Finite Group Databasebeta

← Group #72241520

Character table — Group #72241520

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122333366666666888888889912121212161618181818181818181818242424242424242436363636484848484848484848484848484854545454646464646464108108108108108108108108144144144144
order123622224444666633336666221212121236444444446666666666121212126612121212121212121212121244443336662244444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ411111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ51-11-1-1-111i−ii−i11-1-11111-1-1-1-1-11i−ii−i1-1i−ii−ii−ii−i1-11111-1-1-1-1i−ii−i1-1iii−i−i−iiii−i−i−ii−ii−i111-1-1-11-111-1-11-1i−ii−i
χ61-11-1-1-111i−ii−i11-1-11111-1-1-1-1-11i−ii−i1-1i−i−iii−i−ii1-11111-1-1-1-1i−ii−i1-1iii−i−i−iiii−i−i−i−ii−ii111-1-1-1-11-1-111-11−ii−ii
χ71-11-1-1-111−ii−ii11-1-11111-1-1-1-1-11−ii−ii1-1−iii−i−iii−i1-11111-1-1-1-1−ii−ii1-1−i−i−iiii−i−i−iiiii−ii−i111-1-1-1-11-1-111-11i−ii−i
χ81-11-1-1-111−ii−ii11-1-11111-1-1-1-1-11−ii−ii1-1−ii−ii−ii−ii1-11111-1-1-1-1−ii−ii1-1−i−i−iiii−i−i−iiii−ii−ii111-1-1-11-111-1-11-1−ii−ii
χ92222222200002222222-1222-1220000-1-10022002222222-1222-10000-1-10000000000002222-1-1-1-1-1-100000000-1-1-1-1
χ102222222200002222222-1222-1220000-1-100-2-200-2-222222-1222-10000-1-1000000000000-2-2-2-2-1-1-1-1-1-1000000001111
χ112222222222222222-1-1-12-1-1-12222222222200220022-1-1-12-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1000000000000
χ1222222222-2-2-2-22222-1-1-12-1-1-1222-2-2-2-222-2-200-2-20022-1-1-12-1-1-12-2-2-2-2221111111111110000-1-1-1-1-1-1000000000000
χ1322-1-122222222-1-1-1-12-1-122-1-1222-1-1-1-1-1-122002200-1-12-1-122-1-12-1-1-1-1-1-12-1-12-1-12-1-12-1-100002-1-12-1-1000000000000
χ1422-1-122222222-1-1-1-1-12-12-12-1222-1-1-1-1-1-122002200-1-1-12-12-12-12-1-1-1-1-1-1-12-1-12-1-12-1-12-10000-12-1-12-1000000000000
χ1522-1-122222222-1-1-1-1-1-122-1-12222-1-1-1-1-1-122002200-1-1-1-122-1-122-1-1-1-1-1-1-1-12-1-12-1-12-1-120000-1-12-1-12000000000000
χ1622-1-12222-2-2-2-2-1-1-1-12-1-122-1-12221111-1-1-2-200-2-200-1-12-1-122-1-121111-1-1-211-211-211-21100002-1-12-1-1000000000000
χ1722-1-12222-2-2-2-2-1-1-1-1-12-12-12-12221111-1-1-2-200-2-200-1-1-12-12-12-121111-1-11-211-211-211-210000-12-1-12-1000000000000
χ1822-1-12222-2-2-2-2-1-1-1-1-1-122-1-122221111-1-1-2-200-2-200-1-1-1-122-1-1221111-1-111-211-211-211-20000-1-12-1-12000000000000
