Finite Group Databasebeta

← Group #13168754

Character table — Group #13168754

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666633346666666661212121212121212224412121212366612121212121212121222446666661212121212121212121212121212121244666666666121212244441212121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-11111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-111-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-11-1-11-1-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111111-1-11111111111111111111-1111-1-1-1-1-1-11111111111111111-1-1-11111-1-1-1-11111-1-11-1-1-1-1-1-1-11-11-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1111-1-1-1-11-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-11-11-1-1-111-1-1-111-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-111-1-11111-1-1-1-111-1-1-1-1-111-1-11111-11-1-11111-1-11-1-11-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-111-1-111-1-111-1-1-1-11111-1-1-1111111-1-1-1-1-111-1-11-1-1-1-11111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-111-1-1111-1-111111-1-111-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111-1-111-1-1-1-1-111111-1-111-1-111-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-111-1-11111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-11-1-1-1-11111-1-11
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-111-1-111-1-1-1-111111111111-1-111-1-1-11-11-1-11111-1-11-1-1-11
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-111111-11-11-1-1-111-1-1-1111-1
χ17222222-122-12-122-12-1-122-122-1-12-1-1-122-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-10222000000-1-12222-1-1-1-1-1-1-1-1-1-10002-1-1-10000-1-1-120020000000-10-100
χ18222222-122-12-122-12-1-122-122-1-12-1-1-122-1-1-1-1-1-100222222-1-1-1-1222-1-1-1-1-1-10-22-2000000-1-122-2-2-1-1-1-1-1-1-1-1-1-1000-21110000111-200-2000000010100
χ19222222-122-12-122-12-1-122-122-1-12-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-102-2200000011-2-22211111111110002-1-1-10000-1-1-1-200-2000000010100
χ20222222-122-12-122-12-1-122-122-1-12-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-1-1-1-1222-1-1-1-1-1-10-2-2-200000011-2-2-2-21111111111000-2111000011120020000000-10-100
χ21222222-122-12-122-12-1-12-2-122-1-12-1-1-1-2-211111100222222-1-1-1-1-2-2-211111102-2-2000000-1-1-2-2-2-211-1-1-1-111110002-1-1-10000111-2002000000010-100
χ22222222-122-12-122-12-1-12-2-122-1-12-1-1-1-2-211111100222222-1-1-1-1-2-2-21111110-2-22000000-1-1-2-22211-1-1-1-11111000-21110000-1-1-1200-20000000-10100
χ23222222-122-12-122-12-1-12-2-122-1-12-1-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-2111111022-20000001122-2-2-1-11111-1-1-1-10002-1-1-10000111200-20000000-10100
χ24222222-122-12-122-12-1-12-2-122-1-12-1-1-1-2-211111100-2-2-2-2-2-2-1-1-1-1-2-2-21111110-222000000112222-1-11111-1-1-1-1000-21110000-1-1-1-2002000000010-100
χ2522222-12-12222-1-1222-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-122022222-1-10000-1-1000000000000-1-12-1-1-1-1-1-12-1-102200-1-100000-1000
χ2622222-12-12222-1-1222-1-12-1-1-12-1-122-12222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-22222-1-1000011000000000000-11-211-1-1-1-1-2110-2-20011000001000
χ2722222-12-12222-1-1222-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-2-2-2110000-1-10000000000001-12-1-111112-1-10-2-20011000001000
