Finite Group Databasebeta

← Group #13172344

Character table — Group #13172344

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order122233366666666623336666666666636666666666666662244446612121212121266666661212121212121212121212121222244466661212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1111111-1-111111111-1-1-111111-1-1-1-11-1-1-11-1-1-1-1-111-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-111111-1-1111-1-111-1-1-1111111-1-11111-1-1-11-11-1-1-1-1-1-111-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-11-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111-11-1111-1-1-1-11111-111-1-1111111-1-1-1111111-111-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-111-1-1-111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-111-1111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-111111-1-1-11-1-1-1-1-111-1-11-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-1-1-1111111111-11-1-1-1-1-1-1-111-1-1-11-111-111-1-11111-1-11-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-111-1-11-111-1-11111-1-1-11-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-111111-1-111-1-111-1-1-1-1-11111-1-11-111-1-1-1-111-1-1111-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-111-1-11-1-111-1-11-111-1-1-111-1-11111-1-1-1111-1-1-1-1-1-1111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-111-1-111-111-1-111-11-1-1111-1-111-1-111-1-1-1111-1-1-1-1-1-111-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-111-1-1-1-1-111-1-111-1-111111-1-1-1-1111-111-1-1-1-111-1-1111-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-111-1-11111111-1-1-1-11-111-1-11111-1-1-111-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-11-11111111-1-111-11-111-111-1-11111-1-1-11
χ17222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10202220000222202-100-1-1-1-12-1000-1-1-1-1-1-1022000-1-1-1-100000000
χ18222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1020-22-2000022-2-202-100-1-1-11-21000-1-111110-2-2000111100000000
χ19222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-202-220000-2-2220-2100111-12-100011-1-1-1-10-2-2000111100000000
χ20222222-1222-1-1-12222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-20-2-2-20000-2-2-2-20-21001111-21000111111022000-1-1-1-100000000
χ21222222-1222-1-1-1222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110202-2-20000-2-22202-100-1-11-1-2100011-1-11102-2000-1-11100000000
χ22222222-1222-1-1-1222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-11111020-2-220000-2-2-2-202-100-1-1112-10001111-1-10-2200011-1-100000000
χ23222222-1222-1-1-1222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-2022-2000022220-210011-1-1-21000-1-1-1-1110-2200011-1-100000000
χ24222222-1222-1-1-1222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-20-222000022-2-20-210011-112-1000-1-111-1-102-2000-1-11100000000
χ2522222-122-1-12222-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-122202022-1-1-1-100-1-12-1-1-1-120002-1-1-1-100002000200000-1-100-1000
χ2622222-122-1-12222-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-12-220-2022-1-11100-11-2-1-111-20002-1-1110000-2000-20000011001000
χ2722222-122-1-12222-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-22-2020-2-211-1-1001-1211-1-12000-211-1-10000-2000-20000011001000
χ2822222-122-1-12222-1222-1-1222-1-1-1-122-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2-2-20-20-2-211110011-21111-2000-2111100002000200000-1-100-1000
χ2922222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-1111122-20-2022111100-1-12-1-1-1-1-2000-211110000-2000200000-1-1001000
χ3022222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-111112-2-20202211-1-100-11-2-1-1112000-211-1-100002000-2000001100-1000
χ3122222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2220-20-2-2-1-111001-1211-1-1-20002-1-11100002000-2000001100-1000
χ3222222-122-1-12222-12-22-1-1-2-22-1-1-1-122-1-1-1-21-2-21111-1-1-11111-2-22020-2-2-1-1-1-10011-2111120002-1-1-1-10000-2000200000-1-1001000
χ332222-122-122222-12-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202202-1-12200-1-1200-1-10002-12-1-1-100-1-1-1-1000202000000-1-10-100
