Finite Group Databasebeta

← Group #13172341

Character table — Group #13172341

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order12223336666666662333666666666663666666666666666224444661212121212126666666121212121212121212121212122224446666661212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-11111-1-11111111111-1-11-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11111111-1-1-11-111-1-1-1111111-1-111111-1-1-1-1111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-1-11-111-1-1-1-1-11-111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111-11-1111-1-1-1-111111-11-1-111111-11-1-1111111-111-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-11-1-11-1-1-1-1-1-1-1111-11-1-1111-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11-1-1-1-11111-1-1-111-1-1-1-1-1-1-1111-111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111-1-111-1-11111111-11-1-1-1-1-1-1-111-1-1-11-11-11-1-111-1-1-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1-1-11111111-1-11-11-1-1-1-1-1-1111-111-1-111-1-111-1-11-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-11111-11-111-1-111-1-1-1-1-11111-1-1-1-11-111-1-1-1-11111-11-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-111-11-111-1-11-11-11-1-111-1-11111-1-11-11111-1-111-1-11-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-11-11-1-111-11-11-111-1-111-1-111-1-11-11111-1-111-1-1-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-111-1-1-1-11-11-1-111-1-111111-1-1-1-111-1-11-111-1-1-1-11111-111-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1111111-1-1-1-1-1-1-111-11-1111111-1-11-111-1-111-1-111-1-11-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-111-1-111-1-111-1-1-1-1-1-1-11-11111111-1-111-11-11-11-1-111-1-1-1-111-11
χ17222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10202220000222220-100-1-1-1-1-10200-1-1-1-1-1-102200000-1-1-1-1000000
χ18222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1020-22-20000-2-22220-100-1-1-1110-200-1-111110-2-2000001111000000
χ19222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-202-22000022-2-2-20100111-1-1020011-1-1-1-10-2-2000001111000000
χ20222222-122-1-1-122222-12-1-1-1-122-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-10-20-2-2-20000-2-2-2-2-20100111110-20011111102200000-1-1-1-1000000
χ21222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110202-2-2000022-2-220-100-1-11-110-20011-1-11102-200000-1-111000000
χ22222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-11111020-2-220000-2-2-2-220-100-1-111-102001111-1-10-220000011-1-1000000
χ23222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-2022-200002222-2010011-1-110-200-1-1-1-1110-220000011-1-1000000
χ24222222-122-1-1-12222-2-12-111-122-1-1-1-12-1-1-2-211-2-211-1-1-111110-20-2220000-2-222-2010011-11-10200-1-111-1-102-200000-1-111000000
χ2522222-122-1222-122-12-1-1222-1-1-122-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-120220222-1-1-1-1000-10-1-1000222-1-1-100-1-1-1-1200002-1-10000000-100
χ2622222-122-1222-122-12-1-1222-1-1-122-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-1202-20-222-1-111000-10-1-1000-2-221-1-1001111-20000-2110000000100
χ2722222-122-1222-122-12-1-1222-1-1-122-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-1-20-2202-2-211-1-1000101100022-2-11100-1-1-1-1-20000-2110000000100
χ2822222-122-1222-122-12-1-1222-1-1-122-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-1-20-2-20-2-2-211110001011000-2-2-2111001111200002-1-10000000-100
χ2922222-122-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-1-211111-2-2-1-1-1111120-220-22211-1-1000-10-1-10002-2-211100-1-111-200002110000000-100
χ3022222-122-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-1-211111-2-2-1-1-1111120-2-202221111000-10-1-1000-22-2-1110011-1-120000-2-1-10000000100
χ3122222-122-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-1-211111-2-2-1-1-11111-20220-2-2-2-1-1-1-100010110002-221-1-100-1-11120000-2-1-10000000100
χ3222222-122-1222-122-1-2-1-12-2-2-1-1-122-1-1-12-1-211111-2-2-1-1-11111-202-202-2-2-1-1110001011000-222-1-1-10011-1-1-200002110000000-100
χ332222-122-122222-1-1222-1-1222-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1222020-1-12200-1-1-122-1-1-1-1200-10-1-1-1-10000000220000000-1-1-1000
