Finite Group Databasebeta

← Group #13172201

Character table — Group #13172201

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666233366666666666443666666666666666244446612121212121222666121212121212121212121212121212121222444666612121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-11111-1-111-1-111111-1-111-1111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-11-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-11-1111-111111-1-111111-1-1-11-1-1-1-1-1-111-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-11111-1-1-11-1-1-11-1-11111-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-1111111111111111111-11111-1-111-1-111111-1111-111-1-1-1-1111111-11-1-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-1111-11-1-1-11-1-1-1-1-111-1-1-1-11-1-1-11-1-1-1-1-1-111111-11
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111-111
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111111111-1-11-1-1-1-111-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-111-1-1111-1-1-11-1-1111-1-1-1-1-1-11111-11-1-1-11111-1-1-1-11-11
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1111111-1-1-1-1-1-111-1-11-111-1-11111-1-1-111-11-1-111-1-111-1-1-111
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-11-11111-1-111-1-1111-11-1-111-1-1-1-1-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1111111-11-11-1-1-1-111-1-111-1-11-11-1-111-1-1-1-1-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111-1-111-11-1-111-1-1-1-111-111-11-1-111-1-11111-11-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1111-111-1-1-1111111-1-111-11-1-1-11111-1-1111-1-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-111-11111-1-11111-1-111-1-1-11111-1-11111-1-1-1-11
χ17222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1220222200220022-1-1-10-1-1-10220000-1-1-1-1-1-102000-1-1-1-1000000000
χ18222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-12-202-22200-2-200-2-2-1-1-10-11102-20000-1-111110-20001111000000000
χ19222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-220-22-2-2002200-2-211101-1-10-22000011-1-1-1-10-20001111000000000
χ20222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-100-12222-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-200-2-2002211101110-2-2000011111102000-1-1-1-1000000000
χ21222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111220-2-22200220022-1-1-101-110-2-2000011-1-1110-2000-1-111000000000
χ22222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-111112-20-222200-2-200-2-2-1-1-1011-10-2200001111-1-10200011-1-1000000000
χ23222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2202-2-2-2002200-2-21110-1-1102-20000-1-1-1-1110200011-1-1000000000
χ24222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-100-1-2-2-2-21111-1-1-11111-2-2022-2-200-2-200221110-11-10220000-1-111-1-10-2000-1-111000000000
χ2522222-122-1-122222-12-1-1222-1-122-1-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-10220200-1-1-1-122000002022-10-1-1-1-1-100-1-1-1-120002000000-1-100-100
χ2622222-122-1-122222-12-1-1222-1-122-1-1-1-1222-12-1-1-1-1-122-1-1-1-1-1-1-10-220-200-1-111220000020-2-2-101-1-1-1-1001111-2000-20000001100100
χ2722222-122-1-122222-12-1-1222-1-122-1-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-102-2020011-1-1-2-200000-202210-1111100-1-1-1-1-2000-20000001100100
χ2822222-122-1-122222-12-1-1222-1-122-1-1-1-12-2-2-12-1-1-1-1-122-1-1-1-1-1-1-10-2-20-2001111-2-200000-20-2-2101111100111120002000000-1-100-100
χ2922222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-1222-1-211111-2-2-1-1-1111102-20-200-1-1-1-12200000-202-2101-1-11100-1-111-20002000000-1-100100
χ3022222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-1222-1-211111-2-2-1-1-111110-2-20200-1-1112200000-20-2210-1-1-1110011-1-12000-20000001100-100
χ3122222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-2-2-1-211111-2-2-1-1-111110220-20011-1-1-2-200000202-2-10111-1-100-1-1112000-20000001100-100
χ3222222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-2-2-1-211111-2-2-1-1-111110-2202001111-2-20000020-22-10-111-1-10011-1-1-20002000000-1-100100
χ332222-122-122222-1-122-12-122-12-1-1-1-122-122-1-12-1-122-1-1-1-1-1-1-1-1-120220-1-12200-1-1002-1-1-12002-10-1-1-1-1-1-10000002200000-1-100000-10
χ342222-122-122222-1-122-12-122-12-1-1-1-122-122-1-12-1-122-1-1-1-1-1-1-1-1-1-202-20112200-1-100-211-1-200210-1-1-1-111000000-2-200000110000010
