Finite Group Databasebeta

← Group #13137424

Character table — Group #13137424

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222222244446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222344444466612121212121212123366666612121212121212123666121212121212121212121212121212121212121222444444666688881212121212121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ811111-1-1-1-111111-1-1-1-111-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1
χ91-11-11i−ii−i1-11-1-1ii−i−i1-1i−i111-1-1-11-1ii−i−i11-1-111-1-1ii−i−i1-1i−i11-1-1iiii−i−i−i−i1-11-1i−ii−i11-1-11-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-11-11i−ii−i1-11-1-1ii−i−i1-1i−i111-1-1-11-1ii−i−i11-1-111-1-1ii−i−i1-1i−i11-1-1iiii−i−i−i−i1-1-11i−i−ii11-1-1-11−iiii−i−i-1-111−i−iii-1-111−i−iii
χ111-11-11i−ii−i1-11-1-1ii−i−i1-1i−i111-1-1-11-1ii−i−i11-1-111-1-1ii−i−i1-1i−i11-1-1iiii−i−i−i−i-111-1−iii−i-1-111-11−ii−i−iii11-1-1ii−i−i-1-111−i−iii
χ121-11-11i−ii−i1-11-1-1ii−i−i1-1i−i111-1-1-11-1ii−i−i11-1-111-1-1ii−i−i1-1i−i11-1-1iiii−i−i−i−i-11-11−ii−ii-1-1111-1i−i−i−iii-1-111−i−iii11-1-1ii−i−i
χ131-11-11−ii−ii1-11-1-1−i−iii1-1−ii111-1-1-11-1−i−iii11-1-111-1-1−i−iii1-1−ii11-1-1−i−i−i−iiiii1-11-1−ii−ii11-1-11-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-11-11−ii−ii1-11-1-1−i−iii1-1−ii111-1-1-11-1−i−iii11-1-111-1-1−i−iii1-1−ii11-1-1−i−i−i−iiiii1-1-11−iii−i11-1-1-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-11-11−ii−ii1-11-1-1−i−iii1-1−ii111-1-1-11-1−i−iii11-1-111-1-1−i−iii1-1−ii11-1-1−i−i−i−iiiii-111-1i−i−ii-1-111-11i−iii−i−i11-1-1−i−iii-1-111ii−i−i
χ161-11-11−ii−ii1-11-1-1−i−iii1-1−ii111-1-1-11-1−i−iii11-1-111-1-1−i−iii1-1−ii11-1-1−i−i−i−iiiii-11-11i−ii−i-1-1111-1−iiii−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222222222222222-1222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220022000000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-1222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-20000000000001111111100000000
χ192222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111
χ212222222-2-2-2-2222-2-2-2-2-2-222222222222222-2-2-2-222222-22-2-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ222222222-2-2-2-2222-2-2-2-2-2-2222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-22-211111111-1-111-1-11100000000000000000000−i3i3−i3i3−i3i3−i3i300000000
χ232222222-2-2-2-2222-2-2-2-2-2-2222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12-22-211111111-1-111-1-11100000000000000000000i3−i3i3−i3i3−i3i3−i300000000
χ242222222-2-2-2-2222-2-2-2-2-2-222-12-1-1-122222221111-1-1-1-1-11-11-2-2-2-21111-1-111-1-11100000000000000000000000000003−33−33−33−3
χ252222222-2-2-2-2222-2-2-2-2-2-222-12-1-1-122222221111-1-1-1-1-11-11-2-2-2-21111-1-111-1-1110000000000000000000000000000−33−33−33−33
χ2622222-2-222-2-22222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-22-22-2-222-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ2722222-2-222-2-22222222-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-1-22-2211-1-1111111-1-111-1-100000000000000000000−i3i3−i3i3i3−i3i3−i300000000
χ2822222-2-222-2-22222222-2-2-2-22-1222-1-1-11111-2-2-2-2-1-1-1-1-22-2211-1-1111111-1-111-1-100000000000000000000i3−i3i3−i3−i3i3−i3i300000000