χ342222-122-122222-1-1222-1-1222-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-12-220-20-1-122001112-2-1-111-200-10-1-1110000000-2-20000000111000
χ352222-122-122222-1-1222-1-1222-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-22-202011-2-200-1-1-1-2211-1-12001011-1-10000000-2-20000000111000
χ362222-122-122222-1-1222-1-1222-1-1-1-122-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-2-20-2011-2-200111-2-21111-2001011110000000220000000-1-1-1000
χ372222-122-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-11-2-2-21111-1-1-1111122-20-20-1-1-2-20011-122-1-1-1-1-20010111100000002-2000000011-1000
χ382222-122-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-11-2-2-21111-1-1-111112-2-2020-1-1-2-200-1-112-2-1-1112001011-1-10000000-220000000-1-11000
χ392222-122-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-11-2-2-21111-1-1-11111-2220-2011220011-1-2211-1-1-200-10-1-1110000000-220000000-1-11000
χ402222-122-122222-1-12-22-1-1-2-22-1-1-1-122-1-1-11-2-2-21111-1-1-11111-2-22020112200-1-11-2-21111200-10-1-1-1-100000002-2000000011-1000
χ4144444-2-24-2-2-2-2-244-241-2-2-2-21-2-2-2-211-2-214-211-2-2-2-211111110004040000-2-20000000000-2-20-200001111000000000000000000
χ4244444-2-24-2-2-2-2-244-241-2-2-2-21-2-2-2-211-2-214-211-2-2-2-21111111000-40-4000022000000000022020000-1-1-1-1000000000000000000
χ4344444-2-24-2-2-2-2-244-2-41-2-2221-2-2-2-211-2-21-42-1-12222111-1-1-1-100040-40000-2-20000000000-2202000011-1-1000000000000000000
χ4444444-2-24-2-2-2-2-244-2-41-2-2221-2-2-2-211-2-21-42-1-12222111-1-1-1-1000-40400002200000000002-20-20000-1-111000000000000000000
χ454444-24-2-24-2-2-24-2-244-2-21-2-2-2-2-211-2-2-211-24-2-2-2-2111111111040040000000-2-2-20-20011-2000000110000000000000000000000
χ464444-24-2-24-2-2-24-2-244-2-21-2-2-2-2-211-2-2-211-24-2-2-2-21111111110-400-400000002220200-1-12000000-1-10000000000000000000000
χ474444-24-2-24-2-2-24-2-24-4-2-2122-2-2-211-2-2-2112-42222-1-1111-1-1-1-10400-4000000022-20-200112000000-1-10000000000000000000000
χ484444-24-2-24-2-2-24-2-24-4-2-2122-2-2-211-2-2-2112-42222-1-1111-1-1-1-10-40040000000-2-220200-1-1-2000000110000000000000000000000
χ494444-2-24-2-2444-2-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111404000-2-2-2-200000-201100000-2011000000000000000000000000
χ504444-2-24-2-2444-2-2-2-24-21-244-211-2-2-2-21-21-2-2-2-211-2-21111111-40-400022220000020-1-10000020-1-1000000000000000000000000
χ514444-2-24-2-2444-2-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-140-4000-2-22200000-20110000020-1-1000000000000000000000000
χ524444-2-24-2-2444-2-2-2-2-4-21-2-4-4-211-2-2-2-21-212222-1-122111-1-1-1-1-40400022-2-20000020-1-100000-2011000000000000000000000000
χ5344-4-4444-4-44-4-444-4-4044400-4-4-44-44-44-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2-4-4-22244-4-40-24-2002-4-4-22-2242-200000000-2220000000000000000000000000000000000000000000000−2i32i300000000
χ5544-4-444-2-4-4-22244-4-40-24-2002-4-4-22-2242-200000000-22200000000000000000000000000000000000000000000002i3−2i300000000
χ5644-4-44-24-424-4-4-24-420-2-24002224-4-22-2-4-200000000-222000000000000−2i32i30000000000000000−2i32i3000000000000000000000000
χ5744-4-44-24-424-4-4-24-420-2-24002224-4-22-2-4-200000000-2220000000000002i3−2i300000000000000002i3−2i3000000000000000000000000
χ5844-4-4-2442-44-4-44-22-404-2-200-422-224-4-22-200000000-2220000000000−2i32i3000000000−2i32i3000000000000000000000000000000000
χ5944-4-4-2442-44-4-44-22-404-2-200-422-224-4-22-200000000-22200000000002i3−2i30000000002i3−2i3000000000000000000000000000000000
χ6044-4-4-2-24224-4-4-2-2220-21-2002-1-1-22-2212100003-3001-1-133-3-3000000−2i32i3−2i32i30000000i3−i30000000i3−i3000000000000000000000000
χ6144-4-4-2-24224-4-4-2-2220-21-2002-1-1-22-2212100003-3001-1-133-3-30000002i3−2i32i3−2i30000000−i3i30000000−i3i3000000000000000000000000
χ6244-4-4-2-24224-4-4-2-2220-21-2002-1-1-22-221210000-33001-1-1-3-333000000−2i32i32i3−2i30000000i3−i30000000−i3i3000000000000000000000000
χ6344-4-4-2-24224-4-4-2-2220-21-2002-1-1-22-221210000-33001-1-1-3-3330000002i3−2i3−2i32i30000000−i3i30000000i3−i3000000000000000000000000
χ644-44-44444-4-44-4-4-4-44044400-44-4-44-44-4-4400000000-44-400000000000000000000000000000000000000000000000000000000