χ342222-122-122222-12-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202-20-2-1-1220011200-1-1000-21-2-1-1-1001111000-20-2000000110100
χ352222-122-122222-12-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-220211-2-200-1-1-200110002-1211100-1-1-1-1000-20-2000000110100
χ362222-122-122222-12-12-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2-20-211-2-20011-20011000-21-2111001111000202000000-1-10-100
χ372222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-220-2-1-1-2-200-1-1200-1-100021-211100-1-11100020-2000000-1-10100
χ382222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-2-202-1-1-2-20011200-1-1000-2-121110011-1-1000-202000000110-100
χ392222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20220-2112200-1-1-2001100021-2-1-1-100-1-111000-202000000110-100
χ402222-122-122222-12-1-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-202-20211220011-20011000-2-12-1-1-10011-1-100020-2000000-1-10100
χ4144444-2-24-2-2-2-2-24-244-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110400400000-2-2000-2-20011-2000000110000000000000000000000
χ4244444-2-24-2-2-2-2-24-244-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-400-400000220002200-1-12000000-1-10000000000000000000000
χ4344444-2-24-2-2-2-2-24-24-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10400-40000022000-2-200112000000-1-10000000000000000000000
χ4444444-2-24-2-2-2-2-24-24-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-400400000-2-20002200-1-1-2000000110000000000000000000000
χ454444-24-2-244-2-2-2-24-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-21111111000404000000-2-200000000-2-2-2000001111000000000000000000
χ464444-24-2-244-2-2-2-24-241-2-2-2-21-2-2-2-211-2-21-2411-2-2-2-21111111000-40-4000000220000000022200000-1-1-1-1000000000000000000
χ474444-24-2-244-2-2-2-24-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-100040-4000000-2-200000000-2220000011-1-1000000000000000000
χ484444-24-2-244-2-2-2-24-2-41-2-2221-2-2-2-211-2-212-4-1-12222111-1-1-1-1000-40400000022000000002-2-200000-1-111000000000000000000
χ494444-2-24-2-2-2444-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111404000-2-2-2-20000-20011000000-211000000000000000000000000
χ504444-2-24-2-2-2444-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111-40-400022220000200-1-10000002-1-1000000000000000000000000
χ514444-2-24-2-2-2444-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-140-4000-2-2220000-200110000002-1-1000000000000000000000000
χ524444-2-24-2-2-2444-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-1-40400022-2-20000200-1-1000000-211000000000000000000000000
χ5344-4-4444-44-44-4-4-4-44044400-4-4-44-44-44-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2-44-4-222-4-440-24-2002-4-4-22-2242-200000000-22200000000000000000000000000000000000000000000−2i32i30000000000
χ5544-4-444-2-44-4-222-4-440-24-2002-4-4-22-2242-200000000-222000000000000000000000000000000000000000000002i3−2i30000000000
χ5644-4-44-24-4-224-4-4-42404-2-200-422-224-4-22-200000000-222000000000000−2i32i30000000000000000−2i32i3000000000000000000000000
χ5744-4-44-24-4-224-4-4-42404-2-200-422-224-4-22-200000000-2220000000000002i3−2i300000000000000002i3−2i3000000000000000000000000
χ5844-4-4-24424-44-4-42-4-20-2-24002224-4-22-2-4-200000000-2220000000000−2i32i3000000000−2i32i3000000000000000000000000000000000
χ5944-4-4-24424-44-4-42-4-20-2-24002224-4-22-2-4-200000000-22200000000002i3−2i30000000002i3−2i3000000000000000000000000000000000
χ6044-4-4-2-242-224-4-422-20-21-2002-1-1-22-2212100003-3001-1-133-3-3000000−2i32i3−2i32i30000000i3−i30000000i3−i3000000000000000000000000
χ6144-4-4-2-242-224-4-422-20-21-2002-1-1-22-2212100003-3001-1-133-3-30000002i3−2i32i3−2i30000000−i3i30000000−i3i3000000000000000000000000
χ6244-4-4-2-242-224-4-422-20-21-2002-1-1-22-221210000-33001-1-1-3-333000000−2i32i32i3−2i30000000i3−i30000000−i3i3000000000000000000000000
χ6344-4-4-2-242-224-4-422-20-21-2002-1-1-22-221210000-33001-1-1-3-3330000002i3−2i3−2i32i30000000−i3i30000000i3−i3000000000000000000000000
χ644-44-44444-4-4-44-4-44-4044400-44-4-44-44-4-4400000000-44-400000000000000000000000000000000000000000000000000000000
χ654-44-444-24-4-42-22-44-40-24-20024-42-22-2-42-2000000002-220000000000000000000000000000000000000000000000−2i32i300000000