χ2922222-2-222-2-22222222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-11-11-1-2-222111111-1-111-1-100000000000000000000000000003−33−3−33−33
χ3022222-2-222-2-22222222-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-1-11-11-1-2-222111111-1-111-1-10000000000000000000000000000−33−333−33−3
χ3122222-2-2-2-222222-2-2-2-222-2-22-1222-1-1-111112222-1-1-1-1-2-2-2-2-1-111-1-1-1-111111111002200-2-2000000000000-1-1-1-1111100000000
χ3222222-2-2-2-222222-2-2-2-222-2-22-1222-1-1-111112222-1-1-1-1-2-2-2-2-1-111-1-1-1-11111111100-2-200220000000000001111-1-1-1-100000000
χ3322222-2-2-2-222222-2-2-2-222-2-2-12-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1111122-2-2-1-1-1-11111111100000000000022-2-2000000000000-1-1-1-11111
χ3422222-2-2-2-222222-2-2-2-222-2-2-12-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1111122-2-2-1-1-1-111111111000000000000-2-2220000000000001111-1-1-1-1
χ352-22-222i−2i2i−2i2-22-2-22i2i−2i−2i2-22i−2i2-12-2-21-11−i−iii22-2-2-1-1112i2i−2i−2i-11−ii-1-111−i−i−i−iiiii002-2002i−2i000000000000-1-111−i−iii00000000
χ362-22-222i−2i2i−2i2-22-2-22i2i−2i−2i2-22i−2i2-12-2-21-11−i−iii22-2-2-1-1112i2i−2i−2i-11−ii-1-111−i−i−i−iiiii00-2200−2i2i00000000000011-1-1ii−i−i00000000
χ372-22-222i−2i2i−2i2-22-2-22i2i−2i−2i2-22i−2i-12-111-22-22i2i−2i−2i-1-111-1-111−i−iii2-22i−2i-1-111−i−i−i−iiiii0000000000002-22i−2i000000000000-1-111−i−iii
χ382-22-222i−2i2i−2i2-22-2-22i2i−2i−2i2-22i−2i-12-111-22-22i2i−2i−2i-1-111-1-111−i−iii2-22i−2i-1-111−i−i−i−iiiii000000000000-22−2i2i00000000000011-1-1ii−i−i
χ392-22-222i−2i−2i2i-222-2-2−2i−2i2i2i-222i−2i222-2-2-22-22i2i−2i−2i-2-22222-2-22i−2i−2i2i-22−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ402-22-222i−2i−2i2i-222-2-2−2i−2i2i2i-222i−2i2-12-2-21-11−i−iii-2-222-1-1112i−2i−2i2i1-1i−i11-1-1−i−iiiii−i−i00000000000000000000−i3i3i3−i33−3−3300000000
χ412-22-222i−2i−2i2i-222-2-2−2i−2i2i2i-222i−2i2-12-2-21-11−i−iii-2-222-1-1112i−2i−2i2i1-1i−i11-1-1−i−iiiii−i−i00000000000000000000i3−i3−i3i3−333−300000000
χ422-22-222i−2i−2i2i-222-2-2−2i−2i2i2i-222i−2i-12-111-22-22i2i−2i−2i11-1-1-1-111−iii−i-22−2i2i11-1-1−i−iiiii−i−i00000000000000000000000000003−3−33i3−i3−i3i3
χ432-22-222i−2i−2i2i-222-2-2−2i−2i2i2i-222i−2i-12-111-22-22i2i−2i−2i11-1-1-1-111−iii−i-22−2i2i11-1-1−i−iiiii−i−i0000000000000000000000000000−333−3−i3i3i3−i3
χ442-22-22−2i2i2i−2i-222-2-22i2i−2i−2i-22−2i2i222-2-2-22-2−2i−2i2i2i-2-22222-2-2−2i2i2i−2i-222i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ452-22-22−2i2i2i−2i-222-2-22i2i−2i−2i-22−2i2i2-12-2-21-11ii−i−i-2-222-1-111−2i2i2i−2i1-1−ii11-1-1ii−i−i−i−iii00000000000000000000−i3i3i3−i3−333−300000000
χ462-22-22−2i2i2i−2i-222-2-22i2i−2i−2i-22−2i2i2-12-2-21-11ii−i−i-2-222-1-111−2i2i2i−2i1-1−ii11-1-1ii−i−i−i−iii00000000000000000000i3−i3−i3i33−3−3300000000
χ472-22-22−2i2i2i−2i-222-2-22i2i−2i−2i-22−2i2i-12-111-22-2−2i−2i2i2i11-1-1-1-111i−i−ii-222i−2i11-1-1ii−i−i−i−iii00000000000000000000000000003−3−33−i3i3i3−i3
χ482-22-22−2i2i2i−2i-222-2-22i2i−2i−2i-22−2i2i-12-111-22-2−2i−2i2i2i11-1-1-1-111i−i−ii-222i−2i11-1-1ii−i−i−i−iii0000000000000000000000000000−333−3i3−i3−i3i3
χ492-22-22−2i2i−2i2i2-22-2-2−2i−2i2i2i2-2−2i2i2-12-2-21-11ii−i−i22-2-2-1-111−2i−2i2i2i-11i−i-1-111iiii−i−i−i−i002-200−2i2i000000000000-1-111ii−i−i00000000
