Finite Group Databasebeta

← Group #13172204

Character table — Group #13172204

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666233366666666666443666666666666666244446612121212121222666121212121212121212121212121212121222444666612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-11111-1-111-11111111-1-1-1-11-1-11-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-1-1111-1111111-1-11111-1-11-11-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-11111-1-111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-1-1-11111111111-111-1-1-1-1-1111111-11-1-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11-11-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-111111-1-11-1-1-1-1-111-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111111111-11-1-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111111-1-1-1-1111-1-11-1-11-111-1-1-1-1-1-111-1111-1-1-11111-1-1-1-1-111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1111111-1-1-1-1-111-1-11-1-111-1-11111-1-111-1-11-1-111-1-111-1-11-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-11111-1-111-1-1-11-11-111-111-1-111-1-1111-11-1-111-1-1-1-1-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-11111111-11-11-1-11-1-111-1-111-1-11-11-1-111-1-1-1-1-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-1-1-1-1-1-1-1111-1-111-111-1-111-1-1-1-11111-1-11-1-111-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1-111-111-11-1-1111111-1-1-1111-1-1-11111-1-111-11-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-11-111111-1-11111-1-111-1-1-11111-1-11111-1-1-1-11
χ17222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1220222200002222-1-1-1-1-1-102200000-1-1-1-1-1-102000-1-1-1-1000000000
χ18222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-2220000-2-2-2-2-1-1-1-11102-200000-1-111110-20001111000000000
χ19222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-22-2-2000022-2-21111-1-10-220000011-1-1-1-10-20001111000000000
χ20222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-20000-2-2221111110-2-20000011111102000-1-1-1-1000000000
χ21222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111220-2-22200002222-1-1-11-110-2-20000011-1-1110-2000-1-111000000000
χ22222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-111112-20-22220000-2-2-2-2-1-1-111-10-22000001111-1-10200011-1-1000000000
χ23222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2202-2-2-2000022-2-2111-1-1102-200000-1-1-1-1110200011-1-1000000000
χ24222222-12-1-1-122222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2-2022-2-20000-2-222111-11-102200000-1-111-1-10-2000-1-111000000000
χ2522222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-120220-1-122-1-100002-1-1200-1-102-1-1-1-1-1-10000200200000-1-10000-100
χ2622222-12-12222-122-12-12-122-12-1-1-1-122-122-12-1-1-122-1-1-1-1-1-1-1-1-1-202-201122-1-10000-211-200-1102-1-1-1-1110000-200-200000110000100
χ2722222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-120-220-1-1-2-21100002-1-12001-10-21111-1-10000-200-200000110000100
χ2822222-12-12222-122-12-12-122-12-1-1-1-122-1-2-2-12-1-1-122-1-1-1-1-1-1-1-1-1-20-2-2011-2-2110000-211-200110-21111110000200200000-1-10000-100
χ2922222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-1111120-2-20-1-122-1-100002-1-1-200110-2-1-111110000-200200000-1-10000100
χ3022222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-122-1-2111-2-211-1-1-11111-20-2201122-1-10000-2112001-10-2-1-111-1-10000200-200000110000-100
χ3122222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111202-20-1-1-2-21100002-1-1-200-110211-1-1110000200-200000110000-100
χ3222222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-2-2-1-2111-2-211-1-1-11111-2022011-2-2110000-211200-1-10211-1-1-1-10000-200200000-1-10000100
χ332222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10220200-1-122-1-10000002220-1-1-1-1-1-100-1-1-1-100202000000-1-1000-10
χ342222-1222222-12-1-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10-220-200-1-12211000000-2-2201-1-1-1-1-100111100-20-20000001100010
χ352222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-102-2020011-2-2-1-100000022-20-11111100-1-1-1-100-20-20000001100010