χ2822222-12-12222-1-1222-1-12-1-1-12-1-122-122222222-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-21100001100000000000011-2111111-21102200-1-100000-1000
χ2922222-12-12222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-220-222-2-2-1-10000110000000000001-12-1-1-1-111-21102-2001100000-1000
χ3022222-12-12222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-222000000-1-1-1-1111111111-2-20222-2-2-1-10000-1-100000000000011-211-1-1112-1-10-2200-1-1000001000
χ3122222-12-12222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-1111111111220-2-2-22211000011000000000000-1-12-1-111-1-1-2110-2200-1-1000001000
χ3222222-12-12222-1-1222-1-1-2-1-1-12-1-122-1-2-2-2-2-2-2-2-2-2-2000000-1-1-1-11111111112-202-2-222110000-1-1000000000000-11-21111-1-12-1-102-2001100000-1000
χ332222-1222-12-12222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-12020-1-1-1-12222-1-10022-1-1-1-1-1-1-1-12220000-1-1-1-10000000200-1-1-1-100000
χ342222-1222-12-12222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-122-2-21111-1-1-1-12-1-122-1-1-1-120-20-1-1-1-122-2-21100-2-211111111-2-220000-1-1-1-10000000-200111100000
χ352222-1222-12-12222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-1-2-222-1-1-1-1-1-1-1-12-1-122-1-1-1-1-20201111-2-222-1-10022-1-1-1-1-1-1-1-1-2-2-2000011110000000-200111100000
χ362222-1222-12-12222-1-12-122-1-1-12-1-1-12-1-122-1-1-1-1-2-2-2-21111-1-1-1-12-1-122-1-1-1-1-20-201111-2-2-2-21100-2-21111111122-2000011110000000200-1-1-1-100000
χ372222-1222-12-12222-1-12-1-22-1-1-12-1-1-1211-2-211112222-1-1-1-1-1-1-1-1-211-2-21111-20-20-1-11122221100-2-2-1-1-1-1111122-20000-1-1110000000-200-1-11100000
χ382222-1222-12-12222-1-12-1-22-1-1-12-1-1-1211-2-2111122-2-21111-1-1-1-1-211-2-21111-2020-1-11122-2-2-1-100221111-1-1-1-1-2-2-20000-1-111000000020011-1-100000
χ392222-1222-12-12222-1-12-1-22-1-1-12-1-1-1211-2-21111-2-222-1-1-1-1-1-1-1-1-211-2-2111120-2011-1-1-2-2221100-2-2-1-1-1-11111-2-22000011-1-1000000020011-1-100000
χ402222-1222-12-12222-1-12-1-22-1-1-12-1-1-1211-2-21111-2-2-2-21111-1-1-1-1-211-2-21111202011-1-1-2-2-2-2-1-100221111-1-1-1-1222000011-1-10000000-200-1-11100000
χ4122-2-2222-222-2-22-2-2-22220-2-2-2222-2-2-2000000002-22i−2i2i2i−2i−2i2-2-2200000000000002-2002-22i−2i0000002i2i−2i−2i00002i−2i000002-20000000000002i−2i0000000
χ4222-2-2222-222-2-22-2-2-22220-2-2-2222-2-2-2000000002-2−2i2i−2i−2i2i2i2-2-2200000000000002-2002-2−2i2i000000−2i−2i2i2i0000−2i2i000002-2000000000000−2i2i0000000
χ4322-2-2222-222-2-22-2-2-22220-2-2-2222-2-2-200000000-222i−2i2i2i−2i−2i2-2-220000000000000-2200-222i−2i0000002i2i−2i−2i0000−2i2i00000-22000000000000−2i2i0000000
χ4422-2-2222-222-2-22-2-2-22220-2-2-2222-2-2-200000000-22−2i2i−2i−2i2i2i2-2-220000000000000-2200-22−2i2i000000−2i−2i2i2i00002i−2i00000-220000000000002i−2i0000000
χ4522-2-2-122-2-121-22-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i32-22i−2i−i−iii-111-10−i3i300−i3−i3i3i30000-11−i3i32-22i−2i3−30000−i−iii33−3−32i−2i00000-11−i3i30000000000−ii3−300000
χ4622-2-2-122-2-121-22-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i32-2−2i2iii−i−i-111-10−i3i300−i3−i3i3i30000-11−i3i32-2−2i2i−330000ii−i−i−3−333−2i2i00000-11−i3i30000000000i−i−3300000
χ4722-2-2-122-2-121-22-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i3-222i−2i−i−iii-111-10−i3i300−i3−i3i3i300001-1i3−i3-222i−2i3−30000−i−iii33−3−3−2i2i000001-1i3−i30000000000i−i−3300000
χ4822-2-2-122-2-121-22-2-21-12-10-211-12-111-2−i3i300−i3−i3i3i3-22−2i2iii−i−i-111-10−i3i300−i3−i3i3i300001-1i3−i3-22−2i2i−330000ii−i−i−3−3332i−2i000001-1i3−i30000000000−ii3−300000
