Finite Group Databasebeta

← Group #13172165

Character table — Group #13172165

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666623336666666666644366666666666666624444661212121212124466612121212121212121212121212121212122244466121212121212446122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1111111111-1-1-1-11-11-1-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-111-1-1111111-1-1-1-1-111111-1-11111-1-11111-11-11-111-1-1-1-1-1-1-1-1-11-1
χ41111111111111111111111111111111111111111111111111-11-1-1-1-1-11111-1-111-1-1-11-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-11
χ51111111111111111111111111111111-1-111111111111111111-111111-1-1-1-11111111-1111-111-1-1-1-1111111-1-1-1-11-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111-1-1-1-1-11-11-111-1-1-1-1-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111111-11-1-1-1-111-1-1-1-1111-11
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
χ91111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-11111111111111-11-1-1-1-1-111-1-1-1-111-1-1-111-1-1111111-1-111-1-1-1
χ101111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111111-1-1-1-1111-1-111-1-1-111-1-1-1-1-1-111-1-1111-1-111-1-111-1-1-111
χ111111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-11-1-1-11111-1-11111-1-111-1-1111-1-1-1-111-1-11-11
χ121111111111111111-1111-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11-1-11111-1-111-1-1-1-1-111-11111-1-111-1-1111-1-11-1-1-1-1-111-1-11111-1
χ131111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-11-111-1-1-1-1111111111-1-11-1-1-1-111-1-111-1-11-1-11-1-1-1-1-111-1-1-1-1111
χ141111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-1-1-1-1-11111-1111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1
χ151111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1-111-1-1111-1-1111111-1-1-1-1111-1-111-1-11111-11-1
χ161111111111111111-1111-1-1111111111-1-11-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1-1-11-111111-1-11111-1-111-111-1-1111111-1-1-1-1-1-11
χ17222222-1-12222-1-12222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-122200-1-1-1-12200002-1-12000-1-12-1-1-1-1-1-100002020000-1-1000000-100
χ18222222-1-12222-1-12222-1-1222-1-1-122-1-1-122-12-122-1-1-1-1-1-1-1-1-1-1-1-22-20011-1-1220000-2112000-11-2-1-1-1-1110000-20-2000011000000100
χ19222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-12-2200-1-111-2-200002-1-1-20001-121111-1-10000-20-2000011000000100
χ20222222-1-12222-1-12222-1-1222-1-1-122-1-1-1-2-2-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2001111-2-20000-211-200011-211111100002020000-1-1000000-100
χ21222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-111112-2-200-1-1-1-12200002-1-1-200011-2-1-111110000-2020000-1-1000000100
χ22222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-122-1-21-2-21111-1-1-11111-2-220011-1-1220000-211-20001-12-1-111-1-1000020-2000011000000-100
χ23222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-1111122-200-1-111-2-200002-1-12000-11-211-1-111000020-2000011000000-100
χ24222222-1-12222-1-122-22-1-1-2-22-1-1-122-1-1-1-2-2-1-21-2-21111-1-1-11111-222001111-2-20000-2112000-1-1211-1-1-1-10000-2020000-1-1000000100
χ2522222-12222-1-122-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1020220022-1-1-1-100000-122-1200-1-1-1-100-1-1-1-102020-1-1000000000-10