χ192-22-2-2-222000022-2-2222-1-2-2-21-220000-11002i−2i002i−2i2-2222-1-2-2-210000-110000000000002i−2i2i−2i-1-1-111100000000−ii−ii
χ202-22-2-2-222000022-2-2222-1-2-2-21-220000-1100−2i2i00−2i2i2-2222-1-2-2-210000-11000000000000−2i2i−2i2i-1-1-111100000000i−ii−i
χ212-22-2-2-2222i−2i2i−2i22-2-2-1-1-12111-2-222i−2i2i−2i2-22i−2i002i−2i002-2-1-1-12111-22i−2i2i−2i2-2−i−i−iiii−i−i−iiii0000-1-1-1111000000000000
χ222-22-2-2-222−2i2i−2i2i22-2-2-1-1-12111-2-22−2i2i−2i2i2-2−2i2i00−2i2i002-2-1-1-12111-2−2i2i−2i2i2-2iii−i−i−iiii−i−i−i0000-1-1-1111000000000000
χ232-2-11-2-2222i−2i2i−2i-1-1112-1-12-211-2-22−ii−ii-112i−2i002i−2i00-112-1-12-211-2−ii−ii-112i−i−i−2iii2i−i−i−2iii00002-1-1-211000000000000
χ242-2-11-2-2222i−2i2i−2i-1-111-12-121-21-2-22−ii−ii-112i−2i002i−2i00-11-12-121-21-2−ii−ii-11−i2i−ii−2ii−i2i−ii−2ii0000-12-11-21000000000000
χ252-2-11-2-2222i−2i2i−2i-1-111-1-12211-2-2-22−ii−ii-112i−2i002i−2i00-11-1-12211-2-2−ii−ii-11−i−i2iii−2i−i−i2iii−2i0000-1-1211-2000000000000
χ262-2-11-2-222−2i2i−2i2i-1-1112-1-12-211-2-22i−ii−i-11−2i2i00−2i2i00-112-1-12-211-2i−ii−i-11−2iii2i−i−i−2iii2i−i−i00002-1-1-211000000000000
χ272-2-11-2-222−2i2i−2i2i-1-111-12-121-21-2-22i−ii−i-11−2i2i00−2i2i00-11-12-121-21-2i−ii−i-11i−2ii−i2i−ii−2ii−i2i−i0000-12-11-21000000000000
χ282-2-11-2-222−2i2i−2i2i-1-111-1-12211-2-2-22i−ii−i-11−2i2i00−2i2i00-11-1-12211-2-2i−ii−i-11ii−2i−i−i2iii−2i−i−i2i0000-1-1211-2000000000000
χ2933333-13-133333-1-1300030003-1-1333333-1-111-1-1-1-1-1-1000-1000-1-1-1-1-1-1-100000000000011-1-1000000111-11-1-1-111-1-1
χ3033333-13-133333-1-1300030003-1-1333333-1-1-1-1-1-111-1-1000-1000-1-1-1-1-1-1-1000000000000-1-111000000-1-1-11-1111-1-111
χ3133333-13-1-3-3-3-33-1-1300030003-1-1-3-3-3-333111111-1-1-1-1000-1000-11111-1-100000000000011-1-1000000-1-1-11-111111-1-1
χ3233333-13-1-3-3-3-33-1-1300030003-1-1-3-3-3-33311-1-11111-1-1000-1000-11111-1-1000000000000-1-111000000111-11-1-1-1-1-111
χ333333-13-1311-1-1-133-133303330-1-111-1-1001133-1-133-1-1-1-1-10-1-1-1011-1-100111111-1-1-1-1-1-1-1-1-1-100000011-11-11-1-10000
χ343333-13-1311-1-1-133-133303330-1-111-1-10011-3-3-1-1-3-3-1-1-1-1-10-1-1-1011-1-100111111-1-1-1-1-1-11111000000-1-11-11-1110000
χ353333-13-13-1-111-133-133303330-1-1-1-11100-1-1331133-1-1-1-1-10-1-1-10-1-11100-1-1-1-1-1-1111111-1-1-1-1000000-1-11-11-1110000
χ363333-13-13-1-111-133-133303330-1-1-1-11100-1-1-3-311-3-3-1-1-1-1-10-1-1-10-1-11100-1-1-1-1-1-1111111111100000011-11-11-1-10000
