Finite Group Databasebeta

← Group #13172052

Character table — Group #13172052

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666233366666666666666666444412121212366666666666624446612121212121212121212121212121212121212124466612121212121212121222444121212121212661224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-111-1-1-11111111111111111111111-1-1-11-1-11111-1-1-1-1-11-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-11111111111111111111-1111111111-1-1-1-1-1-111111111-1-1111-111-1-1-1-1111-11-1-1-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-11-1-11-1-1-1-111-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11-11-1-1-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-1-11-11111-1-1-1-1-111
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
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-11-1-1-11111-1-1-1-11111-1-11111-1-1-1-111111-1-1-111-1-1-1-11-1-1-1111-1-1111-1-1-11
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-111-111-1-111-1-1-1-1-1111-1
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-11-11-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-11-1-1-111-1-111-11-1
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-11111-1-1111-1-11111-1-11-11
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-11111-1-1111-1-1-111-1-1-1-1-1-1111-1-11111-1-111-1
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-11-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-11-1-1-111-1-111-1-11
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-111-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-111-1-111-1-1-1-1-111-11
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1111-1-111111-1-1-1111-1-1111-1-11-1
χ17222222-12-122-1222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-12022-1-100000022-1-12200000000002-1-1-1-12-1-1-1-1-1-1020020000-1-10-1000
χ18222222-12-122-1222-122-1-1222222-12222-1-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-202-21100000022-1-1220000000000-211-11-2-1-1-1-1110-200-200001101000
χ19222222-12-122-1222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-120-22-1-1000000-2-211-2-200000000002-1-11-121111-1-10-200-200001101000
χ20222222-12-122-1222-122-1-1222222-12222-1-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-211000000-2-211-2-20000000000-21111-2111111020020000-1-10-1000
χ21222222-12-122-1222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-1111120-2-2-1-100000022-1-1-2-200000000002-1-111-2-1-111110-20020000-1-101000
χ22222222-12-122-1222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200220000-111111-1-1-11111-20-221100000022-1-1-2-20000000000-2111-12-1-111-1-10200-20000110-1000
χ23222222-12-122-1222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-11111202-2-1-1000000-2-2112200000000002-1-1-11-211-1-1110200-20000110-1000
χ24222222-12-122-1222-1-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1200-2-20000-111111-1-1-11111-202211000000-2-211220000000000-211-1-1211-1-1-1-10-20020000-1-101000
χ2522222-12-122-1222-122-12-122-1-1-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-1220222-1-122-1-1000000-1-1-1-1-1-1-1-100-1-1-102-10000-1-120200000000-10-100
χ2622222-12-122-1222-122-12-122-1-1-1-12-1-1-1-1-1-122-1-122002222-1222-1-1-1-1-1-1-1-1-1-220-2-2-2-1-122-1-1000000-1-1-1-1-1-1-1-1001110-21000011-20-20000000010100
χ2722222-12-122-1222-122-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-12-2022211-2-2110000001111111100-1-1-102-10000-1-1-20-20000000010100
χ2822222-12-122-1222-122-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-200-2-2-2-2-1222-1-1-1-1-1-1-1-1-1-2-20-2-2-211-2-21100000011111111001110-2100001120200000000-10-100
χ2922222-12-122-1222-12-2-12-1-2-211-1-121111-1-122-1-122002222-1-2-2-211-1-1-111112-20-222-1-1-2-211000000-1-1-1-1111100-1-1-10-2100001120-200000000-10100
χ3022222-12-122-1222-12-2-12-1-2-211-1-121111-1-122-1-122002222-1-2-2-211-1-1-11111-2-202-2-2-1-1-2-211000000-1-1-1-111110011102-10000-1-1-2020000000010-100
