Finite Group Databasebeta

← Group #13172357

Character table — Group #13172357

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order122233366666666623336666666666636666666666666662444446612121212121266612121212121212121212121212121212122224446666661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-1111111-1-1-11111111-1-1-1-1-1-1-11-11-1-1-1-1-1-1111-1-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-1-11111-1-1111111-1-1-1-111111-1-1-111111111-1-11-11-111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-11111-1-1-11-11-1-1-1-1-1-1111-111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-11111-1-111111-11-11-1-1-1-1-111-1-111-1-11-11-1-111111-1-1-1-11-1-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-111111-1-1-1-1111-11-1-111-1-1-111-1-1-1-111-11-1-111-1-1-1-111-1-1111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-11111111-1-111-1-1-1-1-1-1-11111-1-11-1-111-1-1-111-1-111-111-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-1111-1-111-1-1111-1-11-111-1-1-1-1-111-1-111-1111-1-111-1-11111-1-1-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-111-1-111-1-1-111-11-1-111111-1-111-1-1-1111-1-111-1-11111-1-11-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-111-1-11111111-1-1-1-1111-1-111-1-1-111-1-111-11-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-1-11111-1-1-11-111-1-1111-1-11111-1-1-11-1-111-1-1-1-111-1-111-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-11-1-1-1-111-1-1-1-1-11-11-111111-1-111-1-1111-11-1-111111-1-1-1-11-11-1
χ17222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122002222000022-1-1-1-100-12-12-1-10000-1-1-1-122000000-1-1-1-1000000
χ18222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-12200-2-2220000-2-2-1-1-1-1001-212-1-100001111-2-20000001111000000
χ19222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-20022-2-2000022111100-12-1-2110000-1-1-1-1-2-20000001111000000
χ20222222-1222-1-1-122222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000-2-21111001-21-2110000111122000000-1-1-1-1000000
χ21222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-111112-2002-222000022-1-1-1100-1-21-2110000-1-1112-2000000-1-111000000
χ22222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-111112-200-22220000-2-2-1-1-110012-1-211000011-1-1-2200000011-1-1000000
χ23222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-22002-2-2-2000022111-100-1-212-1-10000-1-111-2200000011-1-1000000
χ24222222-1222-1-1-1222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-2200-22-2-20000-2-2111-10012-12-1-1000011-1-12-2000000-1-111000000
χ2522222-122-1-122222-12-1-1222-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-100222200-1-122-1-100002-12-12000-1-1-1-1-1-1-1-1002020-1-10000000-100
χ2622222-122-1-122222-12-1-1222-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-10022-2-200-1-1221100002-1-21-2000-1-1-1-1111100-20-20110000000100
χ2722222-122-1-122222-12-1-1222-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-100-2-2220011-2-2-1-10000-212-120001111-1-1-1-100-20-20110000000100
χ2822222-122-1-122222-12-1-1222-1-122-1-1-1-12-12-1-1-1-1-122-1-1-1-1-1-1-100-2-2-2-20011-2-2110000-21-21-200011111111002020-1-10000000-100
χ2922222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-1-211111-2-2-1-1-11111002-22-200-1-1-2-2-1-100002121-2000-1-111-1-1110020-20-1-10000000100
χ3022222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-1-211111-2-2-1-1-11111002-2-2200-1-1-2-211000021-2-12000-1-11111-1-100-2020110000000-100
χ3122222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-1-211111-2-2-1-1-1111100-222-2001122-1-10000-2-121-200011-1-1-1-11100-2020110000000-100
χ3222222-122-1-122222-1-2-1-12-2-2-1-122-1-1-1-12-1-211111-2-2-1-1-1111100-22-22001122110000-2-1-2-1200011-1-111-1-10020-20-1-10000000100
χ332222-122-122222-1-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1222200-1-122-1-1002-1-12-12000-1-1-1-1-1-1-10000000202000000-1-1-1000
χ342222-122-122222-1-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-122-2-200-1-1-2-211002-1-121-2000-1-1-111110000000-20-2000000111000
