Finite Group Databasebeta

← Group #13172174

Character table — Group #13172174

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666623336666666666666666644441212121236666666666662444661212121212121212121212121212121212121212446661212121212121212122244466121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111111111111111-1-1-11-1-11111-1-11-1-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-111-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-11-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-11-1-11-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111111-1-1111111111111111111111-1111-1-11111-1-111-1-111111111-1-1111-111-1-1-1-111-11-1-11-1-1-1-1-1-11-11-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-1-11-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-11-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1-1-1-11111-1-1-1-1-111
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
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-11-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111111-1-1-111-1-1-1-1-1-1-111-1-11111-1-111-1
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-111-1-111-1-11
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-1-111111-1-111-1-11111-1-1-1-11111-1-1111-1-1-111-1-1-1-111-11-111-1-1111-1-1-11
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-11-11-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1111-11-1111-1-1-1-1-1111-1
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-11-11-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-11-11-1111-1-1-1-1-111-11
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1111111-11-111-1-1111-1-11-1
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-11111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-111-1-1-111-1-1-1-111-1-111-11-1
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1111-1-11111-1-1-111-1-11111-1-11-11
χ17222222-1-122-1222-1222-1-122-1-12-1-1-1-1-1-1-1-122-1-100222222-1222-1-1-1-1-1-1-1-1-122022200-1-1-1-1002200-1-1-1-1-1-1-1-100-1-1-10-120000-1-102002000000-10-100
χ18222222-1-122-1222-1222-1-122-1-12-1-1-1-1-1-1-1-122-1-100222222-1222-1-1-1-1-1-1-1-1-1-2-202-2-200-1-1-1-1002200-1-1-1-1-1-1-1-10011101-20000110-200-200000010100
χ19222222-1-122-1222-1222-1-122-1-12-1-1-1-1-1-1-1-122-1-100-2-2-2-2-2-2-1222-1-1-1-1-1-1-1-1-1220-22200111100-2-2001111111100-1-1-10-120000-1-10-200-200000010100
χ20222222-1-122-1222-1222-1-122-1-12-1-1-1-1-1-1-1-122-1-100-2-2-2-2-2-2-1222-1-1-1-1-1-1-1-1-1-2-20-2-2-200111100-2-200111111110011101-200001102002000000-10-100
χ21222222-1-122-1222-12-22-1-1-2-2112-1-11111-1-122-1-100222222-1-2-2-211-1-1-111112-20-22200-1-11100-2-200-1-1-1-1111100-1-1-101-20000110-200200000010-100
χ22222222-1-122-1222-12-22-1-1-2-2112-1-11111-1-122-1-100222222-1-2-2-211-1-1-11111-220-2-2-200-1-11100-2-200-1-1-1-11111001110-120000-1-10200-2000000-10100