χ664-44-444-24-4-42-22-44-40-24-20024-42-22-2-42-2000000002-2200000000000000000000000000000000000000000000002i3−2i300000000
χ674-44-44-24422-44-4-4-2-404-2-200-4-222-2-4422-2000000002-22000000000000000000000000000000000000000000000000−2i32i3000000
χ684-44-44-24422-44-4-4-2-404-2-200-4-222-2-4422-2000000002-220000000000000000000000000000000000000000000000002i3−2i3000000
χ694-44-4-244-2-4-4-44-42420-2-24002-22-442-22-4-2000000002-220000000000000000000000000000000000000000000000000023−230000
χ704-44-4-244-2-4-4-44-42420-2-24002-22-442-22-4-2000000002-2200000000000000000000000000000000000000000000000000−23230000
χ714-4-44444-4-44-4-444-4-40444004-44-4-4-4-4-44400000000-4-4400000000000000000000000000000000000000000000000000000000
χ724-4-4444-2-4-4422-24-4-40-24-2−2i32i3-2-442222-4-2-200−2i32i300−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ734-4-4444-2-4-4422-24-4-40-24-22i3−2i3-2-442222-4-2-2002i3−2i3002i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ744-4-444-24-42-2-4-4442-404-2-20042-222-4-42-2-20000000022-200000000000000−2i32i30000000000000000−2i32i30000000000000000000000
χ754-4-444-24-42-2-4-4442-404-2-20042-222-4-42-2-20000000022-2000000000000002i3−2i300000000000000002i3−2i30000000000000000000000
χ764-4-444-2-2-42-222-242-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i30000000000−2i32i300000003-30000000i3−i30000000000000000000000
χ774-4-444-2-2-42-222-242-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i300000000002i3−2i30000000-330000000−i3i30000000000000000000000
χ784-4-444-2-2-42-222-242-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i30000000000−2i32i30000000-330000000i3−i30000000000000000000000
χ794-4-444-2-2-42-222-242-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i300000000002i3−2i300000003-30000000−i3i30000000000000000000000
χ804-4-44-2442-44-4-44-2-420-2-2400-22-2-4-42224-20000000022-2000000000000000023−23000000000000000023−2300000000000000000000
χ814-4-44-2442-44-4-44-2-420-2-2400-22-2-4-42224-20000000022-20000000000000000−23230000000000000000−232300000000000000000000
χ824-4-44-24-22-4422-2-2-4201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i300000000000023−230000000000000000−333i−3i000000000000000000
χ834-4-44-24-22-4422-2-2-4201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i3000000000000−232300000000000000003−3−3i3i000000000000000000
χ844-4-44-24-22-4422-2-2-4201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i300000000000023−230000000000000000−33−3i3i000000000000000000
χ854-4-44-24-22-4422-2-2-4201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i3000000000000−232300000000000000003−33i−3i000000000000000000
χ868888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000
χ878888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000
χ8888-8-88-4-4-8-44-444-8480-4-42004442-2-44-4-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-448-8-4444-8-402-4-400-244-442-2-442000000002-2-200000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4-44-44-44444-4022200-2-2-22-22-22-2-100006-600-111-3-3330000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-44-44-44444-4022200-2-2-22-22-22-2-10000-6600-11133-3-30000000000000000000000000000000000000000000000000000
χ928-88-88-4-48444-44-8-4-80-4-42004-44-224-44-2200000000-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-48-4-4-8-84-4448402-4-400-2-444-4-2244200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-48-444-88-84-440-42-40042-24-44-4-24200000000-22-200000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-4-4444-444-44022200-22-2-22-22-2-2-1000000001-11−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-4444-444-44022200-22-2-22-22-2-2-1000000001-113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ978-8-88-4-4844-4-8-88-4440-42-400-4-224444-2-4200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-444-444-4-4440222−4i34i32-22-2-2-2-2-22-1002i3−2i3002i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-444-444-4-44402224i3−4i32-22-2-2-2-2-22-100−2i32i300−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000

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