χ654-44-444-24-42-22-4-4-440-24-20024-42-22-2-42-2000000002-22000000000000000000000000000000000000000000000000−2i32i3000000
χ664-44-444-24-42-22-4-4-440-24-20024-42-22-2-42-2000000002-220000000000000000000000000000000000000000000000002i3−2i3000000
χ674-44-44-2442-44-42-4-4-20-2-24002-22-442-22-4-2000000002-2200000000000000000000000000000000000000000000−2i32i30000000000
χ684-44-44-2442-44-42-4-4-20-2-24002-22-442-22-4-2000000002-22000000000000000000000000000000000000000000002i3−2i30000000000
χ694-44-4-244-2-4-44-4-422404-2-200-4-222-2-4422-2000000002-220000000000000000000000000000000000000000000000000023−230000
χ704-44-4-244-2-4-44-4-422404-2-200-4-222-2-4422-2000000002-2200000000000000000000000000000000000000000000000000−23230000
χ714-4-44444-44-4-44-4-44-40444004-44-4-4-4-4-44400000000-4-4400000000000000000000000000000000000000000000000000000000
χ724-4-4444-2-4422-2-4-44-40-24-2−2i32i3-2-442222-4-2-200−2i32i300−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ734-4-4444-2-4422-2-4-44-40-24-22i3−2i3-2-442222-4-2-2002i3−2i3002i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ744-4-444-24-4-2-4-442-4420-2-2400-22-2-4-42224-20000000022-20000000000000023−2300000000000000000023−2300000000000000000000
χ754-4-444-24-4-2-4-442-4420-2-2400-22-2-4-42224-20000000022-200000000000000−2323000000000000000000−232300000000000000000000
χ764-4-444-2-2-4-222-22-44201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i3000000000023−23000000000000000000−333i−3i000000000000000000
χ774-4-444-2-2-4-222-22-44201-2-2−2i32i312-222-1-12-2100i3−i300−2i32i3-1-11i3−i3i3−i30000000000−23230000000000000000003−3−3i3i000000000000000000
χ784-4-444-2-2-4-222-22-44201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i3000000000023−23000000000000000000−33−3i3i000000000000000000
χ794-4-444-2-2-4-222-22-44201-2-22i3−2i312-222-1-12-2100−i3i3002i3−2i3-1-11−i3i3−i3i30000000000−23230000000000000000003−33i−3i000000000000000000
χ804-4-44-24424-4-44-42-2-404-2-20042-222-4-42-2-20000000022-20000000000000000−2i32i300000000000000−2i32i30000000000000000000000
χ814-4-44-24424-4-44-42-2-404-2-20042-222-4-42-2-20000000022-200000000000000002i3−2i3000000000000002i3−2i30000000000000000000000
χ824-4-44-24-22422-2-42-2-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i3000000000000−2i32i3000003-30000000i3−i30000000000000000000000
χ834-4-44-24-22422-2-42-2-40-2-21−2i32i3-22-2-1-12221100−2i32i300i3−i3-1-11i3−i3i3−i30000000000002i3−2i300000-330000000−i3i30000000000000000000000
χ844-4-44-24-22422-2-42-2-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i3000000000000−2i32i300000-330000000i3−i30000000000000000000000
χ854-4-44-24-22422-2-42-2-40-2-212i3−2i3-22-2-1-122211002i3−2i300−i3i3-1-11−i3i3−i3i30000000000002i3−2i3000003-30000000−i3i30000000000000000000000
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
χ8888-8-88-4-4-84-444-48-8402-4-400-244-442-2-442000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-44-8-4448-44-80-4-42004442-2-44-4-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4-444-444-4-444022200-2-2-22-22-22-2-100006-600-111-3-3330000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-444-444-4-444022200-2-2-22-22-22-2-10000-6600-11133-3-30000000000000000000000000000000000000000000000000000
χ928-88-88-4-4844-444-8-8-402-4-400-2-444-4-2244200000000-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-48-4-4-84-44-84480-4-42004-44-224-44-2200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-48-44-88-8444-40-42-40042-24-44-4-24200000000-22-200000000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-4-444-44444-4022200-22-2-22-22-2-2-1000000001-11−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-444-44444-4022200-22-2-22-22-2-2-1000000001-113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ978-8-88-4-484-4-8-8844-440-42-400-4-224444-2-4200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-44-444-444-440222−4i34i32-22-2-2-2-2-22-1002i3−2i3002i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-44-444-444-4402224i3−4i32-22-2-2-2-2-22-100−2i32i300−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000

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