χ352222-122-122222-1-122-12-122-12-1-1-1-122-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-120-220-1-1-2-20011002-1-11200-2-101111-1-1000000-2-200000110000010
χ362222-122-122222-1-122-12-122-12-1-1-1-122-1-2-2-1-12-1-122-1-1-1-1-1-1-1-1-1-20-2-2011-2-2001100-2111-200-2101111110000002200000-1-100000-10
χ372222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-122-11-211-2-211-1-1-1111120-2-20-1-12200-1-1002-1-11-200-210-1-11111000000-2200000-1-10000010
χ382222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-122-11-211-2-211-1-1-11111-20-220112200-1-100-2111200-2-10-1-111-1-10000002-2000001100000-10
χ392222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-2-2-11-211-2-211-1-1-11111202-20-1-1-2-20011002-1-1-1-20021011-1-1110000002-2000001100000-10
χ402222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-2-2-11-211-2-211-1-1-11111-2022011-2-2001100-211-12002-1011-1-1-1-1000000-2200000-1-10000010
χ4122-2-2222-22-22-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-2000000000002i−2i002i−2i2-200000000002i−2i00000000000002-20000002i−2i000
χ4222-2-2222-22-22-2-22-2-20222002-22-2-2-22-2-22i−2i2000000002-2-2000000000002i−2i002i−2i-2200000000002i−2i0000000000000-22000000−2i2i000
χ4322-2-2222-22-22-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i2-20000000000−2i2i00000000000002-2000000−2i2i000
χ4422-2-2222-22-22-2-22-2-20222002-22-2-2-22-2-2−2i2i2000000002-2-200000000000−2i2i00−2i2i-220000000000−2i2i0000000000000-220000002i−2i000
χ4544444-2-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-20014-2-2-211-2-21111111040040000-2-2000000000-2-200-20000001111000000000000000000
χ4644444-2-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-20014-2-2-211-2-211111110-400-400002200000000022002000000-1-1-1-1000000000000000000
χ4744444-2-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-2001-4222-1-122111-1-1-1-10400-40000-2-2000000000-2200200000011-1-1000000000000000000
χ4844444-2-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-2001-4222-1-122111-1-1-1-10-40040000220000000002-200-2000000-1-111000000000000000000
χ494444-24-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-21001-24-2-2-2-211111111140040-2-200000000-2110-2000-200000110000000000000000000000
χ504444-24-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-21001-24-2-2-2-2111111111-400-4022000000002-1-102000200000-1-10000000000000000000000
χ514444-24-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-210012-42222-1-1111-1-1-1-1400-40-2-200000000-21102000200000-1-10000000000000000000000
χ524444-24-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-210012-42222-1-1111-1-1-1-1-4004022000000002-1-10-2000-200000110000000000000000000000
χ534444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-2441-2-211-2-2-2-211111110040000-2-200-2-200000-2000-2001111000000000000000000000000
χ544444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-2-4-41-2-211-2-2-2-2111111100-40000220022000002000200-1-1-1-1000000000000000000000000
χ554444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-244122-1-12222111-1-1-1-100-40000-2-200-2-200000200020011-1-1000000000000000000000000
χ564444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-2-4-4122-1-12222111-1-1-1-1004000022002200000-2000-200-1-111000000000000000000000000
χ5744-4-444-2-44-4-2224-4-404-2-20042-22-4-4-22200-200000000-222000000000000000004-40000000000000000000000000-2200000000000
χ5844-4-444-2-44-4-2224-4-404-2-20042-22-4-4-22200-200000000-22200000000000000000-4400000000000000000000000002-200000000000
χ5944-4-44-24-4-224-4-44-420-2-2400-224-422-22-44i−4i-200000000-22200000000000−2i2i004i−4i000000000000−2i2i00000000000000000000000000
χ6044-4-44-24-4-224-4-44-420-2-2400-224-422-22-4−4i4i-200000000-222000000000002i−2i00−4i4i0000000000002i−2i00000000000000000000000000
χ6144-4-4-24424-44-4-4-22-40-24-200-2-4-22224-424i−4i-200000000-222000000000004i−4i00−2i2i000000000000−2i2i00000000000000000000000000
χ6244-4-4-24424-44-4-4-22-40-24-200-2-4-22224-42−4i4i-200000000-22200000000000−4i4i002i−2i0000000000002i−2i00000000000000000000000000
χ6344-4-4-2-242-224-4-4-22201-2-20012-22-1-1-2224i−4i1003-300001-1-133-3-30000000−2i2i00−2i2i000000000000i−i3i−3i000000000000000000000000
χ6444-4-4-2-242-224-4-4-22201-2-20012-22-1-1-2224i−4i100-3300001-1-1-3-3330000000−2i2i00−2i2i000000000000i−i−3i3i000000000000000000000000
χ6544-4-4-2-242-224-4-4-22201-2-20012-22-1-1-222−4i4i1003-300001-1-133-3-300000002i−2i002i−2i000000000000−ii−3i3i000000000000000000000000
