Finite Group Databasebeta

← Group #13172175

Character table — Group #13172175

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666623336666666666644366666666666666624444661212121212124466612121212121212121212121212121212124444412121212121212122212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-111-1-11111-1-11111-1-11-111111111-1-1-1-11-1-11-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-11-1-1111111-1-1-1-1-111111-1-11111-1-11111-11-1-1111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1111111-1-1-11-1-11-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-111111111111111111-11111111-1-1-1-111111-111-1111-1-1-1-1111111-1-11-1-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1-1111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111111-1-11-1-1-111-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11111111111111-11-1-1-1-1-111-1-1-1-111-1-11-1-1-11111111-1-111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111-1-11111-1-1111-1-11-11-1-111-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-111111-1-1-1-111-1-11-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-11-111111-1-111-1-111-11-11-1-1-1-1-111-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1111-1-11111-1-1-1-11111111-11-1-1-1-1-111-1-111-1-1-11-11-1-1-1-1-111-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-111-1-111111-1-1-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-111-1-1-1-1-1-1-1-1-111-11-111-1-1111111-1-1111-1-1-1-111-1-11111-11-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-1-1-1-1-111-1-1-11-111111-1-11111-1-1111-1-1-11111111-1-1-1-1-1-11
χ17222222-122-12-122-1222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-122020-1-10022-1-1002-1-1-10020-12-1-1-1-1-1-100002002000-1-1000000-100
χ18222222-122-12-122-1222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-1-220-20110022-1-100-211-100201-2-1-1-1-1110000-200-200011000000100
χ19222222-122-12-122-1222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-12-2020-1-100-2-211002-1-1100-20-121111-1-10000-200-200011000000100
χ20222222-122-12-122-1222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2-20-201100-2-21100-211100-201-211111100002002000-1-1000000-100
χ21222222-122-12-122-12-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-111112-20-20-1-10022-1-1002-1-1100-201-2-1-111110000200-2000-1-1000000100
χ22222222-122-12-122-12-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-11111-2-2020110022-1-100-211100-20-12-1-111-1-10000-200200011000000-100
χ23222222-122-12-122-12-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-11111220-20-1-100-2-211002-1-1-100201-211-1-1110000-200200011000000-100
χ24222222-122-12-122-12-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-11111-220201100-2-21100-211-10020-1211-1-1-1-10000200-2000-1-1000000100
χ2522222-12-1-1222222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1202222222000022-1-1-10-1-1022-10000-1-1-1-1-1-1002000000-1-1-1-100000
χ2622222-12-1-1222222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-120-22-222-2-20000-2-2-1-1-10110-22-10000-1-1111100-2000000111100000
χ2722222-12-1-1222222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1-202-22-2-2220000-2-21110-1-102-21000011-1-1-1-100-2000000111100000
χ2822222-12-1-1222222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1-20-2-2-2-2-2-2-20000221110110-2-210000111111002000000-1-1-1-100000
χ2922222-12-1-1222222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-11111202-2-22222000022-1-1-10-110-2-21000011-1-11100-2000000-1-11100000
χ3022222-12-1-1222222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-1111120-2-2222-2-20000-2-2-1-1-101-102-2100001111-1-100200000011-1-100000
χ3122222-12-1-1222222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-11111-2022-2-2-2220000-2-21110-110-22-10000-1-1-1-11100200000011-1-100000
χ3222222-12-1-1222222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-11111-20-222-2-2-2-200002211101-1022-10000-1-111-1-100-2000000-1-11100000
χ332222-122222-12-1-1222-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-10220200-1-1-1-12200000222-1-100-1-1-1-100-1-1-1-102002-1-1000000000-10
χ342222-122222-12-1-1222-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-102-20-20011-1-122000002-2-2-1100-1-1-1-10011110-200-21100000000010