χ3122222-12-122-1222-12-2-12-1-2-211-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-11111220-2221122-1-10000001111-1-1-1-100-1-1-10-21000011-2020000000010-100
χ3222222-12-122-1222-12-2-12-1-2-211-1-121111-1-122-1-1-2-200-2-2-2-2-1-2-2-211-1-1-11111-2202-2-21122-1-10000001111-1-1-1-10011102-10000-1-120-200000000-10100
χ332222-12222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-102200022-1-122-1-122-1-1-1-1-1-1-1-1-1-122000200-1-1-1-10000020-1-1-1-10000000
χ342222-12222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-122-2-2-1-1-1-1-12-1-122-1-1-1-1-1-1-102-200022-1-12211-2-211-1-1-1-1-1-1-1-1-2-2000-200111100000-2011110000000
χ352222-12222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2221111-12-1-122-1-1-1-1-1-1-10-22000-2-211-2-2-1-122-1-111111111-2-2000200-1-1-1-100000-2011110000000
χ362222-12222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-2-21111-12-1-122-1-1-1-1-1-1-10-2-2000-2-211-2-211-2-2111111111122000-20011110000020-1-1-1-10000000
χ372222-12222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-12222-1-1-1-1-1-211-2-2-1-1-111110-2-20002211-2-2-1-12211-1-1-1-1111122000-200-1-11100000-20-1-1110000000
χ382222-12222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-122-2-2-1-1-1-1-1-211-2-2-1-1-111110-220002211-2-211-2-2-1-1-1-1-1-11111-2-200020011-1-1000002011-1-10000000
χ392222-12222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-1-2-2221111-1-211-2-2-1-1-1111102-2000-2-2-1-122-1-122111111-1-1-1-1-2-2000-200-1-111000002011-1-10000000
χ402222-12222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-2-21111-1-211-2-2-1-1-11111022000-2-2-1-12211-2-2-1-11111-1-1-1-12200020011-1-100000-20-1-1110000000
χ4122-2-2222-2222-2-2-2-2-202220000-2-2200002-2-2-2-222-22i−2i22-2-22000002-2-200000000002-200002i−2i2i−2i0022-2-200002i−2i0000002i−2i0000000002i−2i000000000
χ4222-2-2222-2222-2-2-2-2-202220000-2-2200002-2-2-2-222-2−2i2i22-2-22000002-2-200000000002-20000−2i2i−2i2i0022-2-20000−2i2i000000−2i2i000000000−2i2i000000000
χ4322-2-2222-2222-2-2-2-2-202220000-2-2200002-2-2-2-22-222i−2i-2-2222000002-2-20000000000-2200002i−2i2i−2i00-2-2220000−2i2i0000002i−2i000000000−2i2i000000000
χ4422-2-2222-2222-2-2-2-2-202220000-2-2200002-2-2-2-22-22−2i2i-2-2222000002-2-20000000000-220000−2i2i−2i2i00-2-22200002i−2i000000−2i2i0000000002i−2i000000000
χ4522-2-2-122-22-12-211-2-20-1-12−i3i30011-1−i3−i3i3i32-211-2-12-22i−2i-1-111-10−i3i300-111−i3−i3i3i30000002-2−i3i300−ii2i−2i3−3-1-111−i3−i3i3i32i−2i000000−ii3−30000000−ii3−30000000
χ4622-2-2-122-22-12-211-2-20-1-12−i3i30011-1−i3−i3i3i32-211-2-12-2−2i2i-1-111-10−i3i300-111−i3−i3i3i30000002-2−i3i300i−i−2i2i−33-1-111−i3−i3i3i3−2i2i000000i−i−330000000i−i−330000000
χ4722-2-2-122-22-12-211-2-20-1-12−i3i30011-1−i3−i3i3i32-211-2-1-222i−2i11-1-1-10−i3i300-111−i3−i3i3i3000000-22i3−i300−ii2i−2i3−311-1-1i3i3−i3−i3−2i2i000000−ii3−30000000i−i−330000000
χ4822-2-2-122-22-12-211-2-20-1-12−i3i30011-1−i3−i3i3i32-211-2-1-22−2i2i11-1-1-10−i3i300-111−i3−i3i3i3000000-22i3−i300i−i−2i2i−3311-1-1i3i3−i3−i32i−2i000000i−i−330000000−ii3−30000000
χ4922-2-2-122-22-12-211-2-20-1-12i3−i30011-1i3i3−i3−i32-211-2-12-22i−2i-1-111-10i3−i300-111i3i3−i3−i30000002-2i3−i300−ii2i−2i−33-1-111i3i3−i3−i32i−2i000000−ii−330000000−ii−330000000
χ5022-2-2-122-22-12-211-2-20-1-12i3−i30011-1i3i3−i3−i32-211-2-12-2−2i2i-1-111-10i3−i300-111i3i3−i3−i30000002-2i3−i300i−i−2i2i3−3-1-111i3i3−i3−i3−2i2i000000i−i3−30000000i−i3−30000000
χ5122-2-2-122-22-12-211-2-20-1-12i3−i30011-1i3i3−i3−i32-211-2-1-222i−2i11-1-1-10i3−i300-111i3i3−i3−i3000000-22−i3i300−ii2i−2i−3311-1-1−i3−i3i3i3−2i2i000000−ii−330000000i−i3−30000000
χ5222-2-2-122-22-12-211-2-20-1-12i3−i30011-1i3i3−i3−i32-211-2-1-22−2i2i11-1-1-10i3−i300-111i3i3−i3−i3000000-22−i3i300i−i−2i2i3−311-1-1−i3−i3i3i32i−2i000000i−i3−30000000−ii−330000000
χ5344444-2-2-2-24-2-244-2-24-2-2144-2-2-2-2-2-2-2-2-211-2-21-2000000001-2-2-21111111114004-2-20000000000000000000000-2110-2-20000110000000000000000
