Finite Group Databasebeta

← Group #13139951

Character table — Group #13139951

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order12222234444666121212126612123366666666661212121236666666661212121212121212121212121212444444448888121212121212121212121212121212122424242424242424
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
χ51111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111111-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111111-1-111-1-1-1-11-1-111-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111111-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111111-1-111-1-1-1-11-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1-111-1111-1-11-1-111-1-11-11-111-1-1-1-111-1-11111-1-111-1-1-111-1-111-11-11-111-1-111-1-1i−ii−i1-11-1i−ii−iii−i−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101-1-111-1111-1-11-1-111-1-11-11-111-1-1-1-111-1-11111-1-111-1-1-111-1-111-11-11-111-1-111-1-1i−ii−i-11-11−ii−iiii−i−iii−i−i-1-111-1-111−i−iii−i−iii
χ111-1-111-1111-1-11-1-111-1-11-11-111-1-1-1-111-1-11111-1-111-1-1-111-1-111-11-11-111-1-111-1-1−ii−ii1-11-1−ii−ii−i−iii−i−iii11-1-111-1-1−i−iii−i−iii
χ121-1-111-1111-1-11-1-111-1-11-11-111-1-1-1-111-1-11111-1-111-1-1-111-1-111-11-11-111-1-111-1-1−ii−ii-11-11i−ii−i−i−iii−i−iii-1-111-1-111ii−i−iii−i−i
χ131-1-11-1111-11-11-1-1-1-111-111-111-1-1-1-1-1-1111111-1-11-11-1-1-1-1111-111-1-1111-1-1-1-111i−i−ii1-1-11i−i−iiii−i−i−i−iii11-1-1-1-111ii−i−i−i−iii
χ141-1-11-1111-11-11-1-1-1-111-111-111-1-1-1-1-1-1111111-1-11-11-1-1-1-1111-111-1-1111-1-1-1-111i−i−ii-111-1−iii−iii−i−i−i−iii-1-11111-1-1−i−iiiii−i−i
χ151-1-11-1111-11-11-1-1-1-111-111-111-1-1-1-1-1-1111111-1-11-11-1-1-1-1111-111-1-1111-1-1-1-111−iii−i1-1-11−iii−i−i−iiiii−i−i11-1-1-1-111−i−iiiii−i−i
χ161-1-11-1111-11-11-1-1-1-111-111-111-1-1-1-1-1-1111111-1-11-11-1-1-1-1111-111-1-1111-1-1-1-111−iii−i-111-1i−i−ii−i−iiiii−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222222222222222-122-1-12222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122-1-12222-12-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ192222222222222222222222-12-1-122-1-1-1-12-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-122-1-1-1-12-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ212222222-2-2-2-2222-2-2-2-222-2-2222222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ222222222-2-2-2-2222-2-2-2-222-2-22-122-1-12222-121111-1-1-1-1-1-1-1-1-1-111-2-2-2-21111111100000000000000000000000000003−33−33−33−3
χ232222222-2-2-2-2222-2-2-2-222-2-22-122-1-12222-121111-1-1-1-1-1-1-1-1-1-111-2-2-2-2111111110000000000000000000000000000−33−33−33−33
χ242222222-2-2-2-2222-2-2-2-222-2-2-12-1-122-1-1-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-2-211111111111100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ252222222-2-2-2-2222-2-2-2-222-2-2-12-1-122-1-1-1-12-1-2-2-2-2-122-1-1-1-1-1-1-1-2-211111111111100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ262222-2-222-2-22222-2-2-2-2-2-2222-122-1-1-2-2-2-2-12-1-1-1-1-111-1-11111-11122-2-2-1-1-1-111110000000022-2-20000000000000000-1-1-1-11111
χ272222-2-222-2-22222-2-2-2-2-2-2222-122-1-1-2-2-2-2-12-1-1-1-1-111-1-11111-11122-2-2-1-1-1-1111100000000-2-22200000000000000001111-1-1-1-1
χ282222-2-222-2-22222-2-2-2-2-2-222-12-1-12211112-12222-1-2-2-1-11111-1-2-2-1-111-1-1-1-11111000022-2-2000000000000-1-1-1-1111100000000
χ292222-2-222-2-22222-2-2-2-2-2-222-12-1-12211112-12222-1-2-2-1-11111-1-2-2-1-111-1-1-1-111110000-2-2220000000000001111-1-1-1-100000000
χ302222-2-22-222-22222222-2-2-2-2222222-2-2-2-222-2-2-2-22-2-222-2-2-2-2222-2-222-2-2-2-22222000000000000000000000000000000000000
χ312222-2-22-222-22222222-2-2-2-22-122-1-1-2-2-2-2-121111-111-1-11111-1-1-1-2-2221111-1-1-1-100000000000000000000000000003−33−3−33−33
χ322222-2-22-222-22222222-2-2-2-22-122-1-1-2-2-2-2-121111-111-1-11111-1-1-1-2-2221111-1-1-1-10000000000000000000000000000−33−333−33−3