χ373-33-31-3-13i−i−ii-13-313330-3-3-301-1i−i−ii00i−i3i−3i−ii3i−3i-11-1-1-101110i−i−ii00iii−i−i−i−i−i−iiii−ii−ii0000001-1-111-1-110000
χ383-33-31-3-13i−i−ii-13-313330-3-3-301-1i−i−ii00i−i−3i3i−ii−3i3i-11-1-1-101110i−i−ii00iii−i−i−i−i−i−iiiii−ii−i000000-111-1-111-10000
χ393-33-31-3-13−iii−i-13-313330-3-3-301-1−iii−i00−ii3i−3ii−i3i−3i-11-1-1-101110−iii−i00−i−i−iiiiiii−i−i−i−ii−ii000000-111-1-111-10000
χ403-33-31-3-13−iii−i-13-313330-3-3-301-1−iii−i00−ii−3i3ii−i−3i3i-11-1-1-101110−iii−i00−i−i−iiiiiii−i−i−ii−ii−i0000001-1-111-1-110000
χ413-33-3-313-13i−3i3i−3i3-11-30003000-31-13i−3i3i−3i3-3−iii−i−ii−ii-11000-10001−ii−ii-11000000000000i−i−ii0000001-11-1-11-11i−i−ii
χ423-33-3-313-13i−3i3i−3i3-11-30003000-31-13i−3i3i−3i3-3−ii−ii−iii−i-11000-10001−ii−ii-11000000000000−iii−i000000-11-111-11-1−iii−i
χ433-33-3-313-1−3i3i−3i3i3-11-30003000-31-1−3i3i−3i3i3-3i−ii−ii−i−ii-11000-10001i−ii−i-11000000000000i−i−ii000000-11-111-11-1i−i−ii
χ443-33-3-313-1−3i3i−3i3i3-11-30003000-31-1−3i3i−3i3i3-3i−i−iii−ii−i-11000-10001i−ii−i-11000000000000−iii−i0000001-11-1-11-11−iii−i
χ454444444400004444-2-2-2-2-2-2-2-2440000-2-20000000044-2-2-2-2-2-2-2-20000-2-20000000000000000111111000000000000
χ4644-2-244440000-2-2-2-24-2-2-24-2-2-24400001100000000-2-24-2-2-24-2-2-20000110000000000000000-211-211000000000000
χ4744-2-244440000-2-2-2-2-24-2-2-24-2-24400001100000000-2-2-24-2-2-24-2-200001100000000000000001-211-21000000000000
χ4844-2-244440000-2-2-2-2-2-24-2-2-24-24400001100000000-2-2-2-24-2-2-24-2000011000000000000000011-211-2000000000000
χ494-44-4-4-444000044-4-4-2-2-2-22222-440000-22000000004-4-2-2-2-222220000-220000000000000000111-1-1-1000000000000
χ504-4-22-4-4440000-2-2224-2-2-2-4222-4400001-100000000-224-2-2-2-422200001-10000000000000000-2112-1-1000000000000
χ514-4-22-4-4440000-2-222-24-2-22-422-4400001-100000000-22-24-2-22-42200001-100000000000000001-21-12-1000000000000
χ524-4-22-4-4440000-2-222-2-24-222-42-4400001-100000000-22-2-24-222-4200001-1000000000000000011-2-1-12000000000000
χ5366666-26-200006-2-26000-3000-3-2-20000-3-3002200-2-2-2-20001000100001100000000000022-2-200000000000000-1-111
χ5466666-26-200006-2-26000-3000-3-2-20000-3-300-2-20022-2-200010001000011000000000000-2-2220000000000000011-1-1
χ556666-26-2622-2-2-266-2-3-3-30-3-3-30-2-222-2-2002200-2-200-2-21110111022-2-200-1-1-1-1-1-11111110000000000000000000000
χ566666-26-26-2-222-266-2-3-3-30-3-3-30-2-2-2-22200-2-2002200-2-211101110-2-22200111111-1-1-1-1-1-10000000000000000000000