χ352222-122222-12-1-1222-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-220200-1-111-2-200000-2221-100111100-1-1-1-10-200-21100000000010
χ362222-122222-12-1-1222-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-2-20-2001111-2-200000-2-2-21100111100111102002-1-1000000000-10
χ372222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-220-200-1-1-1-12200000-22-21100-1-11100-1-1110-2002-1-100000000010
χ382222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-2-2020011-1-12200000-2-221-100-1-1110011-1-10200-211000000000-10
χ392222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110220-200-1-111-2-20000022-2-110011-1-100-1-1110200-211000000000-10
χ402222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-1111102-202001111-2-2000002-22-1-10011-1-10011-1-10-2002-1-100000000010
χ412-2-222222-2-2-222-2-2-2022200-222-22-2-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i2i−2i00000000002i−2i000000000000000002i−2i002-2000
χ422-2-222222-2-2-222-2-2-2022200-222-22-2-2-2-22i−2i2000000002-2-200000000000002i−2i2i−2i−2i2i00000000002i−2i00000000000000000−2i2i00-22000
χ432-2-222222-2-2-222-2-2-2022200-222-22-2-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i2i−2i0000000000−2i2i000000000000000002i−2i00-22000
χ442-2-222222-2-2-222-2-2-2022200-222-22-2-2-2-2−2i2i2000000002-2-20000000000000−2i2i−2i2i−2i2i0000000000−2i2i00000000000000000−2i2i002-2000
χ4544444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-211111111140040-2-200000000-21100000-2-20000110000000000000000000000
χ4644444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-2111111111-400-4022000000002-1-100000220000-1-10000000000000000000000
χ4744444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1400-40-2-200000000-21100000220000-1-10000000000000000000000
χ4844444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-4004022000000002-1-100000-2-20000110000000000000000000000
χ494444-24-244-2-2-2-2-2-244-21-244-21-2-2-2-211-2441-2-2-2-211-2-21111111040000000-2-2-2-200000-200-20001111000000000000000000000000
χ504444-24-244-2-2-2-2-2-244-21-244-21-2-2-2-211-2-4-41-2-2-2-211-2-211111110-400000002222000002002000-1-1-1-1000000000000000000000000
χ514444-24-244-2-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-24412222-1-122111-1-1-1-10-40000000-2-2-2-200000200200011-1-1000000000000000000000000
χ524444-24-244-2-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2-4-412222-1-122111-1-1-1-1040000000222200000-200-2000-1-111000000000000000000000000
χ534444-2-24-2-24-24-2-24-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-211111110040400-2-20000000000-2-20-2000000001111000000000000000000
χ544444-2-24-2-24-24-2-24-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-2111111100-40-400220000000000220200000000-1-1-1-1000000000000000000
χ554444-2-24-2-24-24-2-24-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-10040-400-2-20000000000-22020000000011-1-1000000000000000000
χ564444-2-24-2-24-24-2-24-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-100-404002200000000002-20-200000000-1-111000000000000000000
χ5744-4-4444-4444-4-4-4-4-4044400-4-4-44-444-4-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-44-242-4-42-404-2-200-422-2-44-22200-2000000002-22000000000000000000000000000000000000000000000023−23000000000
χ5944-4-444-2-44-242-4-42-404-2-200-422-2-44-22200-2000000002-220000000000000000000000000000000000000000000000−2323000000000
χ6044-4-44-242-244-4-4-4-420-24-2002-42-22-24-4200-2000000002-220000000000000000000000000000000000000000000000000023−2300000
χ6144-4-44-242-244-4-4-4-420-24-2002-42-22-24-4200-2000000002-2200000000000000000000000000000000000000000000000000−232300000
χ6244-4-4-244-444-2-422-4-40-2-240022-442-2-22-400-2000000002-220000000000000000000000000000000000000000000023−2300000000000
χ6344-4-4-244-444-2-422-4-40-2-240022-442-2-22-400-2000000002-2200000000000000000000000000000000000000000000−232300000000000
χ644-44-4444-4-4-4-4-4-44440444004-4-4-4-4-4-44400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ654-44-444-2-4-42-42-44-2404-2-2004222-4-42-2-200-20000000022-2000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ664-44-444-2-4-42-42-44-2404-2-2004222-4-42-2-200-20000000022-20000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ674-44-44-2422-4-4-4-444-20-24-2−2i32i3-2-42222-44-200-200−2i32i300−2i32i322-2−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ684-44-44-2422-4-4-4-444-20-24-22i3−2i3-2-42222-44-200-2002i3−2i3002i3−2i322-22i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ694-44-44-2-2222-42-44-2-20-2-21−2i32i3-22-1-1222-2100100−2i32i300i3−i3-1-11i3i3−i3−i300000−2i32i3000000000i3−i3000000000003-30000000000000000000000