χ2622222-12222-1-122-122-1-1222-1-122-1-1-1-1222-1-12-1-1-1-122-1-1-1-1-1-1-1020-2-20022-1-11100000-1-2-21200-1-1-1-10011110-20-201100000000010
χ2722222-12222-1-122-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-202200-2-211-1-100000122-1-200111100-1-1-1-10-20-201100000000010
χ2822222-12222-1-122-122-1-1222-1-122-1-1-1-12-2-2-1-12-1-1-1-122-1-1-1-1-1-1-10-20-2-200-2-21111000001-2-21-200111100111102020-1-1000000000-10
χ2922222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-202-20022-1-1-1-10000012-21-200-1-11100-1-111020-20-1-100000000010
χ3022222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-1222-11-21111-2-2-1-1-111110-20-220022-1-111000001-22-1-200-1-1110011-1-10-202011000000000-10
χ3122222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-111110202-200-2-211-1-100000-12-2120011-1-100-1-1110-202011000000000-10
χ3222222-12222-1-122-12-2-1-12-2-2-1-122-1-1-1-12-2-2-11-21111-2-2-1-1-11111020-2200-2-2111100000-1-22-120011-1-10011-1-1020-20-1-100000000010
χ332222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1202222200002222-1-1-10-1-1202-10000-1-1-1-1-1-1000020000-1-1-1-100000
χ342222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1202-2-2220000-2-2-2-2-1-1-1011-202-10000-1-111110000-20000111100000
χ352222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1-20-222-2-2000022-2-21110-1-120-21000011-1-1-1-10000-20000111100000
χ362222-1222-1-122222-12-12-1-1-1-12-1-1-1-122-100-122-1-122-1-1-1-1-1-1-1-1-1-20-2-2-2-2-20000-2-222111011-20-210000111111000020000-1-1-1-100000
χ372222-1222-1-122222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-1111120-22-22200002222-1-1-10-11-20-21000011-1-1110000-20000-1-11100000
χ382222-1222-1-122222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-1111120-2-22220000-2-2-2-2-1-1-101-120-2100001111-1-100002000011-1-100000
χ392222-1222-1-122222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-11111-2022-2-2-2000022-2-21110-11-202-10000-1-1-1-11100002000011-1-100000
χ402222-1222-1-122222-1-2-12-111-12-1-1-1-122-100-1-2-211-2-211-1-1-11111-202-22-2-20000-2-22211101-1202-10000-1-111-1-10000-20000-1-11100000
χ412-2-2222222-22-2-2-2-2-2022200-222-22-2-2-2-22i−2i2000000002-2-2000000000002i−2i2i−2i002i−2i00000000002i−2i000000000000000002i−2i002-2000
χ422-2-2222222-22-2-2-2-2-2022200-222-22-2-2-2-22i−2i2000000002-2-2000000000002i−2i2i−2i00−2i2i00000000002i−2i00000000000000000−2i2i00-22000
χ432-2-2222222-22-2-2-2-2-2022200-222-22-2-2-2-2−2i2i2000000002-2-200000000000−2i2i−2i2i002i−2i0000000000−2i2i000000000000000002i−2i00-22000
χ442-2-2222222-22-2-2-2-2-2022200-222-22-2-2-2-2−2i2i2000000002-2-200000000000−2i2i−2i2i00−2i2i0000000000−2i2i00000000000000000−2i2i002-2000
χ4544444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-2441-2-2-2-211-2-211111110400000-2-2-2-20000000-2000-2001111000000000000000000000000
χ4644444-2-2-244-2-2-2-2-244-21-244-21-2-2-2-211-2-4-41-2-2-2-211-2-211111110-400000222200000002000200-1-1-1-1000000000000000000000000
χ4744444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-24412222-1-122111-1-1-1-10-400000-2-2-2-20000000200020011-1-1000000000000000000000000
χ4844444-2-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-2-4-412222-1-122111-1-1-1-1040000022220000000-2000-200-1-111000000000000000000000000
χ494444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-211111111140400-2-200000000-21100000-2-20000110000000000000000000000