χ332222-2-22-222-22222222-2-2-2-2-12-1-12211112-1-2-2-2-2-1-2-2-1-11111-12211-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ342222-2-22-222-22222222-2-2-2-2-12-1-12211112-1-2-2-2-2-1-2-2-1-11111-12211-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ352-2-222-2222-2-22-2-222-2-22-22-22-1-2-21122-2-2-12-1-111-1-1111-1-111-1-112-22-2-1-111-1-111000000002i−2i2i−2i0000000000000000−i−iii−i−iii
χ362-2-222-2222-2-22-2-222-2-22-22-22-1-2-21122-2-2-12-1-111-1-1111-1-111-1-112-22-2-1-111-1-11100000000−2i2i−2i2i0000000000000000ii−i−iii−i−i
χ372-2-222-2222-2-22-2-222-2-22-22-2-1211-2-2-1-1112-122-2-2-12-211-1-111-12-2-11-11-1-111-1-11100002-22-2000000000000-1-111-1-11100000000
χ382-2-222-2222-2-22-2-222-2-22-22-2-1211-2-2-1-1112-122-2-2-12-211-1-111-12-2-11-11-1-111-1-1110000-22-2200000000000011-1-111-1-100000000
χ392-2-222-22-2-2222-2-2-2-2222-2-2222-2-2-2-222-2-222-2-22222-2-2-222-2-22-22-22-22-2-222-2-222000000000000000000000000000000000000
χ402-2-222-22-2-2222-2-2-2-2222-2-222-1-2-21122-2-2-1211-1-1-1-1111-1-111-11-1-22-2211-1-111-1-10000000000000000000000000000−i3i3i3−i3−i3i3i3−i3
χ412-2-222-22-2-2222-2-2-2-2222-2-222-1-2-21122-2-2-1211-1-1-1-1111-1-111-11-1-22-2211-1-111-1-10000000000000000000000000000i3−i3−i3i3i3−i3−i3i3
χ422-2-222-22-2-2222-2-2-2-2222-2-22-1211-2-2-1-1112-1-2-222-12-211-1-111-1-221-11-111-1-111-1-100000000000000000000−i3i3i3−i3−i3i3i3−i300000000
χ432-2-222-22-2-2222-2-2-2-2222-2-22-1211-2-2-1-1112-1-2-222-12-211-1-111-1-221-11-111-1-111-1-100000000000000000000i3−i3−i3i3i3−i3−i3i300000000
χ442-2-22-2222-22-22-2-2-2-222-222-22-1-2-211-2-222-12-1-111-11-11111-1-1-11-12-2-22-1-11111-1-1000000002i−2i−2i2i0000000000000000−i−iiiii−i−i
χ452-2-22-2222-22-22-2-2-2-222-222-22-1-2-211-2-222-12-1-111-11-11111-1-1-11-12-2-22-1-11111-1-100000000−2i2i2i−2i0000000000000000ii−i−i−i−iii
χ462-2-22-2222-22-22-2-2-2-222-222-2-1211-2-211-1-12-122-2-2-1-221111-1-1-1-22-111-1-1-11111-1-100002-2-22000000000000-1-11111-1-100000000
χ472-2-22-2222-22-22-2-2-2-222-222-2-1211-2-211-1-12-122-2-2-1-221111-1-1-1-22-111-1-1-11111-1-10000-222-200000000000011-1-1-1-11100000000
χ482-2-22-222-22-222-2-222-2-2-22-2222-2-2-2-2-2-22222-2-2222-22-2-2-2-22222-2-222-2-2-22222-2-2000000000000000000000000000000000000
χ492-2-22-222-22-222-2-222-2-2-22-222-1-2-211-2-222-1211-1-1-11-11111-1-1-1-11-222-211-1-1-1-1110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ502-2-22-222-22-222-2-222-2-2-22-222-1-2-211-2-222-1211-1-1-11-11111-1-1-1-11-222-211-1-1-1-1110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ512-2-22-222-22-222-2-222-2-2-22-22-1211-2-211-1-12-1-2-222-1-221111-1-1-12-21-1-1111-1-1-1-11100000000000000000000−i3i3i3−i3i3−i3−i3i300000000
χ522-2-22-222-22-222-2-222-2-2-22-22-1211-2-211-1-12-1-2-222-1-221111-1-1-12-21-1-1111-1-1-1-11100000000000000000000i3−i3−i3i3−i3i3i3−i300000000
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
χ554444-4-444-4-44444-4-4-4-4-4-444-2-2-2-2-2-22222-2-2-2-2-2-212211-1-1-1-1122-2-2221111-1-1-1-1000000000000000000000000000000000000
χ564444-4-44-444-44444444-4-4-4-4-2-2-2-2-2-22222-2-2222212211-1-1-1-11-2-222-2-2-1-1-1-11111000000000000000000000000000000000000
χ5744-4-40040000-44-400000000444-44-40000-4-400004004-40000-400000000000000000000000000000000000000000000000000
χ5844-4-40040000-44-4000000004-24-4-2200002-423−2323−23-200-220000200000023−2323−230000000000000000000000000000000000000000
χ5944-4-40040000-44-4000000004-24-4-2200002-4−2323−2323-200-2200002000000−2323−23230000000000000000000000000000000000000000
χ6044-4-40040000-44-400000000-24-224-4−2i32i3−2i32i3-420000-200-22−2i32i3−2i32i3200000000000000000000000000000000000000000000000000
χ6144-4-40040000-44-400000000-24-224-42i3−2i32i3−2i3-420000-200-222i3−2i32i3−2i3200000000000000000000000000000000000000000000000000
χ6244-4-40040000-44-400000000-2-2-22-22−2i32i3−2i32i32223−2323−231001-1i3−i3i3−i3-1000000−33−333i−3i3i−3i000000000000000000000000000000000000
χ6344-4-40040000-44-400000000-2-2-22-22−2i32i3−2i32i322−2323−23231001-1i3−i3i3−i3-10000003−33−3−3i3i−3i3i000000000000000000000000000000000000
