Finite Group Databasebeta

← Group #13172931

Character table — Group #13172931

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222244444444444444466888888888888888812121212121212121212121212181818181818181824242424242424242424242424242424242424243636363636363636363654547272108
order122233366666666623336666666666644366666666666666624444121212121212121222222244666612121212121212121212121212121212246666661212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111-1-1111111-1-1-1-1-1-111111-1-111-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-1-11-1
χ31111111111111111111111111111111111111111111111111-11-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111111-1-111111-1-1-1-1-1-1-111-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-111-1-111-1-11111-1-11111111-1-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-111111-11
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1111-1-1-1-1-1-111-111
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-1-1-111-1-1111111-11-1-1-1-111-1-1-1-111-1-1-11-1-111-1-11111-11-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111-1-111-1-1-1-1-1-111-1-11111-1-11-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11111111111-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-1111-1-111111111-1-1-1-1-1-1-1-11-11-1-1111-1-111-1-1111-11111-1-1-1-1111-1-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-111-1-1-1-11111-1-1-1-11111-11-111-1-1-111-1-111-1-11-11111-1-1-1-1-1-11-11
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-111111111-1-11111-1-111-1-1-1-111-1-111-1-1111111-1-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-111-1-111-1-1-1-111-1-1-1-1-1-111-111-1-1-1111111-1-111-1-1-1-111-1-11111-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-111-1-1-1-11-11111-1-11111-1-111-11-1-111-1-111-1-1-111
χ17222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12220200220022002222002-1-1-1-1-1-10020000-1-1-1-1-1-10000-1-1-1-10000000
χ18222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-220-200-2-2002200-2-2-2-2002-1-1-1-11100-20000-1-11111000011110000000
χ19222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-22-202002200-2-200-2-2-2-200-21111-1-1002000011-1-1-1-1000011110000000
χ20222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-20-200-2-200-2-200222200-211111100-200001111110000-1-1-1-10000000
χ21222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-1111122-20-2002200-2-20022-2-2002-1-1-11-1100-2000011-1-1110000-1-1110000000
χ22222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-111112-2-20200-2-200-2-200-2-222002-1-1-111-100200001111-1-1000011-1-10000000
χ23222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2220-20022002200-2-22200-2111-1-1100-20000-1-1-1-111000011-1-10000000
χ24222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2-220200-2-200220022-2-200-2111-11-10020000-1-111-1-10000-1-1110000000
χ2522222-12-122222-1-122-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-1202202200-1-1-1-122000000-12-1-1200-120-1-1-1-1-1-1000002-1-1000000000-10
χ2622222-12-122222-1-122-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2202200-1-111-2-20000001-211-200-120-1-1-1-11100000-21100000000010
χ2722222-12-122222-1-122-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1202-20-2-20011-1-1-2-2000000-12-1-12001-201111-1-100000-21100000000010
χ2822222-12-122222-1-122-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2-20-2-2001111220000001-211-2001-20111111000002-1-1000000000-10
χ2922222-12-122222-1-12-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-1111120-2-202200-1-111-2-2000000-12-1-1-2001-20-1-1111100000211000000000-10
χ3022222-12-122222-1-12-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-11111-202-202200-1-1-1-1220000001-2112001-20-1-111-1-100000-2-1-100000000010
χ3122222-12-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-1111120-220-2-200111122000000-12-1-1-200-12011-1-11100000-2-1-100000000010
χ3222222-12-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111-20220-2-20011-1-1-2-20000001-211200-12011-1-1-1-100000211000000000-10
χ332222-1222-1-122222-12-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-102022-1-1-1-122000000002200000222-1-1-1-1-1-100-1-1-1-120000000-1-100-100
χ342222-1222-1-122222-12-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10-202-2-1-1112200000000-2-200000-2-22-11-1-1-1-1001111-200000001100100
χ352222-1222-1-122222-12-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-1020-2211-1-1-2-200000000-2-20000022-21-1111100-1-1-1-1-200000001100100