χ4922-2-2-122-2-121-22-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i32-22i−2i−i−iii-111-10i3−i300i3i3−i3−i30000-11i3−i32-22i−2i−330000−i−iii−3−3332i−2i00000-11i3−i30000000000−ii−3300000
χ5022-2-2-122-2-121-22-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i32-2−2i2iii−i−i-111-10i3−i300i3i3−i3−i30000-11i3−i32-2−2i2i3−30000ii−i−i33−3−3−2i2i00000-11i3−i30000000000i−i3−300000
χ5122-2-2-122-2-121-22-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i3-222i−2i−i−iii-111-10i3−i300i3i3−i3−i300001-1−i3i3-222i−2i−330000−i−iii−3−333−2i2i000001-1−i3i30000000000i−i3−300000
χ5222-2-2-122-2-121-22-2-21-12-10-211-12-111-2i3−i300i3i3−i3−i3-22−2i2iii−i−i-111-10i3−i300i3i3−i3−i300001-1−i3i3-22−2i2i3−30000ii−i−i33−3−32i−2i000001-1−i3i30000000000−ii−3300000
χ5344444-2-2-24-24-2-2-2-24-21-241-2-2-21-2-2-2144-2-2-2-2-2-2000000001111-2-2-211111104040000000000-2-20000000000000-2-2110000-2110000000000000000
χ5444444-2-2-24-24-2-2-2-24-21-241-2-2-21-2-2-2144-2-2-2-2-2-2000000001111-2-2-21111110-40-4000000000022000000000000022-1-100002-1-10000000000000000
χ5544444-2-2-24-24-2-2-2-24-21-2-41-2-2-21-2-2-21-4-4222222000000001111222-1-1-1-1-1-1040-40000000000220000000000000-2-21100002-1-10000000000000000
χ5644444-2-2-24-24-2-2-2-24-21-2-41-2-2-21-2-2-21-4-4222222000000001111222-1-1-1-1-1-10-4040000000000-2-2000000000000022-1-10000-2110000000000000000
χ574444-24-24-2-2-2-244-2-21-2-24-2-2-21-2-211-2-2-2-2-211110044-2-2-2-211114-2-2-2-211110040000000-2-2-2-200-2-211111111000000000000000000000000000000
χ584444-24-24-2-2-2-244-2-21-2-24-2-2-21-2-211-2-2-2-2-2111100-4-4222211114-2-2-2-2111100-4000000022220022-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-24-2-2-2-244-2-21-2-2-4-2-2-21-2-211-22222-1-1-1-10044-2-2-2-21111-42222-1-1-1-100-40000000-2-22200221111-1-1-1-1000000000000000000000000000000
χ604444-24-24-2-2-2-244-2-21-2-2-4-2-2-21-2-211-22222-1-1-1-100-4-422221111-42222-1-1-1-1004000000022-2-200-2-2-1-1-1-11111000000000000000000000000000000
χ614444-2-24-2-24-24-2-24-2-2-214-211-2-21-2-2-2-2-244-2-2-2-2440000001111-211-2-211114000-2-2-2-2-2-2000000000000000000-2000011110000000000000000000
χ624444-2-24-2-24-24-2-24-2-2-214-211-2-21-2-2-2-2-244-2-2-2-2-4-40000001111-211-2-21111-400022222200000000000000000020000-1-1-1-10000000000000000000
χ634444-2-24-2-24-24-2-24-2-2-21-4-211-2-21-2-2-222-4-422224400000011112-1-122-1-1-1-1-4000-2-222-2-20000000000000000002000011-1-10000000000000000000
χ644444-2-24-2-24-24-2-24-2-2-21-4-211-2-21-2-2-222-4-42222-4-400000011112-1-122-1-1-1-1400022-2-222000000000000000000-20000-1-1110000000000000000000
χ6544-4-444-2-44-2-424-42-4-2-2402-4-4-2-2422200000000004i−4i4i4i−4i−4i-222-20000000000000000000−2i2i000000−2i−2i2i2i0000000000000000000000000000000000
χ6644-4-444-2-44-2-424-42-4-2-2402-4-4-2-242220000000000−4i4i−4i−4i4i4i-222-200000000000000000002i−2i0000002i2i−2i−2i0000000000000000000000000000000000
χ6744-4-44-24244-4-4-22-4-44-2-202224-2-2-4-42000000004-4000000-222-200000000000004-400-2200000000000000000000000-22000000000000000000000
χ6844-4-44-24244-4-4-22-4-44-2-202224-2-2-4-4200000000-44000000-222-20000000000000-44002-2000000000000000000000002-2000000000000000000000
χ6944-4-4-24-2-4-2-2224-4221-2-202221-2-2-1-12−2i32i300i3i3−i3−i3004i−4i−2i−2i2i2i1-1-110−2i32i300i3i3−i3−i30000000000−2i2i23−230000ii−i−i−3−333000000000000000000000000000000