χ502-22-22−2i2i−2i2i2-22-2-2−2i−2i2i2i2-2−2i2i2-12-2-21-11ii−i−i22-2-2-1-111−2i−2i2i2i-11i−i-1-111iiii−i−i−i−i00-22002i−2i00000000000011-1-1−i−iii00000000
χ512-22-22−2i2i−2i2i2-22-2-2−2i−2i2i2i2-2−2i2i-12-111-22-2−2i−2i2i2i-1-111-1-111ii−i−i2-2−2i2i-1-111iiii−i−i−i−i0000000000002-2−2i2i000000000000-1-111ii−i−i
χ522-22-22−2i2i−2i2i2-22-2-2−2i−2i2i2i2-2−2i2i-12-111-22-2−2i−2i2i2i-1-111-1-111ii−i−i2-2−2i2i-1-111iiii−i−i−i−i000000000000-222i−2i00000000000011-1-1−i−iii
χ534444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ544444444-4-4-4-4444-4-4-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-222221111-22-222222-1-1-1-111-1-111-1-1000000000000000000000000000000000000
χ5544444-4-444-4-44444444-4-4-4-4-2-2-2-2-2-2-2-22222222211112-22-222-2-2-1-1-1-1-1-111-1-111000000000000000000000000000000000000
χ5644444-4-4-4-444444-4-4-4-444-4-4-2-2-2-2-2-2-2-22222-2-2-2-211112222-2-2221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5744-4-44000000-44-40000000044-44-44-4-4000000004-44-400000000000000000000000000000000000000000000000000000000
χ5844-4-44000000-44-4000000004-2-44-4-222−2i32i3−2i32i30000-22-22000000000000−2i32i300−2i32i300000000000000000000000000000000000000
χ5944-4-44000000-44-4000000004-2-44-4-2222i3−2i32i3−2i30000-22-220000000000002i3−2i3002i3−2i300000000000000000000000000000000000000
χ6044-4-44000000-44-400000000-242-224-4-4000023−2323−23-22-220000000023−2323−2300000000000000000000000000000000000000000000
χ6144-4-44000000-44-400000000-242-224-4-40000−2323−2323-22-2200000000−2323−232300000000000000000000000000000000000000000000
χ6244-4-44000000-44-400000000-2-22-22-222−2i32i3−2i32i323−2323−231-11-100000000−33−33i3−i33i−3ii3−i33i−3i000000000000000000000000000000000000
χ6344-4-44000000-44-400000000-2-22-22-222−2i32i3−2i32i3−2323−23231-11-1000000003−33−3i3−i3−3i3ii3−i3−3i3i000000000000000000000000000000000000
χ6444-4-44000000-44-400000000-2-22-22-2222i3−2i32i3−2i323−2323−231-11-100000000−33−33−i3i3−3i3i−i3i3−3i3i000000000000000000000000000000000000
χ6544-4-44000000-44-400000000-2-22-22-2222i3−2i32i3−2i3−2323−23231-11-1000000003−33−3−i3i33i−3i−i3i33i−3i000000000000000000000000000000000000
χ664-44-444i−4i4i−4i4-44-4-44i4i−4i−4i4-44i−4i-2-2-2222-22−2i−2i2i2i-2-22211-1-1−2i−2i2i2i-22−2i2i11-1-1iiii−i−i−i−i000000000000000000000000000000000000
χ674-44-444i−4i−4i4i-444-4-4−4i−4i4i4i-444i−4i-2-2-2222-22−2i−2i2i2i22-2-211-1-1−2i2i2i−2i2-22i−2i-1-111ii−i−i−i−iii000000000000000000000000000000000000
χ684-44-44−4i4i4i−4i-444-4-44i4i−4i−4i-44−4i4i-2-2-2222-222i2i−2i−2i22-2-211-1-12i−2i−2i2i2-2−2i2i-1-111−i−iiiii−i−i000000000000000000000000000000000000
χ694-44-44−4i4i−4i4i4-44-4-4−4i−4i4i4i4-4−4i4i-2-2-2222-222i2i−2i−2i-2-22211-1-12i2i−2i−2i-222i−2i11-1-1−i−i−i−iiiii000000000000000000000000000000000000
χ704-4-444000000-4-440000000044-4-44-4-44000000004-4-4400000000000000000000000000000000000000000000000000000000
χ714-4-444000000-4-44000000004-2-4-4422-223−23−23230000-222-200000000000023−2300−232300000000000000000000000000000000000000
χ724-4-444000000-4-44000000004-2-4-4422-2−232323−230000-222-2000000000000−23230023−2300000000000000000000000000000000000000