χ362222-1222222-12-1-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-20-20011-2-211000000-2-2-2011111100111100202000000-1-1000-10
χ372222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-1111102-20-200-1-122-1-10000002-2-2011-1-11100-1-11100-202000000-1-100010
χ382222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-2-20200-1-12211000000-22-20-11-1-1110011-1-10020-200000011000-10
χ392222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110220-20011-2-2-1-10000002-2201-111-1-100-1-1110020-200000011000-10
χ402222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110-22020011-2-211000000-2220-1-111-1-10011-1-100-202000000-1-100010
χ4122-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-2000000000002i−2i2i−2i002-200000000002i−2i00000000000002-20000002i−2i000
χ4222-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-2000000000002i−2i2i−2i00-2200000000002i−2i0000000000000-22000000−2i2i000
χ4322-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-200000000000−2i2i−2i2i002-20000000000−2i2i00000000000002-2000000−2i2i000
χ4422-2-222222-2-2-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-200000000000−2i2i−2i2i00-220000000000−2i2i0000000000000-220000002i−2i000
χ4544444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-211111111140040-2-200000000-211-2000-2000000110000000000000000000000
χ4644444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-2111111111-400-4022000000002-1-120002000000-1-10000000000000000000000
χ4744444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1400-40-2-200000000-21120002000000-1-10000000000000000000000
χ4844444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-4004022000000002-1-1-2000-2000000110000000000000000000000
χ494444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-2111111104004000000-2-2000000-2-200-200000001111000000000000000000
χ504444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-2001-24-2-211-2-211111110-400-400000022000000220020000000-1-1-1-1000000000000000000
χ514444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10400-4000000-2-2000000-22002000000011-1-1000000000000000000
χ524444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-20012-422-1-122111-1-1-1-10-4004000000220000002-200-20000000-1-111000000000000000000
χ534444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-2441-2-211-2-2-2-211111110040000-2-2-2-20000000000-200-21111000000000000000000000000
χ544444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-2-4-41-2-211-2-2-2-2111111100-40000222200000000002002-1-1-1-1000000000000000000000000
χ554444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-244122-1-12222111-1-1-1-100-40000-2-2-2-20000000000200211-1-1000000000000000000000000
χ564444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2-4-4122-1-12222111-1-1-1-1004000022220000000000-200-2-1-111000000000000000000000000
χ5744-4-444-24-222-4-44-4-404-2-20042-22-4-4-22200-200000000-222000000000000000004-40000000000000000000000000-2200000000000
χ5844-4-444-24-222-4-44-4-404-2-20042-22-4-4-22200-200000000-22200000000000000000-4400000000000000000000000002-200000000000
χ5944-4-44-24-24-4-4-424-420-24-200-2-4-22224-424i−4i-200000000-222000000000004i−4i−2i2i00000000000000−2i2i00000000000000000000000000
χ6044-4-44-24-24-4-4-424-420-24-200-2-4-22224-42−4i4i-200000000-22200000000000−4i4i2i−2i000000000000002i−2i00000000000000000000000000
χ6144-4-4-24444-4-42-4-22-40-2-2400-224-422-22-44i−4i-200000000-22200000000000−2i2i4i−4i00000000000000−2i2i00000000000000000000000000
χ6244-4-4-24444-4-42-4-22-40-2-2400-224-422-22-4−4i4i-200000000-222000000000002i−2i−4i4i000000000000002i−2i00000000000000000000000000
χ6344-4-4-2-24-24-4-422-22201-2-20012-22-1-1-2224i−4i1003-300001-1-133-3-30000000−2i2i−2i2i00000000000000i−i3i−3i000000000000000000000000
χ6444-4-4-2-24-24-4-422-22201-2-20012-22-1-1-2224i−4i100-3300001-1-1-3-3330000000−2i2i−2i2i00000000000000i−i−3i3i000000000000000000000000
χ6544-4-4-2-24-24-4-422-22201-2-20012-22-1-1-222−4i4i1003-300001-1-133-3-300000002i−2i2i−2i00000000000000−ii−3i3i000000000000000000000000
χ6644-4-4-2-24-24-4-422-22201-2-20012-22-1-1-222−4i4i100-3300001-1-1-3-33300000002i−2i2i−2i00000000000000−ii3i−3i000000000000000000000000