χ7044-4-4-24-2-4-2-2224-4221-2-202221-2-2-1-12−2i32i300i3i3−i3−i300−4i4i2i2i−2i−2i1-1-110−2i32i300i3i3−i3−i300000000002i−2i−23230000−i−iii33−3−3000000000000000000000000000000
χ7144-4-4-24-2-4-2-2224-4221-2-202221-2-2-1-122i3−2i300−i3−i3i3i3004i−4i−2i−2i2i2i1-1-1102i3−2i300−i3−i3i3i30000000000−2i2i−23230000ii−i−i33−3−3000000000000000000000000000000
χ7244-4-4-24-2-4-2-2224-4221-2-202221-2-2-1-122i3−2i300−i3−i3i3i300−4i4i2i2i−2i−2i1-1-1102i3−2i300−i3−i3i3i300000000002i−2i23−230000−i−iii−3−333000000000000000000000000000000
χ7344-4-4-2-242-242-4-22-42-2-2102-1-1-2-21222−2i32i300−2i3−2i32i32i34-40000001-1-110i3−i300i3i3−i3−i30000-22−2i32i3-22000000000000000000000001-1i3−i30000000000000000000
χ7444-4-4-2-242-242-4-22-42-2-2102-1-1-2-21222−2i32i300−2i3−2i32i32i3-440000001-1-110i3−i300i3i3−i3−i300002-22i3−2i32-200000000000000000000000-11−i3i30000000000000000000
χ7544-4-4-2-242-242-4-22-42-2-2102-1-1-2-212222i3−2i3002i32i3−2i3−2i34-40000001-1-110−i3i300−i3−i3i3i30000-222i3−2i3-22000000000000000000000001-1−i3i30000000000000000000
χ7644-4-4-2-242-242-4-22-42-2-2102-1-1-2-212222i3−2i3002i32i3−2i3−2i3-440000001-1-110−i3i300−i3−i3i3i300002-2−2i32i32-200000000000000000000000-11i3−i30000000000000000000
χ774-44-4444-4-4-44-4-444-44440-44-4-4-4-44-44000000000000000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ784-44-444-2-4-4242-44-2-4-2-24024-422-4-22-20000000000000000-2-2220000000000000000000000000−2i32i30000−2i32i3−2i32i3000000000000000000000000000000
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χ804-44-44-242-4-44-42-24-44-2-202-22-4224-4-20000000000000000-2-222000000000000000000000000000000000000000000000000000000−2i32i3000000000
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χ984-4-44-24442-424-4-4-4-2-24-2042-22-422-2-40000000000002i3−2i3−2i32i3-22-220000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ994-4-44-24-24222-2-4-42-21-2-20-22-2-122-1120023−23−333−30000−2i32i32i3−2i31-11-100023−23−333−3000000000000000000i3−i3−i3i3−3i3i3i−3i000000000000000000000000000000
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χ1014-4-44-24-24222-2-4-42-21-2-20-22-2-122-11200−23233−3−330000−2i32i32i3−2i31-11-1000−23233−3−33000000000000000000i3−i3−i3i33i−3i−3i3i000000000000000000000000000000
χ1024-4-44-24-24222-2-4-42-21-2-20-22-2-122-11200−23233−3−3300002i3−2i3−2i32i31-11-1000−23233−3−33000000000000000000−i3i3i3−i3−3i3i3i−3i000000000000000000000000000000
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χ10788-8-8-4-4-44-4-444-44442220-2-2-2222-2-2-24i3−4i300−2i3−2i32i32i300000000-111-10−2i32i300i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-44-84844-4-4-8-42-40-2-444-24-442000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4844-8-4-84-484-4-42042-244-2-44-4000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-444-4-442220-22-2-2-2-22-2200006i−6i6i−6i00000000-1-11100000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4444-444-4-442220-22-2-2-2-22-220000−6i6i−6i6i00000000-1-111000003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-48-44-84844-8-4-4-420-4-2244-24-4400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
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χ1148-8-88-4-4-4-4444-4444-422202-22-2-2-2-22-200−434323−23−232300000000-11-1100023−23−333−300000000000000000000000000000000000000000000000000000000

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