χ23222222-1-122-1222-12-22-1-1-2-2112-1-11111-1-122-1-100-2-2-2-2-2-2-1-2-2-211-1-1-111112-202220011-1-10022001111-1-1-1-100-1-1-101-20000110200-2000000-10100
χ24222222-1-122-1222-12-22-1-1-2-2112-1-11111-1-122-1-100-2-2-2-2-2-2-1-2-2-211-1-1-11111-2202-2-20011-1-10022001111-1-1-1-1001110-120000-1-10-200200000010-100
χ2522222-1222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-1002200-1-12222-1-1-1-122-1-1-1-1-1-1-1-122000200-1-1-1-10020000-1-1-1-10000000
χ2622222-1222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-122-2-21111-12-1-122-1-1-1-1-1-1-1002-200-1-1-2-2-2-2-1-1112211111111-2-2000200-1-1-1-100-2000011110000000
χ2722222-1222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-222-1-1-1-1-12-1-122-1-1-1-1-1-1-100-220011222211-1-1-2-2-1-1-1-1-1-1-1-1-2-2000-200111100-2000011110000000
χ2822222-1222-122-1-1222-1-12-1-122-1-1-1-1-1-1-122-1-12-1-2-2-2-21111-12-1-122-1-1-1-1-1-1-100-2-20011-2-2-2-21111-2-21111111122000-20011110020000-1-1-1-10000000
χ2922222-1222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-12222-1-1-1-1-1-211-2-2-1-1-1111100-2-200-1-122-2-2111122-1-1-1-1111122000-200-1-11100-2000011-1-10000000
χ3022222-1222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-122-2-21111-1-211-2-2-1-1-1111100-2200-1-1-2-22211-1-1221111-1-1-1-1-2-2000-200-1-1110020000-1-1110000000
χ3122222-1222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-1-2-222-1-1-1-1-1-211-2-2-1-1-11111002-2001122-2-2-1-111-2-2-1-1-1-11111-2-200020011-1-10020000-1-1110000000
χ3222222-1222-122-1-122-2-1-1211-2-2-1-1-1111122-1-12-1-2-2-2-21111-1-211-2-2-1-1-1111100220011-2-222-1-1-1-1-2-21111-1-1-1-12200020011-1-100-2000011-1-10000000
χ332222-1222-122-1222-12-12-12222-1222222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-12220-1-12200002200-1-100000000002-1-1-12-1-1-1-1-1-1-1002200000-1-10-1000
χ342222-1222-122-1222-12-12-12222-1222222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-220112200002200-1-10000000000-211-1-21-1-1-1-11100-2-2000001101000
χ352222-1222-122-1222-12-12-12222-1222222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-122-20-1-1-2-20000-2-2001100000000002-1-112-11111-1-100-2-2000001101000
χ362222-1222-122-1222-12-12-12222-1222222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2011-2-20000-2-200110000000000-2111-21111111002200000-1-10-1000
χ372222-1222-122-1222-1-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1222000000-111111-1-1-111112-2-20-1-1220000-2-200-1-100000000002-1-11-21-1-1111100-2200000-1-101000
χ382222-1222-122-1222-1-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-1222000000-111111-1-1-11111-22-2011220000-2-200-1-10000000000-21112-1-1-111-1-1002-200000110-1000
χ392222-1222-122-1222-1-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-111112-220-1-1-2-2000022001100000000002-1-1-1-2111-1-111002-200000110-1000
χ402222-1222-122-1222-1-2-12-1-2-2-2-2-122-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-11111-222011-2-200002200110000000000-211-12-111-1-1-1-100-2200000-1-101000