χ504444-24-2-2-2-244-2-24-24-2-21-2-2-2-211-2-2-2-210014-2-2-2-2-2111111111-40-40022000000002-1-100000220000-1-10000000000000000000000
χ514444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-140-400-2-200000000-21100000220000-1-10000000000000000000000
χ524444-24-2-2-2-244-2-24-2-4-2-2122-2-211-2-2-2-21001-422222-1-1111-1-1-1-1-4040022000000002-1-100000-2-20000110000000000000000000000
χ534444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-2111111100044000000-2-2000000-2-2-20000000001111000000000000000000
χ544444-2-244-2-2-2-244-2-241-2-2-2-21-2-2-211-2-2-2001-2411-2-2-2-21111111000-4-400000022000000222000000000-1-1-1-1000000000000000000
χ554444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-10004-4000000-2-2000000-22200000000011-1-1000000000000000000
χ564444-2-244-2-2-2-244-2-2-41-2-2221-2-2-211-2-2-20012-4-1-12222111-1-1-1-1000-44000000220000002-2-2000000000-1-111000000000000000000
χ5744-4-4444-4-44-4-4-444-4044400-4-4-44-444-4-400400000000-44-4000000000000000000000000000000000000000000000000000000000
χ5844-4-444-22-44-4-42-24-404-2-200-422-2-44-22200-2000000002-220000000000000000000000000000000000000000000000−2i32i3000000000
χ5944-4-444-22-44-4-42-24-404-2-200-422-2-44-22200-2000000002-2200000000000000000000000000000000000000000000002i3−2i3000000000
χ6044-4-44-24-4-4422-44-2-40-2-240022-442-2-22-400-2000000002-2200000000000000000000000000000000000000000000−2i32i300000000000
χ6144-4-44-24-4-4422-44-2-40-2-240022-442-2-22-400-2000000002-22000000000000000000000000000000000000000000002i3−2i300000000000
χ6244-4-4-244-42-2-4-4-44420-24-2002-42-22-24-4200-2000000002-220000000000000000000000000000000000000000000000000023−2300000
χ6344-4-4-244-42-2-4-4-44420-24-2002-42-22-24-4200-2000000002-2200000000000000000000000000000000000000000000000000−232300000
χ644-44-4444-4-4-4-444-4-440444004-4-4-4-4-4-44400400000000-4-44000000000000000000000000000000000000000000000000000000000
χ654-44-444-22-4-4-44-22-4404-2-2004222-4-42-2-200-20000000022-2000000000−2i32i3000000000−2i32i300000000000000000000000000000000000
χ664-44-444-22-4-4-44-22-4404-2-2004222-4-42-2-200-20000000022-20000000002i3−2i30000000002i3−2i300000000000000000000000000000000000
χ674-44-44-24-4-4-42-24-4240-2-2400-22-4-4222-2400-20000000022-200000000000000023−2300000000000000000023−2300000000000000000000
χ684-44-44-24-4-4-42-24-4240-2-2400-22-4-4222-2400-20000000022-2000000000000000−2323000000000000000000−232300000000000000000000
χ694-44-4-244-422-444-4-4-20-24-2−2i32i3-2-42222-44-200-200−2i32i300−2i32i322-2−2i3−2i32i32i300000000000000000000000000000000000000000000000000000
χ704-44-4-244-422-444-4-4-20-24-22i3−2i3-2-42222-44-200-2002i3−2i3002i3−2i322-22i32i3−2i3−2i300000000000000000000000000000000000000000000000000000
χ714-44-4-24-2222-44-22-4-20-2-21−2i32i3-22-1-1222-2100100−2i32i300i3−i3-1-11i3i3−i3−i300000−2i32i3000000000i3−i3000000000003-30000000000000000000000
χ724-44-4-24-2222-44-22-4-20-2-21−2i32i3-22-1-1222-2100100−2i32i300i3−i3-1-11i3i3−i3−i3000002i3−2i3000000000−i3i300000000000-330000000000000000000000
χ734-44-4-24-2222-44-22-4-20-2-212i3−2i3-22-1-1222-21001002i3−2i300−i3i3-1-11−i3−i3i3i300000−2i32i3000000000i3−i300000000000-330000000000000000000000
χ744-44-4-24-2222-44-22-4-20-2-212i3−2i3-22-1-1222-21001002i3−2i300−i3i3-1-11−i3−i3i3i3000002i3−2i3000000000−i3i3000000000003-30000000000000000000000