χ362222-1222-1-122222-12-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-20-2-21111-2-2000000002200000-2-2-211111100111120000000-1-100-100
χ372222-1222-1-122222-1-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-11111020-2-2-1-1-1-1220000000022000002-2-211-1-11100-1-111-20000000-1-100100
χ382222-1222-1-122222-1-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-20-22-1-1112200000000-2-200000-22-21-1-1-1110011-1-1200000001100-100
χ392222-1222-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110202-211-1-1-2-200000000-2-2000002-22-1111-1-100-1-111200000001100-100
χ402222-1222-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110-20221111-2-2000000002200000-222-1-111-1-10011-1-1-20000000-1-100100
χ4122-2-222222-22-2-2-2-2-20222002-22-2-2-22-2-22i−2i2000000002-2-20000000002i−2i002i−2i00002-2000000000000002i−2i0000000000002-200002i−2i000
χ4222-2-222222-22-2-2-2-2-20222002-22-2-2-22-2-22i−2i2000000002-2-20000000002i−2i002i−2i0000-22000000000000002i−2i000000000000-220000−2i2i000
χ4322-2-222222-22-2-2-2-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-2000000000−2i2i00−2i2i00002-200000000000000−2i2i0000000000002-20000−2i2i000
χ4422-2-222222-22-2-2-2-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-2000000000−2i2i00−2i2i0000-2200000000000000−2i2i000000000000-2200002i−2i000
χ452-2-22222-2-2-2-22-2-222022200-2-2-222-2-22-200200000000-22-2000000000000000002-2002-22-200000000000000000000002-2002-22-200000
χ462-2-22222-2-2-2-22-2-222022200-2-2-222-2-22-200200000000-22-2000000000000000002-200-22-2200000000000000000000002-200-22-2200000
χ472-2-22222-2-2-2-22-2-222022200-2-2-222-2-22-200200000000-22-200000000000000000-22002-2-220000000000000000000000-22002-2-2200000
χ482-2-22222-2-2-2-22-2-222022200-2-2-222-2-22-200200000000-22-200000000000000000-2200-222-20000000000000000000000-2200-222-200000
χ4944444-2-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-211111111140400000000-2-200000000-2-211-2000000000110000000000000000000
χ5044444-2-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-2111111111-40-400000000220000000022-1-12000000000-1-10000000000000000000
χ5144444-2-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-140-4000000002200000000-2-2112000000000-1-10000000000000000000
χ5244444-2-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-40400000000-2-20000000022-1-1-2000000000110000000000000000000
χ534444-24-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-211111110400400-2-200000000000000000-2-200-20000001111000000000000000
χ544444-24-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-211111110-400-400220000000000000000022002000000-1-1-1-1000000000000000
χ554444-24-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10400-400-2-200000000000000000-2200200000011-1-1000000000000000
χ564444-24-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10-40040022000000000000000002-200-2000000-1-111000000000000000
χ574444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-2441-2-211-2-2-2-2111111100040-2-200-2-200000000000000000-2-201111000000000000000000000
χ584444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-2-4-41-2-211-2-2-2-21111111000-4022002200000000000000000220-1-1-1-1000000000000000000000
χ594444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-244122-1-12222111-1-1-1-1000-40-2-200-2-20000000000000000022011-1-1000000000000000000000
χ604444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-2-4-4122-1-12222111-1-1-1-10004022002200000000000000000-2-20-1-111000000000000000000000
χ6144-4-444-244-4-222-4-4-404-2-20042-22-4-4-22200-200000000-22200000000000000000004-40000000000000000000000000000-22000000000
χ6244-4-444-244-4-222-4-4-404-2-20042-22-4-4-22200-200000000-2220000000000000000000-4400000000000000000000000000002-2000000000
χ6344-4-44-24-24-44-4-422-40-24-200-2-4-22224-424i−4i-200000000-2220000000004i−4i00−2i2i00000000000000000000−2i2i00000000000000000000000
χ6444-4-44-24-24-44-4-422-40-24-200-2-4-22224-42−4i4i-200000000-222000000000−4i4i002i−2i000000000000000000002i−2i00000000000000000000000
χ6544-4-4-2444-224-4-4-4-420-2-2400-224-422-22-44i−4i-200000000-222000000000−2i2i004i−4i00000000000000000000−2i2i00000000000000000000000
χ6644-4-4-2444-224-4-4-4-420-2-2400-224-422-22-4−4i4i-200000000-2220000000002i−2i00−4i4i000000000000000000002i−2i00000000000000000000000
χ6744-4-4-2-24-2-224-4-422201-2-20012-22-1-1-2224i−4i1003-300001-1-133-3-300000−2i2i00−2i2i00000000000000000000i−i3i−3i000000000000000000000
χ6844-4-4-2-24-2-224-4-422201-2-20012-22-1-1-2224i−4i100-3300001-1-1-3-33300000−2i2i00−2i2i00000000000000000000i−i−3i3i000000000000000000000