χ6444-4-40040000-44-400000000-2-2-22-222i3−2i32i3−2i32223−2323−231001-1−i3i3−i3i3-1000000−33−33−3i3i−3i3i000000000000000000000000000000000000
χ6544-4-40040000-44-400000000-2-2-22-222i3−2i32i3−2i322−2323−23231001-1−i3i3−i3i3-10000003−33−33i−3i3i−3i000000000000000000000000000000000000
χ664-44-40040000-4-440000000044-44-440000-4-40000400-440000-400000000000000000000000000000000000000000000000000
χ674-44-40040000-4-44000000004-2-442-200002-423−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000000000
χ684-44-40040000-4-44000000004-2-442-200002-4−232323−23-2002-200002000000−232323−230000000000000000000000000000000000000000
χ694-44-40040000-4-4400000000-242-2-44−2i32i32i3−2i3-420000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ704-44-40040000-4-4400000000-242-2-442i3−2i3−2i32i3-420000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ714-44-40040000-4-4400000000-2-22-22-2−2i32i32i3−2i32223−23−2323100-11i3−i3−i3i3-1000000−333−33i−3i−3i3i000000000000000000000000000000000000
χ724-44-40040000-4-4400000000-2-22-22-2−2i32i32i3−2i322−232323−23100-11i3−i3−i3i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000000000
χ734-44-40040000-4-4400000000-2-22-22-22i3−2i3−2i32i32223−23−2323100-11−i3i3i3−i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000000000
χ744-44-40040000-4-4400000000-2-22-22-22i3−2i3−2i32i322−232323−23100-11−i3i3i3−i3-10000003−3−333i−3i−3i3i000000000000000000000000000000000000
χ754-4-444-4444-4-44-4-444-4-44-44-4-2-22222-2-222-2-2-2-2221-22-1-111-1-11-22-22-2211-1-111-1-1000000000000000000000000000000000000
χ764-4-444-44-4-4444-4-4-4-4444-4-44-2-22222-2-222-2-222-2-21-22-1-111-1-112-22-22-2-1-111-1-111000000000000000000000000000000000000
χ774-4-44-4444-44-44-4-4-4-444-444-4-2-2222222-2-2-2-2-2-22212-2-1-1-1-11112-2-222-211-1-1-1-111000000000000000000000000000000000000
χ784-4-44-444-44-444-4-444-4-4-44-44-2-2222222-2-2-2-222-2-212-2-1-1-1-1111-222-2-22-1-11111-1-1000000000000000000000000000000000000
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
χ81666666-3-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000000000000000
χ82666666-3-6-6-6-6-3-3-33333-3-3330000000000000000000000000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000000000000000
χ836666-6-6-36-6-66-3-3-3333333-3-3000000000000000000000000000000000000000022-2-200000000-1-1-1-111110000000000000000
χ846666-6-6-36-6-66-3-3-3333333-3-30000000000000000000000000000000000000000-2-222000000001111-1-1-1-10000000000000000
χ856666-6-6-3-666-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000−i3i3−i3i3i3−i3i3−i30000000000000000
χ866666-6-6-3-666-6-3-3-3-3-3-3-333330000000000000000000000000000000000000000000000000000i3−i3i3−i3−i3i3−i3i30000000000000000
χ876-6-666-6-366-6-6-333-3-333-33-3300000000000000000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii0000000000000000
χ886-6-666-6-366-6-6-333-3-333-33-330000000000000000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000000000
χ896-6-666-6-3-6-666-33333-3-3-333-300000000000000000000000000000000000000000000000000003−3−333−3−330000000000000000
χ906-6-666-6-3-6-666-33333-3-3-333-30000000000000000000000000000000000000000000000000000−333−3−333−30000000000000000
χ916-6-66-66-36-66-6-33333-3-33-3-3300000000000000000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i0000000000000000
χ926-6-66-66-36-66-6-33333-3-33-3-330000000000000000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii0000000000000000
χ936-6-66-66-3-66-66-333-3-3333-33-300000000000000000000000000000000000000000000000000003−3−33−333−30000000000000000
χ946-6-66-66-3-66-66-333-3-3333-33-30000000000000000000000000000000000000000000000000000−333−33−3−330000000000000000
χ951212-12-1200-600006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-1200-600006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-1200-6000066-663−63−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-1212-1200-6000066-6−636363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000

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