Finite Group Databasebeta

← Group #13172056

Character table — Group #13172056

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order1222333666666666233366666666666666666444412121212366666666666622446612121212121212121212121212121212121212124466666661212121212244441212121212126121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-1111111-1-11111111111111111-11-111-1-1-111-1-1-1-11-1-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-111-1-11-1-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-1-11-1-11-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111-1-11111111111111111111-1111-1-1-1-1-1-11111111111111111-1-11-11-1-1111-1-111-11-1-11-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-111-1-11-1-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111-1-111-1-11-1-111-1-111-1-1-111
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
χ91111111111111111-1111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1111-1-1-1-1-11-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111-11-1-111-111-1-11-1-1-1111-1-1-1-111-1-11
χ101111111111111111-1111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1111-1-1-1-1-1-1-11-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111111-11-11-11111-1-1-1-111-1
χ111111111111111111-1111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-11-1-111-111-1-1111-1-1-1-1-1-1111-111-1
χ121111111111111111-1111-1-1-1-111-1-1-1-1111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1111-1-11111-11-1-11
χ131111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11111111-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1111-1-11111-11-11-1
χ141111111111111111-1111-1-1-1-111-1-1-1-11111111-1-11111111-1-1-1-1-1111-1-1-1-11-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-111-1-11-1-111111-1-1-1-1-1-1111-11-11
χ151111111111111111-1111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-11-11-11111-1-1-1-11-11
χ161111111111111111-1111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-11111-1-1-1-111-1-11111-1-1-1-1111111-11-111-1-11-1-1111-1-1-1111-1-1-1-111-11-1
χ17222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-122022222-1-1-1-100000000000000002-1-1-1-1-1-12-1-1-1-12002000-1-100-10000
χ18222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-22222-1-1110000000000000000-2-11-1-111-2-1-111-200-2000110010000
χ19222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-2-2-211-1-1000000000000000021-111-1-1211-1-1-200-2000110010000
χ20222222-12-1-12222-1222-1-12222222222-1-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-211110000000000000000-2111111-211112002000-1-100-10000
χ21222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1222000000-111111-1-1-11111-220-2-2-222-1-111000000000000000021-111-1-1-2-1-111200-20001100-10000
χ22222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1222000000-111111-1-1-11111-2-202-2-222-1-1-1-10000000000000000-21111112-1-1-1-1-2002000-1-10010000
χ23222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-12-2-2000000-111111-1-1-11111220-222-2-2111100000000000000002-1-1-1-1-1-1-21111-2002000-1-10010000