χ5444444-2-2-2-24-2-244-2-24-2-2144-2-2-2-2-2-2-2-2-211-2-21-2000000001-2-2-2111111111-400-42200000000000000000000002-1-10220000-1-10000000000000000
χ5544444-2-2-2-24-2-244-2-2-4-2-21-4-422-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1400-4-2-20000000000000000000000-2110220000-1-10000000000000000
χ5644444-2-2-2-24-2-244-2-2-4-2-21-4-422-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1-40042200000000000000000000002-1-10-2-20000110000000000000000
χ574444-24-24-2-24-2-2-24-24-21-2-2-244-2-21-2-2-2-2-2-211-2-2004400001-211-2-21111111004000000000-2-2-2-2-2-20000000000000-2001111000000000000000000
χ584444-24-24-2-24-2-2-24-24-21-2-2-244-2-21-2-2-2-2-2-211-2-200-4-400001-211-2-2111111100-40000000002222220000000000000200-1-1-1-1000000000000000000
χ594444-24-24-2-24-2-2-24-2-4-21-222-4-4-2-212222-2-211-2-20044000012-1-122111-1-1-1-100-4000000000-2-2-2-222000000000000020011-1-1000000000000000000
χ604444-24-24-2-24-2-2-24-2-4-21-222-4-4-2-212222-2-211-2-200-4-4000012-1-122111-1-1-1-10040000000002222-2-20000000000000-200-1-111000000000000000000
χ614444-2-24-24-2-24-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-214400-2-2-2-214-2-2-2-21111111040000-2-2-2-2-2-200000011111111000000000000000000000000000000
χ624444-2-24-24-2-24-2-2-2441-2-2-2-2-2-211-21111-2-2-2-2-21-4-400222214-2-2-2-211111110-40000222222000000-1-1-1-1-1-1-1-1000000000000000000000000000000
χ634444-2-24-24-2-24-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-214400-2-2-2-21-42222111-1-1-1-10-40000-2-222220000001111-1-1-1-1000000000000000000000000000000
χ644444-2-24-24-2-24-2-2-24-41-2-2222211-2-1-1-1-1-2-2-2-2-21-4-40022221-42222111-1-1-1-104000022-2-2-2-2000000-1-1-1-11111000000000000000000000000000000
χ6544-4-444-2-4-2442-4-4-4204-2-20000-4-4-20000-222224004i−4i0000-200000-22200000000000000004i−4i−2i2i000000000000000000−2i2i00000000000000000000
χ6644-4-444-2-4-2442-4-4-4204-2-20000-4-4-20000-22222400−4i4i0000-200000-2220000000000000000−4i4i2i−2i0000000000000000002i−2i00000000000000000000
χ6744-4-44-24244-2-4-4-42-40-24-200002240000-22-4-42-24-40044-4-4-200000-2220000000000-220000000000-2-2220000000000000000000000000000000000
χ6844-4-44-24244-2-4-4-42-40-24-200002240000-22-4-42-2-4400-4-444-200000-22200000000002-2000000000022-2-20000000000000000000000000000000000
χ6944-4-4-24-2-4-2-24222-420-21-2−2i32i300221−2i3−2i32i32i3-22-1-12-2004i−4i000010i3−i3001-1-1i3i3−i3−i3000000000000−2i2i−2i2i23−230000000000000000i−i−33000000000000000000
χ7044-4-4-24-2-4-2-24222-420-21-2−2i32i300221−2i3−2i32i32i3-22-1-12-200−4i4i000010i3−i3001-1-1i3i3−i3−i30000000000002i−2i2i−2i−23230000000000000000−ii3−3000000000000000000
χ7144-4-4-24-2-4-2-24222-420-21-22i3−2i3002212i32i3−2i3−2i3-22-1-12-2004i−4i000010−i3i3001-1-1−i3−i3i3i3000000000000−2i2i−2i2i−23230000000000000000i−i3−3000000000000000000
χ7244-4-4-24-2-4-2-24222-420-21-22i3−2i3002212i32i3−2i3−2i3-22-1-12-200−4i4i000010−i3i3001-1-1−i3−i3i3i30000000000002i−2i2i−2i23−230000000000000000−ii−33000000000000000000
χ7344-4-4-2-2424-2-2-4222-401-2-2−2i32i300-1-1-2i3i3−i3−i3-2222214-400-2-22210−2i32i3001-1-1i3i3−i3−i3000000-22−2i32i30000000011-1-1i3i3−i3−i3000000000000000000000000000000
χ7444-4-4-2-2424-2-2-4222-401-2-2−2i32i300-1-1-2i3i3−i3−i3-222221-440022-2-210−2i32i3001-1-1i3i3−i3−i30000002-22i3−2i300000000-1-111−i3−i3i3i3000000000000000000000000000000
χ7544-4-4-2-2424-2-2-4222-401-2-22i3−2i300-1-1-2−i3−i3i3i3-2222214-400-2-222102i3−2i3001-1-1−i3−i3i3i3000000-222i3−2i30000000011-1-1−i3−i3i3i3000000000000000000000000000000
χ7644-4-4-2-2424-2-2-4222-401-2-22i3−2i300-1-1-2−i3−i3i3i3-222221-440022-2-2102i3−2i3001-1-1−i3−i3i3i30000002-2−2i32i300000000-1-111i3i3−i3−i3000000000000000000000000000000
χ774-44-4444-4-4-4-444-44-4044400004-4-40000-4-44-44-400000000400000-44-4000000000000000000000000000000000000000000000000000000000000
χ784-44-444-2-42-4-4-24-44204-2-200004-42000022-22-2-400000000-2000002-2200000000−2i32i300000000000000000000000−2i32i30000000000000000000000000
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Here i is the imaginary unit (i² = −1).