χ6944-4-4-2-24-2-224-4-422201-2-20012-22-1-1-222−4i4i1003-300001-1-133-3-3000002i−2i002i−2i00000000000000000000−ii−3i3i000000000000000000000
χ7044-4-4-2-24-2-224-4-422201-2-20012-22-1-1-222−4i4i100-3300001-1-1-3-333000002i−2i002i−2i00000000000000000000−ii3i−3i000000000000000000000
χ714-44-4444-4-44-4-444-4-4044400-44-4-4-44-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000000
χ724-44-444-2-4-4422-24-4-404-2-2−2i32i3-4-222-4422-200-20000−2i32i3−2i32i322-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000000
χ734-44-444-2-4-4422-24-4-404-2-22i3−2i3-4-222-4422-200-200002i3−2i32i3−2i322-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000000
χ744-44-44-242-44-4-44-22-40-24-20024222-2-4-4-200-20000000022-2000000000000000−2i32i30000000000000000000000−2i32i30000000000000000000
χ754-44-44-242-44-4-44-22-40-24-20024222-2-4-4-200-20000000022-20000000000000002i3−2i300000000000000000000002i3−2i30000000000000000000
χ764-44-44-2-22-4422-2-22-40-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i300000000000−2i32i300000000003-30000000000i3−i30000000000000000000
χ774-44-44-2-22-4422-2-22-40-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i3000000000002i3−2i30000000000-330000000000−i3i30000000000000000000
χ784-44-44-2-22-4422-2-22-40-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i300000000000−2i32i30000000000-330000000000i3−i30000000000000000000
χ794-44-44-2-22-4422-2-22-40-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i3000000000002i3−2i300000000003-30000000000−i3i30000000000000000000
χ804-44-4-244-42-2-4-444-420-2-24002-2-4-42-222400-20000000022-20000000000023−23000000000000000000000000000023−2300000000000000000
χ814-44-4-244-42-2-4-444-420-2-24002-2-4-42-222400-20000000022-200000000000−23230000000000000000000000000000−232300000000000000000
χ824-44-4-24-2-42-222-24-420-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i3000000023−230000000000000000000000000000−333i−3i000000000000000
χ834-44-4-24-2-42-222-24-420-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i30000000−232300000000000000000000000000003−3−3i3i000000000000000
χ844-44-4-24-2-42-222-24-420-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i3000000023−230000000000000000000000000000−33−3i3i000000000000000
χ854-44-4-24-2-42-222-24-420-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i30000000−232300000000000000000000000000003−33i−3i000000000000000
χ864-4-4444-2-4-4-42-22-44404-2-200-422-24-42-2200-2000000002-220000000000000000000004-40000000000000000000000000000-220000000
χ874-4-4444-2-4-4-42-22-44404-2-200-422-24-42-2200-2000000002-22000000000000000000000-4400000000000000000000000000002-20000000
χ884-4-444-242-4-4-44-42-240-24-2002-42-2-22-44200-2000000002-22000000000000000004-40000000000000000000000000000-2200000000000
χ894-4-444-242-4-4-44-42-240-24-2002-42-2-22-44200-2000000002-2200000000000000000-4400000000000000000000000000002-200000000000
χ904-4-44-244-422-44-4-44-20-2-240022-44-222-2-400-2000000002-22000000000000000000000004-40000000000000000000000000000-2200000
χ914-4-44-244-422-44-4-44-20-2-240022-44-222-2-400-2000000002-2200000000000000000000000-4400000000000000000000000000002-200000
χ928888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ938888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
χ9488-8-88-4-4-48-8-44444-80-4-4200-442-244-44-2002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ9588-8-8-48-48-44-444-8-840-42-400-4-2-44442-24002000000002-2-2000000000000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-4-4-44-4444440222002-22-2-2-22-2-200-1006-60000-111-3-33300000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-4-44-4444440222002-22-2-2-22-2-200-100-660000-11133-3-300000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4844-4-8-88-44402-4-400-2-444-2244-400200000000-2-22000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-444-444-4-4440222−4i34i3-22-2-2-22-2-2200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-444-444-4-44402224i3−4i3-22-2-2-22-2-2200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1018-8-888-4-44-8-84-444-480-4-420044-22-444-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-48-4-8444-44-88-40-42-4004-24-4-44-22400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-48444-88-84-4-402-4-400-244-42-24-4400200000000-22-2000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-44444-444-4-4022200-2-2-222-2-22-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44444-444-4-4022200-2-2-222-2-22-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000000

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