χ4122-2-22222-2-2-222-2-2-20222000022-200002-2-2-2-2-22i−2i2i−2i2i2i−2i−2i2000002-2-200000000002i−2i2i−2i0000002i−2i2i2i−2i−2i00002-20000002i−2i000000000002-20000000
χ4222-2-22222-2-2-222-2-2-20222000022-200002-2-2-2-2-22i−2i−2i2i−2i−2i2i2i2000002-2-200000000002i−2i−2i2i0000002i−2i−2i−2i2i2i0000-220000002i−2i00000000000-220000000
χ4322-2-22222-2-2-222-2-2-20222000022-200002-2-2-2-2-2−2i2i2i−2i2i2i−2i−2i2000002-2-20000000000−2i2i2i−2i000000−2i2i2i2i−2i−2i0000-22000000−2i2i00000000000-220000000
χ4422-2-22222-2-2-222-2-2-20222000022-200002-2-2-2-2-2−2i2i−2i2i−2i−2i2i2i2000002-2-20000000000−2i2i−2i2i000000−2i2i−2i−2i2i2i00002-2000000−2i2i000000000002-20000000
χ4522-2-22-122-21-22-11-2-20-1-12−i3i300-1-11−i3−i3i3i32-211-212i−2i2i−2i−i−iii-10−i3i300-111−i3−i3i3i3000000−ii2i−2i003−33−32i−2i−i−iii33−3−32-2000000−ii3−30000000−i3i3-110000000
χ4622-2-22-122-21-22-11-2-20-1-12−i3i300-1-11−i3−i3i3i32-211-212i−2i−2i2iii−i−i-10−i3i300-111−i3−i3i3i3000000−ii−2i2i003−3−332i−2iii−i−i−3−333-22000000−ii3−30000000i3−i31-10000000
χ4722-2-22-122-21-22-11-2-20-1-12−i3i300-1-11−i3−i3i3i32-211-21−2i2i2i−2i−i−iii-10−i3i300-111−i3−i3i3i3000000i−i2i−2i00−333−3−2i2i−i−iii33−3−3-22000000i−i−330000000i3−i31-10000000
χ4822-2-22-122-21-22-11-2-20-1-12−i3i300-1-11−i3−i3i3i32-211-21−2i2i−2i2iii−i−i-10−i3i300-111−i3−i3i3i3000000i−i−2i2i00−33−33−2i2iii−i−i−3−3332-2000000i−i−330000000−i3i3-110000000
χ4922-2-22-122-21-22-11-2-20-1-12i3−i300-1-11i3i3−i3−i32-211-212i−2i2i−2i−i−iii-10i3−i300-111i3i3−i3−i3000000−ii2i−2i00−33−332i−2i−i−iii−3−3332-2000000−ii−330000000i3−i3-110000000
χ5022-2-22-122-21-22-11-2-20-1-12i3−i300-1-11i3i3−i3−i32-211-212i−2i−2i2iii−i−i-10i3−i300-111i3i3−i3−i3000000−ii−2i2i00−333−32i−2iii−i−i33−3−3-22000000−ii−330000000−i3i31-10000000
χ5122-2-22-122-21-22-11-2-20-1-12i3−i300-1-11i3i3−i3−i32-211-21−2i2i2i−2i−i−iii-10i3−i300-111i3i3−i3−i3000000i−i2i−2i003−3−33−2i2i−i−iii−3−333-22000000i−i3−30000000−i3i31-10000000
χ5222-2-22-122-21-22-11-2-20-1-12i3−i300-1-11i3i3−i3−i32-211-21−2i2i−2i2iii−i−i-10i3−i300-111i3i3−i3−i3000000i−i−2i2i003−33−3−2i2iii−i−i33−3−32-2000000i−i3−30000000i3−i3-110000000
χ5344444-2-2-24-2-24-2-2-244-21-2-2-2-2-2-2111111-2-2-2-2-210044-2-2-2-214-2-2-2-2111111100040000-2-2-2-200-2-20011111111000000000000000000000000000000
χ5444444-2-2-24-2-24-2-2-244-21-2-2-2-2-2-2111111-2-2-2-2-2100-4-4222214-2-2-2-21111111000-400002222002200-1-1-1-1-1-1-1-1000000000000000000000000000000
χ5544444-2-2-24-2-24-2-2-24-4-21-22222-211-1-1-1-1-2-2-2-2-210044-2-2-2-21-42222111-1-1-1-1000-40000-2-2220022001111-1-1-1-1000000000000000000000000000000
χ5644444-2-2-24-2-24-2-2-24-4-21-22222-211-1-1-1-1-2-2-2-2-2100-4-422221-42222111-1-1-1-10004000022-2-200-2-200-1-1-1-11111000000000000000000000000000000
χ574444-24-2-2-24-2-244-2-24-2-2144-2-2-2-2-2-2-2-2-211-2-21-2000000001-2-2-21111111114400-2-20000000000000000000000-2110-2-20000110000000000000000
χ584444-24-2-2-24-2-244-2-24-2-2144-2-2-2-2-2-2-2-2-211-2-21-2000000001-2-2-2111111111-4-4002200000000000000000000002-1-10220000-1-10000000000000000