χ734-4-444000000-4-4400000000-2422-2-4-44000023−23−2323-222-20000000023−23−232300000000000000000000000000000000000000000000
χ744-4-444000000-4-4400000000-2422-2-4-440000−232323−23-222-200000000−232323−2300000000000000000000000000000000000000000000
χ754-4-444000000-4-4400000000-2-222-222-223−23−232323−23−23231-1-1100000000−333−3−33-333−33-3000000000000000000000000000000000000
χ764-4-444000000-4-4400000000-2-222-222-223−23−2323−232323−231-1-11000000003−3−33−333-33−3-33000000000000000000000000000000000000
χ774-4-444000000-4-4400000000-2-222-222-2−232323−2323−23−23231-1-1100000000−333−33−33-3−33-33000000000000000000000000000000000000
χ784-4-444000000-4-4400000000-2-222-222-2−232323−23−232323−231-1-11000000003−3−333−3-33−333-3000000000000000000000000000000000000
χ796666-3666666-3-3-3-3-3-3-3-3-3-3-3000000000000000000000000000000000000000022002200-1-1-1-10000-1-1-1-10000000000000000
χ806666-3666666-3-3-3-3-3-3-3-3-3-3-30000000000000000000000000000000000000000-2-200-2-2001111000011110000000000000000
χ816666-366-6-6-6-6-3-3-3333333-3-3000000000000000000000000000000000000000000000000−i3i3−i3i30000−i3i3−i3i30000000000000000
χ826666-366-6-6-6-6-3-3-3333333-3-3000000000000000000000000000000000000000000000000i3−i3i3−i30000i3−i3i3−i30000000000000000
χ836666-3-6-666-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000000−i3i3−i3i30000i3−i3i3−i30000000000000000
χ846666-3-6-666-6-6-3-3-3-3-3-3-33333000000000000000000000000000000000000000000000000i3−i3i3−i30000−i3i3−i3i30000000000000000
χ856666-3-6-6-6-666-3-3-33333-3-33300000000000000000000000000000000000000002200-2-200-1-1-1-1000011110000000000000000
χ866666-3-6-6-6-666-3-3-33333-3-3330000000000000000000000000000000000000000-2-200220011110000-1-1-1-10000000000000000
χ876-66-6-36i−6i6i−6i6-6-333−3i−3i3i3i-33−3i3i00000000000000000000000000000000000000002-2002i−2i00-1-1110000−i−iii0000000000000000
χ886-66-6-36i−6i6i−6i6-6-333−3i−3i3i3i-33−3i3i0000000000000000000000000000000000000000-2200−2i2i0011-1-10000ii−i−i0000000000000000
χ896-66-6-36i−6i−6i6i-66-3333i3i−3i−3i3-3−3i3i000000000000000000000000000000000000000000000000−i3i3i3−i300003−3−330000000000000000
χ906-66-6-36i−6i−6i6i-66-3333i3i−3i−3i3-3−3i3i000000000000000000000000000000000000000000000000i3−i3−i3i30000−333−30000000000000000
χ916-66-6-3−6i6i6i−6i-66-333−3i−3i3i3i3-33i−3i000000000000000000000000000000000000000000000000−i3i3i3−i30000−333−30000000000000000
χ926-66-6-3−6i6i6i−6i-66-333−3i−3i3i3i3-33i−3i000000000000000000000000000000000000000000000000i3−i3−i3i300003−3−330000000000000000
χ936-66-6-3−6i6i−6i6i6-6-3333i3i−3i−3i-333i−3i00000000000000000000000000000000000000002-200−2i2i00-1-1110000ii−i−i0000000000000000
χ946-66-6-3−6i6i−6i6i6-6-3333i3i−3i−3i-333i−3i0000000000000000000000000000000000000000-22002i−2i0011-1-10000−i−iii0000000000000000
χ951212-12-12-60000006-6663−6363−6300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-60000006-66−6363−636300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-600000066-6−6i36i36i3−6i300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-600000066-66i3−6i3−6i36i300000000000000000000000000000000000000000000000000000000000000000000000000000000

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