2-22-22-12111-1-1-2-2-12122-2-2-1-221111-1-1-1-1121-1-2-1-11111-1-1000000000000−333−3−333−30000000000000000
χ482-22-2-222-2-222-2-22-2-222-222-222-2-2-222-2-222-2-2-2222-22-2-2-2-2222-22-22-22-2-22222-2-2000000000000000000000000000000000000
χ492-22-2-222-2-222-2-22-2-222-222-22-1-2-2-222112-1-211-1-1-11-11111-1-1-1-2212-2-111-1-1-1-1110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ502-22-2-222-2-222-2-22-2-222-222-22-1-2-2-222112-1-211-1-1-11-11111-1-1-1-2212-2-111-1-1-1-1110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ512-22-2-222-2-222-2-22-2-222-222-2-12111-1-1-2-2-121-2-222-1-221111-1-1-11-1-2-11211-1-1-1-1110000000000003−3−33−333−30000000000000000
χ522-22-2-222-2-222-2-22-2-222-222-2-12111-1-1-2-2-121-2-222-1-221111-1-1-11-1-2-11211-1-1-1-111000000000000−333−33−3−330000000000000000
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ544444444-4-4-4-4444-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ554444-4-444-4-444444444-4-4-4-4-2-222-222-2-2-2-2-22222122-1-111-1-11-22-2-22-211-1-111-1-1000000000000000000000000000000000000
χ564444-4-44-444-4444-4-4-4-4-4-444-2-222-222-2-2-2-2-2-2-2-2-2122-1-111-1-112-222-22-1-111-1-111000000000000000000000000000000000000
χ5744-4-400400004-4-40000000044004004-4-4-4-40000400004-400-400000000000000000000000000000000000000000000000000
χ5844-4-400400004-4-4000000004-200400-22-42-423−2323−23-20000-220020000000023−230023−23000000000000000000000000000000000000
χ5944-4-400400004-4-4000000004-200400-22-42-4−2323−2323-20000-2200200000000−232300−2323000000000000000000000000000000000000
χ6044-4-400400004-4-400000000-24−2i32i3-2−2i32i34-42-420000-200−2i32i3-22−2i32i3200000000000000000000000000000000000000000000000000
χ6144-4-400400004-4-400000000-242i3−2i3-22i3−2i34-42-420000-2002i3−2i3-222i3−2i3200000000000000000000000000000000000000000000000000
χ6244-4-400400004-4-400000000-2-2−2i32i3-2−2i32i3-2222223−2323−23100i3−i31-1i3−i3-10000003i−3i−333i−3i−33000000000000000000000000000000000000
χ6344-4-400400004-4-400000000-2-2−2i32i3-2−2i32i3-22222−2323−2323100i3−i31-1i3−i3-1000000−3i3i3−3−3i3i3−3000000000000000000000000000000000000
χ6444-4-400400004-4-400000000-2-22i3−2i3-22i3−2i3-2222223−2323−23100−i3i31-1−i3i3-1000000−3i3i−33−3i3i−33000000000000000000000000000000000000
χ6544-4-400400004-4-400000000-2-22i3−2i3-22i3−2i3-22222−2323−2323100−i3i31-1−i3i3-10000003i−3i3−33i−3i3−3000000000000000000000000000000000000
χ664-44-44-444-44-4-4-4444-4-44-44-4-2-2-2-222222-2-2222-2-21-2211-1-1-1-11-2-2-22221111-1-1-1-1000000000000000000000000000000000000
χ674-44-44-44-44-44-4-44-4-4444-4-44-2-2-2-222222-2-22-2-2221-2211-1-1-1-11222-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ684-44-4-44444-4-4-4-4444-4-4-44-44-2-2222-2-222-2-22-2-22212-2-1-1-1-1111-22-22-2211-1-1-1-111000000000000000000000000000000000000
χ694-44-4-444-4-444-4-44-4-444-444-4-2-2222-2-222-2-2222-2-212-2-1-1-1-11112-22-22-2-1-11111-1-1000000000000000000000000000000000000
χ704-4-440040000-44-4000000004400-400-44-4-44000040000-4400-400000000000000000000000000000000000000000000000000
χ714-4-440040000-44-4000000004-200-4002-2-42423−23−2323-200002-200200000000−23230023−23000000000000000000000000000000000000