χ594444-24-2-2-24-2-244-2-2-4-2-21-4-422-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-14-400-2-20000000000000000000000-2110220000-1-10000000000000000
χ604444-24-2-2-24-2-244-2-2-4-2-21-4-422-2-2-2222211-2-21-2000000001222-1-1111-1-1-1-1-44002200000000000000000000002-1-10-2-20000110000000000000000
χ614444-2-244-2-24-2-2-24-241-2-2-2-2441-2-2-2-2-2-2-2-211-2-2440000001-211-2-21111111004000-2-20000-2-200-2-20000000000000-2001111000000000000000000
χ624444-2-244-2-24-2-2-24-241-2-2-2-2441-2-2-2-2-2-2-2-211-2-2-4-40000001-211-2-2111111100-40002200002200220000000000000200-1-1-1-1000000000000000000
χ634444-2-244-2-24-2-2-24-2-41-2-222-4-41-2-22222-2-211-2-24400000012-1-122111-1-1-1-100-4000-2-200002200-2-2000000000000020011-1-1000000000000000000
χ644444-2-244-2-24-2-2-24-2-41-2-222-4-41-2-22222-2-211-2-2-4-400000012-1-122111-1-1-1-1004000220000-2-200220000000000000-200-1-111000000000000000000
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χ6644-4-444-2-2-4-4244-42-404-2-200004-220000-22-4-42200−4i4i−4i−4i4i4i-200000-2220000000000002i−2i000000002i2i−2i−2i0000000000000000000000000000000000
χ6744-4-44-2-2-2-4224-222-40-21-2−2i32i300-21-1i3i3−i3−i3-22222-1004i−4i−2i−2i2i2i10−2i32i3001-1-1i3i3−i3−i300000000−2i2i000023−2300ii−i−i−3−333000000000000000000000000000000
χ6844-4-44-2-2-2-4224-222-40-21-2−2i32i300-21-1i3i3−i3−i3-22222-100−4i4i2i2i−2i−2i10−2i32i3001-1-1i3i3−i3−i3000000002i−2i0000−232300−i−iii33−3−3000000000000000000000000000000
χ6944-4-44-2-2-2-4224-222-40-21-22i3−2i300-21-1−i3−i3i3i3-22222-1004i−4i−2i−2i2i2i102i3−2i3001-1-1−i3−i3i3i300000000−2i2i0000−232300ii−i−i33−3−3000000000000000000000000000000
χ7044-4-44-2-2-2-4224-222-40-21-22i3−2i300-21-1−i3−i3i3i3-22222-100−4i4i2i2i−2i−2i102i3−2i3001-1-1−i3−i3i3i3000000002i−2i000023−2300−i−iii−3−333000000000000000000000000000000
χ7144-4-4-24442-4-4-24-4-420-24-20000-24-40000-22222-44i−4i000000-200000-22200000000004i−4i00000000−2i2i0000000000000000−2i2i00000000000000000000
χ7244-4-4-24442-4-4-24-4-420-24-20000-24-40000-22222-4−4i4i000000-200000-2220000000000−4i4i000000002i−2i00000000000000002i−2i00000000000000000000
χ7344-4-4-2-24422-4-2-22-4201-2-2−2i32i3001-22−2i3−2i32i32i3-22-1-1224i−4i00000010i3−i3001-1-1i3i3−i3−i3000000−2i2i000023−2300−2i2i0000000000000000i−i−33000000000000000000
χ7444-4-4-2-24422-4-2-22-4201-2-2−2i32i3001-22−2i3−2i32i32i3-22-1-122−4i4i00000010i3−i3001-1-1i3i3−i3−i30000002i−2i0000−2323002i−2i0000000000000000−ii3−3000000000000000000
χ7544-4-4-2-24422-4-2-22-4201-2-22i3−2i3001-222i32i3−2i3−2i3-22-1-1224i−4i00000010−i3i3001-1-1−i3−i3i3i3000000−2i2i0000−232300−2i2i0000000000000000i−i3−3000000000000000000
χ7644-4-4-2-24422-4-2-22-4201-2-22i3−2i3001-222i32i3−2i3−2i3-22-1-122−4i4i00000010−i3i3001-1-1−i3−i3i3i30000002i−2i000023−23002i−2i0000000000000000−ii−33000000000000000000
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Here i is the imaginary unit (i² = −1).