χ352222-122-122222-1-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-2-222001122-1-100-211-2-12000111-1-1-1-10000000-20-2000000111000
χ362222-122-122222-1-122-12-122-12-1-1-1-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-2-2-2-20011-2-21100-211-21-200011111110000000202000000-1-1-1000
χ372222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-111112-22-200-1-12211002-1-1-2-1-2000111-1-1110000000-20200000011-1000
χ382222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-111112-2-2200-1-1-2-2-1-1002-1-1-21200011111-1-1000000020-2000000-1-11000
χ392222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-11111-222-20011221100-2112-1-2000-1-1-1-1-111000000020-2000000-1-11000
χ402222-122-122222-1-12-2-12-1-2-2-12-1-1-1-122-1-11-211-2-211-1-1-11111-22-220011-2-2-1-100-211212000-1-1-111-1-10000000-20200000011-1000
χ4144444-2-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-214-2-2-211-2-21111111000044000000-2-2000000-2-2-200000001111000000000000000000
χ4244444-2-24-2-2-2-2-244-24-21-2-2-2-21-2-2-2-211-214-2-2-211-2-211111110000-4-4000000220000002220000000-1-1-1-1000000000000000000
χ4344444-2-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-21-4222-1-122111-1-1-1-100004-4000000-2-2000000-222000000011-1-1000000000000000000
χ4444444-2-24-2-2-2-2-244-2-4-21-222-21-2-2-2-211-21-4222-1-122111-1-1-1-10000-44000000220000002-2-20000000-1-111000000000000000000
χ454444-24-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-211-24-2-2-2-2111111111440000-2-2000000-211-200000-21100000000000000000000000000
χ464444-24-2-244-2-2-2-2-244-2-21-2-2-2-211-2-2-2-211-24-2-2-2-2111111111-4-40000220000002-1-12000002-1-100000000000000000000000000
χ474444-24-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-2112-42222-1-1111-1-1-1-14-40000-2-2000000-2112000002-1-100000000000000000000000000
χ484444-24-2-244-2-2-2-2-24-4-2-2122-2-211-2-2-2-2112-42222-1-1111-1-1-1-1-440000220000002-1-1-200000-21100000000000000000000000000
χ494444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-2111111100440000-2-2-2-2000000-2-200000011110000000000000000000000
χ504444-2-24-2-2-2444-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-2111111100-4-40000222200000022000000-1-1-1-10000000000000000000000
χ514444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-1004-40000-2-222000000-2200000011-1-10000000000000000000000
χ524444-2-24-2-2-2444-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-100-44000022-2-20000002-2000000-1-1110000000000000000000000
χ5344-4-44444-4-44-4-4-4-44044400-4-44-44-44-4-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-24-4-4-222-4-4404-2-200-42-224-4-222-200000000-2220000000000000000000000000000000000000000000000−2i32i300000000
χ5544-4-444-24-4-4-222-4-4404-2-200-42-224-4-222-200000000-22200000000000000000000000000000000000000000000002i3−2i300000000
χ5644-4-44-244224-4-4-4-4-20-2-2400224-4-22-22-4-200000000-22200000000000000000000000000000000000000000000−2i32i30000000000
χ5744-4-44-244224-4-4-4-4-20-2-2400224-4-22-22-4-200000000-222000000000000000000000000000000000000000000002i3−2i30000000000
χ5844-4-4-244-2-4-44-4-42240-24-2002-4-22-224-42-200000000-2220000000000000000000000000000000000000000000000000023−230000
χ5944-4-4-244-2-4-44-4-42240-24-2002-4-22-224-42-200000000-22200000000000000000000000000000000000000000000000000−23230000
χ604-44-4444-44-4-44-4-44-4044400-44-4-4-44-4-44400000000-44-400000000000000000000000000000000000000000000000000000000
χ614-44-444-2-44-42-22-44-404-2-2−2i32i3-4-222-4422-2-20000−2i32i3−2i32i32-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ624-44-444-2-44-42-22-44-404-2-22i3−2i3-4-222-4422-2-200002i3−2i32i3−2i32-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ634-44-44-24-4-22-44-4-4420-2-24002-2-4-42-2224-2000000002-22000000000000000023−23000000000000000023−2300000000000000000000
χ644-44-44-24-4-22-44-4-4420-2-24002-2-4-42-2224-2000000002-220000000000000000−23230000000000000000−232300000000000000000000
χ654-44-44-2-2-4-222-22-4420-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i300000000000023−230000000000000000−333i−3i000000000000000000