χ24222222-12-1-12222-12-22-1-1-2-2-2-222-2-2-2-2-1-1-1-1-1-12-2-2000000-111111-1-1-111112-20222-2-211-1-10000000000000000-2-11-1-111211-1-1200-20001100-10000
χ2522222-122222-1-1-1222-12-122-1-1-1-1-1-1-1-122-1-12-1-100222222-1222-1-1-1-1-1-1-1-1-1022200000022-1-1-1-122-1-1-1-1-1-1-1-100-10200-1-1-100-1-1020020000000-1-100
χ2622222-122222-1-1-1222-12-122-1-1-1-1-1-1-1-122-1-12-1-100222222-1222-1-1-1-1-1-1-1-1-10-22-2000000-2-2-1-1-1-122-1-1-1-1-1-1-1-10010-20011100110-200-200000001100
χ2722222-122222-1-1-1222-12-122-1-1-1-1-1-1-1-122-1-12-1-100-2-2-2-2-2-2-1222-1-1-1-1-1-1-1-1-102-22000000221111-2-21111111100-10200-1-1-100-1-10-200-200000001100
χ2822222-122222-1-1-1222-12-122-1-1-1-1-1-1-1-122-1-12-1-100-2-2-2-2-2-2-1222-1-1-1-1-1-1-1-1-10-2-2-2000000-2-21111-2-2111111110010-2001110011020020000000-1-100
χ2922222-122222-1-1-122-2-12-1-2-211-1-1111122-1-12-1-100222222-1-2-2-211-1-1-1111102-2-2000000-2-2-1-111-2-2-1-1-1-1111100-10200-1-1100110-20020000000-1100
χ3022222-122222-1-1-122-2-12-1-2-211-1-1111122-1-12-1-100222222-1-2-2-211-1-1-111110-2-2200000022-1-111-2-2-1-1-1-111110010-20011-100-1-10200-200000001-100
χ3122222-122222-1-1-122-2-12-1-2-211-1-1111122-1-12-1-100-2-2-2-2-2-2-1-2-2-211-1-1-11111022-2000000-2-211-1-1221111-1-1-1-100-10200-1-1100110200-200000001-100
χ3222222-122222-1-1-122-2-12-1-2-211-1-1111122-1-12-1-100-2-2-2-2-2-2-1-2-2-211-1-1-111110-2220000002211-1-1221111-1-1-1-10010-20011-100-1-10-20020000000-1100
χ332222-122-122-12222-12-1-12-1-122-1-1-1-1-1-1-1-122-12-12222-1-1-1-1-12-1-122-1-1-1-1-1-1-12020-1-1-1-122002222-1-1-1-1-1-1-1-1-1-122020-1-1000-1-10000200-1-100-1-100000
χ342222-122-122-12222-12-1-12-1-122-1-1-1-1-1-1-1-122-12-122-2-21111-12-1-122-1-1-1-1-1-1-120-20-1-1-1-12200-2-2-2-21111111111-2-2020-1-1000-1-10000-20011001100000
χ352222-122-122-12222-12-1-12-1-122-1-1-1-1-1-1-1-122-12-1-2-222-1-1-1-1-12-1-122-1-1-1-1-1-1-1-20201111-2-2002222-1-1-1-1-1-1-1-1-1-1-2-20-2011000110000-20011001100000
χ362222-122-122-12222-12-1-12-1-122-1-1-1-1-1-1-1-122-12-1-2-2-2-21111-12-1-122-1-1-1-1-1-1-1-20-201111-2-200-2-2-2-21111111111220-2011000110000200-1-100-1-100000
χ372222-122-122-12222-1-2-1-1211-2-2-1-11111-1-122-12-12222-1-1-1-1-1-211-2-2-1-1-11111-20-2011-1-1220022-2-211-1-1-1-11111220-2011000-1-10000-200-1-1001100000
χ382222-122-122-12222-1-2-1-1211-2-2-1-11111-1-122-12-122-2-21111-1-211-2-2-1-1-11111-202011-1-12200-2-222-1-11111-1-1-1-1-2-20-2011000-1-100002001100-1-100000
χ392222-122-122-12222-1-2-1-1211-2-2-1-11111-1-122-12-1-2-222-1-1-1-1-1-211-2-2-1-1-1111120-20-1-111-2-20022-2-211-1-1-1-11111-2-2020-1-10001100002001100-1-100000
χ402222-122-122-12222-1-2-1-1211-2-2-1-11111-1-122-12-1-2-2-2-21111-1-211-2-2-1-1-111112020-1-111-2-200-2-222-1-11111-1-1-1-122020-1-1000110000-200-1-1001100000
χ4122-2-222222-2-22-2-2-2-2022200002-20000-2-22-22-2-22-22i−2i2i2i−2i−2i2000002-2-200000000002-22-2002i−2i00002i2i−2i−2i00002i−2i000000002-200000002i−2i000000000