χ704-44-44-2-2222-42-44-2-20-2-21−2i32i3-22-1-1222-2100100−2i32i300i3−i3-1-11i3i3−i3−i3000002i3−2i3000000000−i3i300000000000-330000000000000000000000
χ714-44-44-2-2222-42-44-2-20-2-212i3−2i3-22-1-1222-21001002i3−2i300−i3i3-1-11−i3−i3i3i300000−2i32i3000000000i3−i300000000000-330000000000000000000000
χ724-44-44-2-2222-42-44-2-20-2-212i3−2i3-22-1-1222-21001002i3−2i300−i3i3-1-11−i3−i3i3i3000002i3−2i3000000000−i3i3000000000003-30000000000000000000000
χ734-44-4-244-4-4-42-42-2440-2-2400-22-4-4222-2400-20000000022-20000000000023−23000000000000000000000023−2300000000000000000000
χ744-44-4-244-4-4-42-42-2440-2-2400-22-4-4222-2400-20000000022-200000000000−23230000000000000000000000−232300000000000000000000
χ754-44-4-2-2422-42-42-24-201-2-2−2i32i31222-1-12-2-200100i3−i300−2i32i3-1-11i3i3−i3−i3000000023−230000000000000000000000−333i−3i000000000000000000
χ764-44-4-2-2422-42-42-24-201-2-2−2i32i31222-1-12-2-200100i3−i300−2i32i3-1-11i3i3−i3−i30000000−232300000000000000000000003−3−3i3i000000000000000000
χ774-44-4-2-2422-42-42-24-201-2-22i3−2i31222-1-12-2-200100−i3i3002i3−2i3-1-11−i3−i3i3i3000000023−230000000000000000000000−33−3i3i000000000000000000
χ784-44-4-2-2422-42-42-24-201-2-22i3−2i31222-1-12-2-200100−i3i3002i3−2i3-1-11−i3−i3i3i30000000−232300000000000000000000003−33i−3i000000000000000000
χ794-4-4444-24-42-4-24-42-404-2-200-4-2-224-42224i−4i-200000000-22200000000000004i−4i−2i2i000000000000−2i2i00000000000000000000000000
χ804-4-4444-24-42-4-24-42-404-2-200-4-2-224-4222−4i4i-200000000-2220000000000000−4i4i2i−2i0000000000002i−2i00000000000000000000000000
χ814-4-444-24-22-4-444-4-420-24-20024-22-22-4-4200-200000000-222000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ824-4-444-24-22-4-444-4-420-24-20024-22-22-4-4200-200000000-22200000000000000000−4i4i000000000000000000000000000002i−2i0000000
χ834-4-44-2444-4-424-22-4-40-2-24002-24-4-2222-44i−4i-200000000-2220000000000000−2i2i4i−4i000000000000−2i2i00000000000000000000000000
χ844-4-44-2444-4-424-22-4-40-2-24002-24-4-2222-4−4i4i-200000000-22200000000000002i−2i−4i4i0000000000002i−2i00000000000000000000000000
χ854-4-44-24-24-422-2-222-40-21-20021-22-22-1-124i−4i100003-3001-1-13-33-3000000000−2i2i−2i2i000000000000i−i3i−3i000000000000000000000000
χ864-4-44-24-24-422-2-222-40-21-20021-22-22-1-124i−4i10000-33001-1-1-33-33000000000−2i2i−2i2i000000000000i−i−3i3i000000000000000000000000
χ874-4-44-24-24-422-2-222-40-21-20021-22-22-1-12−4i4i100003-3001-1-13-33-30000000002i−2i2i−2i000000000000−ii−3i3i000000000000000000000000
χ884-4-44-24-24-422-2-222-40-21-20021-22-22-1-12−4i4i10000-33001-1-1-33-330000000002i−2i2i−2i000000000000−ii3i−3i000000000000000000000000
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
χ9188-8-88-4-44-4-484-8-8440-4-420044-224-4-44-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-88-4-44444-80-42-4004-24-44-42-2400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-484-48-4-844-8402-4-400-244-4-22-44400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-4-444444022200-2-2-22-222-2-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-4-4-444444022200-2-2-22-222-2-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-8-84444-4-480-42-400-4-24444-22-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444444-4-4-40222−4i34i32-2-2-2-2-2-22200-1002i3−2i3002i3−2i311-1−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444444-4-4-402224i3−4i32-2-2-2-2-2-22200-100−2i32i300−2i32i311-1i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-444-8-48-8440-4-42004-42-2-4444-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-44-848-44-8402-4-400-2-4-442-2444002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4444-4-4444022200-222-22-2-2-2-200-100006-600-111-33-3300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4444-4-4444022200-222-22-2-2-2-200-10000-6600-1113-33-300000000000000000000000000000000000000000000000000000

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