χ6644-4-4-2-242-224-4-4-22201-2-20012-22-1-1-222−4i4i100-3300001-1-1-3-33300000002i−2i002i−2i000000000000−ii3i−3i000000000000000000000000
χ674-44-44444-4-4-44-4-4-44044400-4-4-444-4-44-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ684-44-444-24-4-42-22-4-4404-2-200-422-24-42-2200-2000000002-220000000000000000000000000000000000000000000000−2i32i3000000000
χ694-44-444-24-4-42-22-4-4404-2-200-422-24-42-2200-2000000002-2200000000000000000000000000000000000000000000002i3−2i3000000000
χ704-44-44-24422-44-4-4-4-20-2-240022-44-222-2-400-2000000002-2200000000000000000000000000000000000000000000000000−2i32i300000
χ714-44-44-24422-44-4-4-4-20-2-240022-44-222-2-400-2000000002-22000000000000000000000000000000000000000000000000002i3−2i300000
χ724-44-4-244-2-4-4-44-42240-24-2002-42-2-22-44200-2000000002-2200000000000000000000000000000000000000000000000023−230000000
χ734-44-4-244-2-4-4-44-42240-24-2002-42-2-22-44200-2000000002-22000000000000000000000000000000000000000000000000−23230000000
χ744-4-44444-4-44-4-44-44-4044400-44-4-4-44-4-4400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-4-4422-2-44-404-2-2−2i32i3-4-222-4422-200-20000−2i32i3−2i32i322-2−2i32i3−2i32i300000000000000000000000000000000000000000000000000000
χ764-4-4444-2-4-4422-2-44-404-2-22i3−2i3-4-222-4422-200-200002i3−2i32i3−2i322-22i3−2i32i3−2i300000000000000000000000000000000000000000000000000000
χ774-4-444-24-42-2-4-44-4420-2-24002-2-4-42-222400-20000000022-2000000000000023−230000000000000000000023−2300000000000000000000
χ784-4-444-24-42-2-4-44-4420-2-24002-2-4-42-222400-20000000022-20000000000000−232300000000000000000000−232300000000000000000000
χ794-4-444-2-2-42-222-2-4420-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i300000000023−2300000000000000000000−333i−3i000000000000000000
χ804-4-444-2-2-42-222-2-4420-21-2−2i32i321222-2-1-1-20010000i3−i3−2i32i3-1-11i3−i3i3−i3000000000−2323000000000000000000003−3−3i3i000000000000000000
χ814-4-444-2-2-42-222-2-4420-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i300000000023−2300000000000000000000−33−3i3i000000000000000000
χ824-4-444-2-2-42-222-2-4420-21-22i3−2i321222-2-1-1-20010000−i3i32i3−2i3-1-11−i3i3−i3i3000000000−2323000000000000000000003−33i−3i000000000000000000
χ834-4-44-2442-44-4-442-2-40-24-20024222-2-4-4-200-20000000022-2000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ844-4-44-2442-44-4-442-2-40-24-20024222-2-4-4-200-20000000022-20000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ854-4-44-24-22-4422-22-2-40-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i300000−2i32i3000000000i3−i3000000000003-30000000000000000000000
χ864-4-44-24-22-4422-22-2-40-2-21−2i32i32-2-1-12-22210010000−2i32i3i3−i3-1-11i3−i3i3−i3000002i3−2i3000000000−i3i300000000000-330000000000000000000000
χ874-4-44-24-22-4422-22-2-40-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i300000−2i32i3000000000i3−i300000000000-330000000000000000000000
χ884-4-44-24-22-4422-22-2-40-2-212i3−2i32-2-1-12-222100100002i3−2i3−i3i3-1-11−i3i3−i3i3000002i3−2i3000000000−i3i3000000000003-30000000000000000000000
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
χ9188-8-88-4-4-8-44-4448-840-42-400-4-2-44442-24002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-448-8-444-44-80-4-4200-442-244-44-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-44-444-4440222002-22-2-2-22-2-200-1006-60000-111-3-33300000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-444-4440222002-22-2-2-22-2-200-100-660000-11133-3-300000000000000000000000000000000000000000000000000000
χ958-88-88-4-48444-44-8-8-40-42-4004-24-4-44-22400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-4-8-84-444480-4-420044-22-444-4-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-444-88-844-402-4-400-244-42-24-4400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444-4444-4022200-2-2-222-2-22-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-4444-4444-4022200-2-2-222-2-22-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-4-8-884-4402-4-400-2-444-2244-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-44-440222−4i34i3-22-2-2-22-2-2200-100002i3−2i32i3−2i311-1−i3i3−i3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-44-4402224i3−4i3-22-2-2-22-2-2200-10000−2i32i3−2i32i311-1i3−i3i3−i300000000000000000000000000000000000000000000000000000

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