χ4222-2-222222-2-22-2-2-2-2022200002-20000-2-22-22-2-22-2−2i2i−2i−2i2i2i2000002-2-200000000002-22-200−2i2i0000−2i−2i2i2i0000−2i2i000000002-20000000−2i2i000000000
χ4322-2-222222-2-22-2-2-2-2022200002-20000-2-22-22-2-2-222i−2i2i2i−2i−2i2000002-2-20000000000-22-22002i−2i00002i2i−2i−2i0000−2i2i00000000-220000000−2i2i000000000
χ4422-2-222222-2-22-2-2-2-2022200002-20000-2-22-22-2-2-22−2i2i−2i−2i2i2i2000002-2-20000000000-22-2200−2i2i0000−2i−2i2i2i00002i−2i00000000-2200000002i−2i000000000
χ4522-2-2-122-12-212-2-2-210-1-12−i3i300-11−i3−i3i3i3112-2-1-212-22i−2i−i−iii-10−i3i300-111−i3−i3i3i30000−i3i3-112-2002i−2i003−3−i−iii33−3−32i−2i000−i3i3000-110000000−ii003−300000
χ4622-2-2-122-12-212-2-2-210-1-12−i3i300-11−i3−i3i3i3112-2-1-212-2−2i2iii−i−i-10−i3i300-111−i3−i3i3i30000−i3i3-112-200−2i2i00−33ii−i−i−3−333−2i2i000−i3i3000-110000000i−i00−3300000
χ4722-2-2-122-12-212-2-2-210-1-12−i3i300-11−i3−i3i3i3112-2-1-21-222i−2i−i−iii-10−i3i300-111−i3−i3i3i30000i3−i31-1-22002i−2i003−3−i−iii33−3−3−2i2i000i3−i30001-10000000i−i00−3300000
χ4822-2-2-122-12-212-2-2-210-1-12−i3i300-11−i3−i3i3i3112-2-1-21-22−2i2iii−i−i-10−i3i300-111−i3−i3i3i30000i3−i31-1-2200−2i2i00−33ii−i−i−3−3332i−2i000i3−i30001-10000000−ii003−300000
χ4922-2-2-122-12-212-2-2-210-1-12i3−i300-11i3i3−i3−i3112-2-1-212-22i−2i−i−iii-10i3−i300-111i3i3−i3−i30000i3−i3-112-2002i−2i00−33−i−iii−3−3332i−2i000i3−i3000-110000000−ii00−3300000
χ5022-2-2-122-12-212-2-2-210-1-12i3−i300-11i3i3−i3−i3112-2-1-212-2−2i2iii−i−i-10i3−i300-111i3i3−i3−i30000i3−i3-112-200−2i2i003−3ii−i−i33−3−3−2i2i000i3−i3000-110000000i−i003−300000
χ5122-2-2-122-12-212-2-2-210-1-12i3−i300-11i3i3−i3−i3112-2-1-21-222i−2i−i−iii-10i3−i300-111i3i3−i3−i30000−i3i31-1-22002i−2i00−33−i−iii−3−333−2i2i000−i3i30001-10000000i−i003−300000
χ5222-2-2-122-12-212-2-2-210-1-12i3−i300-11i3i3−i3−i3112-2-1-21-22−2i2iii−i−i-10i3−i300-111i3i3−i3−i30000−i3i31-1-2200−2i2i003−3ii−i−i33−3−32i−2i000−i3i30001-10000000−ii00−3300000
χ5344444-2-24-2-24-2-2-2-244-2-2144-2-2-2-2-2-2-2-2-2-211-21-2000000001-2-2-21111111110404000000-2-20000000000000000-20-20011-200110000000000000000
χ5444444-2-24-2-24-2-2-2-244-2-2144-2-2-2-2-2-2-2-2-2-211-21-2000000001-2-2-21111111110-40-400000022000000000000000020200-1-1200-1-10000000000000000
χ5544444-2-24-2-24-2-2-2-24-4-2-21-4-422-2-22222-2-211-21-2000000001222-1-1111-1-1-1-1040-4000000220000000000000000-20-20011200-1-10000000000000000
χ5644444-2-24-2-24-2-2-2-24-4-2-21-4-422-2-22222-2-211-21-2000000001222-1-1111-1-1-1-10-404000000-2-2000000000000000020200-1-1-200110000000000000000
χ574444-24-2-2-2-2-2444-2-24-21-2-2-244-2-2-2-2-2-211-2-21-2-2440000001-211-2-211111114000-2-2-2-2-2-20000000000000000000-201100011000000000000000000
χ584444-24-2-2-2-2-2444-2-24-21-2-2-244-2-2-2-2-2-211-2-21-2-2-4-40000001-211-2-21111111-4000222222000000000000000000020-1-1000-1-1000000000000000000
χ594444-24-2-2-2-2-2444-2-2-4-21-222-4-4-2-2222211-2-21-2-24400000012-1-122111-1-1-1-1-400022-2-2-2-2000000000000000000020-1-100011000000000000000000
χ604444-24-2-2-2-2-2444-2-2-4-21-222-4-4-2-2222211-2-21-2-2-4-400000012-1-122111-1-1-1-14000-2-222220000000000000000000-2011000-1-1000000000000000000