χ664-44-44-2-2-4-222-22-4420-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i3000000000000−232300000000000000003−3−3i3i000000000000000000
χ674-44-44-2-2-4-222-22-4420-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i300000000000023−230000000000000000−33−3i3i000000000000000000
χ684-44-44-2-2-4-222-22-4420-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i3000000000000−232300000000000000003−33i−3i000000000000000000
χ694-44-4-24424-4-44-42-2-40-24-20024222-2-4-4-2-2000000002-220000000000−2i32i30000000−2i32i300000000000000000000000000000000000
χ704-44-4-24424-4-44-42-2-40-24-20024222-2-4-4-2-2000000002-2200000000002i3−2i300000002i3−2i300000000000000000000000000000000000
χ714-44-4-24-224-42-222-2-40-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i3000000−2i32i30000000i3−i300000003-300000000000000000000000000
χ724-44-4-24-224-42-222-2-40-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i30000002i3−2i30000000−i3i30000000-3300000000000000000000000000
χ734-44-4-24-224-42-222-2-40-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i3000000−2i32i30000000i3−i30000000-3300000000000000000000000000
χ744-44-4-24-224-42-222-2-40-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i30000002i3−2i30000000−i3i300000003-300000000000000000000000000
χ754-4-44444-4-44-4-444-4-40444004-4-44-4-4-44-4400000000-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-4444-2-4-4422-24-4-404-2-200422-2-4-42-22-20000000022-2000000000000000000000000000000000000000000000000−2i32i3000000
χ774-4-4444-2-4-4422-24-4-404-2-200422-2-4-42-22-20000000022-20000000000000000000000000000000000000000000000002i3−2i3000000
χ784-4-444-24-42-2-4-444-420-2-2400-22-44222-2-4-20000000022-200000000000023−23000000000000000023−23000000000000000000000000
χ794-4-444-24-42-2-4-444-420-2-2400-22-44222-2-4-20000000022-2000000000000−23230000000000000000−2323000000000000000000000000
χ804-4-44-2442-44-4-44-22-40-24-200-2-42-222-442-20000000022-20000000000000023−23000000000000000023−230000000000000000000000
χ814-4-44-2442-44-4-44-22-40-24-200-2-42-222-442-20000000022-200000000000000−23230000000000000000−23230000000000000000000000
χ824-4-44-2-2422-2-4-44-22201-2-200122-2-1-12-221003-30000-1-113-33-30000000023−2323−2300000000000000−33−330000000000000000000000
χ834-4-44-2-2422-2-4-44-22201-2-200122-2-1-12-221003-30000-1-113-33-300000000−2323−2323000000000000003−33−30000000000000000000000
χ844-4-44-2-2422-2-4-44-22201-2-200122-2-1-12-22100-330000-1-11-33-330000000023−23−232300000000000000−333−30000000000000000000000
χ854-4-44-2-2422-2-4-44-22201-2-200122-2-1-12-22100-330000-1-11-33-3300000000−232323−23000000000000003−3−330000000000000000000000
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
χ8888-8-88-4-4844-444-8-8-40-42-4004-2-44-442-242000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-4-4-8-8-4444480-4-4200442-2-44-44-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-48-4448-8-844-402-4-400-24-442-2-4442000000002-2-200000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-4-444-44444-4022200-2-22-22-22-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-4-444-44444-4022200-2-22-22-22-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ938-88-8-4-484-44-88-84-4402-4-400-2-444-2244-4200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-4-44-444-444-440222−4i34i3-22-2-2-22-2-22-100002i3−2i32i3−2i31-11−i3−i3i3i30000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-44-444-444-4402224i3−4i3-22-2-2-22-2-22-10000−2i32i3−2i32i31-11i3i3−i3−i30000000000000000000000000000000000000000000000000000
χ968-8-888-4-4-84-444-48-840-42-400-4-24-444-224200000000-2-2200000000000000000000000000000000000000000000000000000000
χ978-8-88-48-44-8844-4-44-80-4-4200-44-22444-4-2200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-444-444-4-4440222002-2-22-2-2-22-2-1006-6000011-1-33-330000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-444-444-4-4440222002-2-22-2-2-22-2-100-66000011-13-33-30000000000000000000000000000000000000000000000000000

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