χ724-4-440040000-44-4000000004-200-4002-2-424−232323−23-200002-20020000000023−2300−2323000000000000000000000000000000000000
χ734-4-440040000-44-400000000-24−2i32i322i3−2i3-442-4-20000-200−2i32i32-22i3−2i3200000000000000000000000000000000000000000000000000
χ744-4-440040000-44-400000000-242i3−2i32−2i32i3-442-4-20000-2002i3−2i32-2−2i32i3200000000000000000000000000000000000000000000000000
χ754-4-440040000-44-400000000-2-2−2i32i322i3−2i32-222-223−23−2323100i3−i3-11−i3i3-1000000−3i3i3−33i−3i−33000000000000000000000000000000000000
χ764-4-440040000-44-400000000-2-2−2i32i322i3−2i32-222-2−232323−23100i3−i3-11−i3i3-10000003i−3i−33−3i3i3−3000000000000000000000000000000000000
χ774-4-440040000-44-400000000-2-22i3−2i32−2i32i32-222-223−23−2323100−i3i3-11i3−i3-10000003i−3i3−3−3i3i−33000000000000000000000000000000000000
χ784-4-440040000-44-400000000-2-22i3−2i32−2i32i32-222-2−232323−23100−i3i3-11i3−i3-1000000−3i3i−333i−3i3−3000000000000000000000000000000000000
χ79666666-36666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000000002222000000000000-1-1-1-1-1-1-1-100000000
χ80666666-36666-3-3-3-3-3-3-3-3-3-3-300000000000000000000000000000000000000000000-2-2-2-20000000000001111111100000000
χ81666666-3-6-6-6-6-3-3-33333-3-333000000000000000000000000000000000000000000002i2i−2i−2i000000000000−i−i−i−iiiii00000000
χ82666666-3-6-6-6-6-3-3-33333-3-33300000000000000000000000000000000000000000000−2i−2i2i2i000000000000iiii−i−i−i−i00000000
χ836666-6-6-36-6-66-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ846666-6-6-36-6-66-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ856666-6-6-3-666-6-3-3-3333333-3-30000000000000000000000000000000000000000000000000000000000003−33−3−33−3300000000
χ866666-6-6-3-666-6-3-3-3333333-3-3000000000000000000000000000000000000000000000000000000000000−33−333−33−300000000
χ876-66-66-6-36-66-633-3-3-333-33-33000000000000000000000000000000000000000000002i−2i2i−2i000000000000−i−iii−i−iii00000000
χ886-66-66-6-36-66-633-3-3-333-33-3300000000000000000000000000000000000000000000−2i2i−2i2i000000000000ii−i−iii−i−i00000000
χ896-66-66-6-3-66-6633-333-3-3-333-3000000000000000000000000000000000000000000002-2-22000000000000-1-11111-1-100000000
χ906-66-66-6-3-66-6633-333-3-3-333-300000000000000000000000000000000000000000000-222-200000000000011-1-1-1-11100000000
χ916-66-6-66-366-6-633-3-3-3333-33-30000000000000000000000000000000000000000000000000000000000003−3−333−3−3300000000
χ926-66-6-66-366-6-633-3-3-3333-33-3000000000000000000000000000000000000000000000000000000000000−333−3−333−300000000
χ936-66-6-66-3-6-66633-333-3-33-3-33000000000000000000000000000000000000000000000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ946-66-6-66-3-6-66633-333-3-33-3-33000000000000000000000000000000000000000000000000000000000000i3−i3−i3i3−i3i3i3−i300000000
χ951212-12-1200-60000-66663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-1200-60000-666−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-121200-600006-6663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121200-600006-66−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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