χ614444-2-24-244-2-2-2-24-241-2-2-2-2-2-2111111-2-2-2-2-2-210044-2-2-2-214-2-2-2-21111111004000000000-2-2-2-2-2-211111111000000000000000000000000000000
χ624444-2-24-244-2-2-2-24-241-2-2-2-2-2-2111111-2-2-2-2-2-2100-4-4222214-2-2-2-2111111100-4000000000222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ634444-2-24-244-2-2-2-24-2-41-2-2222211-1-1-1-1-2-2-2-2-2-210044-2-2-2-21-42222111-1-1-1-100-4000000000-2-222221111-1-1-1-1000000000000000000000000000000
χ644444-2-24-244-2-2-2-24-2-41-2-2222211-1-1-1-1-2-2-2-2-2-2100-4-422221-42222111-1-1-1-100400000000022-2-2-2-2-1-1-1-11111000000000000000000000000000000
χ6544-4-444-24-22-44-4-42-404-2-200004-4000022-22-22-44-4000000-200000-22200000000004-4-2200000000000000000000000000-22000000000000000000
χ6644-4-444-24-22-44-4-42-404-2-200004-4000022-22-22-4-44000000-200000-2220000000000-442-2000000000000000000000000002-2000000000000000000
χ6744-4-44-2444-4-4-222-4-40-24-20000-220000-4-4-22422004i−4i4i4i−4i−4i-200000-2220000000000000000−2i2i0000−2i−2i2i2i0000000000000000000000000000000000
χ6844-4-44-2444-4-4-222-4-40-24-20000-220000-4-4-2242200−4i4i−4i−4i4i4i-200000-22200000000000000002i−2i00002i2i−2i−2i0000000000000000000000000000000000
χ6944-4-4-24-2-2-2224-4-4220-21-2−2i32i300-22−2i3−2i32i32i3-1-1-221224-400000010i3−i3001-1-1i3i3−i3−i30000−2i32i3-22-22000000000000000000000i3−i30001-1000000000000000000
χ7044-4-4-24-2-2-2224-4-4220-21-2−2i32i300-22−2i3−2i32i32i3-1-1-22122-4400000010i3−i3001-1-1i3i3−i3−i300002i3−2i32-22-2000000000000000000000−i3i3000-11000000000000000000
χ7144-4-4-24-2-2-2224-4-4220-21-22i3−2i300-222i32i3−2i3−2i3-1-1-221224-400000010−i3i3001-1-1−i3−i3i3i300002i3−2i3-22-22000000000000000000000−i3i30001-1000000000000000000
χ7244-4-4-24-2-2-2224-4-4220-21-22i3−2i300-222i32i3−2i3−2i3-1-1-22122-4400000010−i3i3001-1-1−i3−i3i3i30000−2i32i32-22-2000000000000000000000i3−i3000-11000000000000000000
χ7344-4-4-2-24-24-42-222-4201-2-2−2i32i3001-1i3i3−i3−i322-22-22-1004i−4i−2i−2i2i2i10−2i32i3001-1-1i3i3−i3−i3000000000000−2i2i0023−23ii−i−i−3−333000000000000000000000000000000
χ7444-4-4-2-24-24-42-222-4201-2-2−2i32i3001-1i3i3−i3−i322-22-22-100−4i4i2i2i−2i−2i10−2i32i3001-1-1i3i3−i3−i30000000000002i−2i00−2323−i−iii33−3−3000000000000000000000000000000
χ7544-4-4-2-24-24-42-222-4201-2-22i3−2i3001-1−i3−i3i3i322-22-22-1004i−4i−2i−2i2i2i102i3−2i3001-1-1−i3−i3i3i3000000000000−2i2i00−2323ii−i−i33−3−3000000000000000000000000000000
χ7644-4-4-2-24-24-42-222-4201-2-22i3−2i3001-1−i3−i3i3i322-22-22-100−4i4i2i2i−2i−2i102i3−2i3001-1-1−i3−i3i3i30000000000002i−2i0023−23−i−iii−3−333000000000000000000000000000000
χ774-44-4444-4-44-4-44-4-4404440000-4-400004-4-4-4-44400000000400000-44-4000000000000000000000000000000000000000000000000000000000000
χ784-44-444-2-42-2-4-44-42404-2-20000-4-40000-22222-2400000000-2000002-2200000000000000−2i32i300000000000000000000000000−2i32i30000000000000000
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Here i is the imaginary unit (i² = −1).