χ754-44-4-2-24-4222-24-42-201-2-2−2i32i31222-1-12-2-200100i3−i300−2i32i3-1-11i3i3−i3−i30000000000023−23000000000000000000−333i−3i000000000000000000
χ764-44-4-2-24-4222-24-42-201-2-2−2i32i31222-1-12-2-200100i3−i300−2i32i3-1-11i3i3−i3−i300000000000−23230000000000000000003−3−3i3i000000000000000000
χ774-44-4-2-24-4222-24-42-201-2-22i3−2i31222-1-12-2-200100−i3i3002i3−2i3-1-11−i3−i3i3i30000000000023−23000000000000000000−33−3i3i000000000000000000
χ784-44-4-2-24-4222-24-42-201-2-22i3−2i31222-1-12-2-200100−i3i3002i3−2i3-1-11−i3−i3i3i300000000000−23230000000000000000003−33i−3i000000000000000000
χ794-4-4444-2-24-44-422-4-404-2-200-4-2-224-42224i−4i-200000000-22200000000000−2i2i4i−4i00000000000000−2i2i00000000000000000000000000
χ804-4-4444-2-24-44-422-4-404-2-200-4-2-224-4222−4i4i-200000000-222000000000002i−2i−4i4i000000000000002i−2i00000000000000000000000000
χ814-4-444-2444-4-22-4-42-40-2-24002-24-4-2222-44i−4i-200000000-222000000000004i−4i−2i2i00000000000000−2i2i00000000000000000000000000
χ824-4-444-2444-4-22-4-42-40-2-24002-24-4-2222-4−4i4i-200000000-22200000000000−4i4i2i−2i000000000000002i−2i00000000000000000000000000
χ834-4-444-2-2-24-4-22222-40-21-20021-22-22-1-124i−4i100003-3001-1-13-33-30000000−2i2i−2i2i00000000000000i−i3i−3i000000000000000000000000
χ844-4-444-2-2-24-4-22222-40-21-20021-22-22-1-124i−4i10000-33001-1-1-33-330000000−2i2i−2i2i00000000000000i−i−3i3i000000000000000000000000
χ854-4-444-2-2-24-4-22222-40-21-20021-22-22-1-12−4i4i100003-3001-1-13-33-300000002i−2i2i−2i00000000000000−ii−3i3i000000000000000000000000
χ864-4-444-2-2-24-4-22222-40-21-20021-22-22-1-12−4i4i10000-33001-1-1-33-3300000002i−2i2i−2i00000000000000−ii3i−3i000000000000000000000000
χ874-4-44-2444-224-4-4-4-420-24-20024-22-22-4-4200-200000000-222000000000000000004i−4i00000000000000000000000000000−2i2i0000000
χ884-4-44-2444-224-4-4-4-420-24-20024-22-22-4-4200-200000000-22200000000000000000−4i4i000000000000000000000000000002i−2i0000000
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
χ9188-8-88-4-44-88444-4-4-80-42-4004-24-44-42-2400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-444-4-8-84-4840-4-420044-224-4-44-200200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-48-84-444-88-4402-4-400-244-4-22-44400200000000-22-2000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-4444-4-44022200-2-2-22-222-2-200-1000000001-11−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-444-4444-4-44022200-2-2-22-222-2-200-1000000001-113i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ968-88-88-4-44-8-84-4-44480-42-400-4-24444-22-400200000000-2-22000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-4-444-40222−4i34i32-2-2-2-2-2-22200-1002i3−2i3002i3−2i311-1−i3−i3i3i300000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-4-444-402224i3−4i32-2-2-2-2-2-22200-100−2i32i300−2i32i311-1i3i3−i3−i300000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-4-448-844-840-4-42004-42-2-4444-2002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-488-44-44-8-84402-4-400-2-4-442-2444002000000002-2-2000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-4-44-444444022200-222-22-2-2-2-200-100006-600-111-33-3300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-4-44-444444022200-222-22-2-2-2-200-10000-6600-1113-33-300000000000000000000000000000000000000000000000000000

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