χ674-44-4444-4-44-44-4-4-44044400-4-4-444-4-44-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-42-224-4-4-4404-2-200-422-24-42-2200-2000000002-220000000000000000000000000000000000000000000000−2i32i3000000000
χ694-44-444-2-42-224-4-4-4404-2-200-422-24-42-2200-2000000002-2200000000000000000000000000000000000000000000002i3−2i3000000000
χ704-44-44-242-44-442-4-4-20-24-2002-42-2-22-44200-2000000002-22000000000000000000000000000000000000000000000000−2i32i30000000
χ714-44-44-242-44-442-4-4-20-24-2002-42-2-22-44200-2000000002-220000000000000000000000000000000000000000000000002i3−2i30000000
χ724-44-4-244-4-44-4-2-42240-2-240022-44-222-2-400-2000000002-220000000000000000000000000000000000000000000000000023−2300000
χ734-44-4-244-4-44-4-2-42240-2-240022-44-222-2-400-2000000002-2200000000000000000000000000000000000000000000000000−232300000
χ744-4-44444-4-4-44-44-44-4044400-44-4-4-44-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-422-2-44-44-404-2-2−2i32i3-4-222-4422-200-20000−2i32i3−2i32i322-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ764-4-4444-2-422-2-44-44-404-2-22i3−2i3-4-222-4422-200-200002i3−2i32i3−2i322-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ774-4-444-242-4-44-4-2-4420-24-20024222-2-4-4-200-20000000022-2000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ784-4-444-242-4-44-4-2-4420-24-20024222-2-4-4-200-20000000022-20000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ794-4-444-2-2222-2-4-2-4420-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i300000−2i32i3000000000i3−i3000000000003-30000000000000000000000
χ804-4-444-2-2222-2-4-2-4420-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i3000002i3−2i3000000000−i3i300000000000-330000000000000000000000
χ814-4-444-2-2222-2-4-2-4420-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i300000−2i32i3000000000i3−i300000000000-330000000000000000000000
χ824-4-444-2-2222-2-4-2-4420-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i3000002i3−2i3000000000−i3i3000000000003-30000000000000000000000
χ834-4-44-244-4-4-44242-2-40-2-24002-2-4-42-222400-20000000022-200000000000000023−2300000000000000000023−2300000000000000000000
χ844-4-44-244-4-4-44242-2-40-2-24002-2-4-42-222400-20000000022-2000000000000000−2323000000000000000000−232300000000000000000000
χ854-4-44-24-2-422-2242-2-40-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i30000000000023−23000000000000000000−333i−3i000000000000000000
χ864-4-44-24-2-422-2242-2-40-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i300000000000−23230000000000000000003−3−3i3i000000000000000000
χ874-4-44-24-2-422-2242-2-40-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i30000000000023−23000000000000000000−33−3i3i000000000000000000
χ884-4-44-24-2-422-2242-2-40-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i300000000000−23230000000000000000003−33i−3i000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-422222222200-1-4-4222222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-82224422222222200-144-2-2-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-4-444-848-840-4-4200-442-244-44-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-48-4444-8-44-80-42-400-4-2-44442-24002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-44444-4440222002-22-2-2-22-2-200-1006-60000-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-44444-4440222002-22-2-2-22-2-200-100-660000-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-444-4484-8-8-40-4-420044-22-444-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-84-44-4-84480-42-4004-24-4-44-22400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-484-88-8-4444-402-4-400-244-42-24-4400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-444-44-4444-4022200-2-2-222-2-22-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-444-44-4444-4022200-2-2-222-2-22-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-884-44-4402-4-400-2-444-2244-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-44-44-440222−4i34i3-22-2-2-22-2-2200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-44-44-4402224i3−4i3-22-2-2-22-2-2200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000

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