χ5766-3-36-26-26666-311-300060006-2-2-3-3-3-3-3-3-2-200-2-20011000-2000-21111110000000000000000000000000000000000
χ5866-3-36-26-2-6-6-6-6-311-300060006-2-23333-3-32200220011000-2000-2-1-1-1-1110000000000000000000000000000000000
χ5966-3-3-26-2622-2-21-3-316-3-306-3-30-2-2-1-111002200-2-20011-2110-2110-1-111002-1-12-1-1-211-2110000000000000000000000
χ6066-3-3-26-2622-2-21-3-31-36-30-36-30-2-2-1-111002200-2-200111-2101-210-1-11100-12-1-12-11-211-210000000000000000000000
χ6166-3-3-26-2622-2-21-3-31-3-360-3-360-2-2-1-111002200-2-2001111-2011-20-1-11100-1-12-1-1211-211-20000000000000000000000
χ6266-3-3-26-26-2-2221-3-316-3-306-3-30-2-211-1-100-2-200220011-2110-211011-1-100-211-2112-1-12-1-10000000000000000000000
χ6366-3-3-26-26-2-2221-3-31-36-30-36-30-2-211-1-100-2-2002200111-2101-21011-1-1001-211-21-12-1-12-10000000000000000000000
χ6466-3-3-26-26-2-2221-3-31-3-360-3-360-2-211-1-100-2-20022001111-2011-2011-1-10011-211-2-1-12-1-120000000000000000000000
χ656-66-62-6-262i−2i−2i2i-26-62-3-3-3033302-22i−2i−2i2i002i−2i00−2i2i00-221110-1-1-102i−2i−2i2i00−i−i−iiiiiii−i−i−i0000000000000000000000
χ666-66-62-6-26−2i2i2i−2i-26-62-3-3-3033302-2−2i2i2i−2i00−2i2i002i−2i00-221110-1-1-10−2i2i2i−2i00iii−i−i−i−i−i−iiii0000000000000000000000
χ676-66-6-626-200006-22-6000-300032-20000-33002i−2i00−2i2i-220001000-100001-10000000000002i−2i−2i2i00000000000000−iii−i
χ686-66-6-626-200006-22-6000-300032-20000-3300−2i2i002i−2i-220001000-100001-1000000000000−2i2i2i−2i00000000000000i−i−ii
χ696-6-332-6-262i−2i−2i2i1-33-16-3-30-63302-2−iii−i002i−2i00−2i2i001-1-21102-1-10−iii−i002i−i−i−2iii−2iii2i−i−i0000000000000000000000
χ706-6-332-6-262i−2i−2i2i1-33-1-36-303-6302-2−iii−i002i−2i00−2i2i001-11-210-12-10−iii−i00−i2i−ii−2iii−2ii−i2i−i0000000000000000000000
χ716-6-332-6-262i−2i−2i2i1-33-1-3-36033-602-2−iii−i002i−2i00−2i2i001-111-20-1-120−iii−i00−i−i2iii−2iii−2i−i−i2i0000000000000000000000
χ726-6-332-6-26−2i2i2i−2i1-33-16-3-30-63302-2i−i−ii00−2i2i002i−2i001-1-21102-1-10i−i−ii00−2iii2i−i−i2i−i−i−2iii0000000000000000000000
χ736-6-332-6-26−2i2i2i−2i1-33-1-36-303-6302-2i−i−ii00−2i2i002i−2i001-11-210-12-10i−i−ii00i−2ii−i2i−i−i2i−ii−2ii0000000000000000000000
χ746-6-332-6-26−2i2i2i−2i1-33-1-3-36033-602-2i−i−ii00−2i2i002i−2i001-111-20-1-120i−i−ii00ii−2i−i−i2i−i−i2iii−2i0000000000000000000000
χ756-6-33-626-26i−6i6i−6i-31-130006000-62-2−3i3i−3i3i-33−2i2i00−2i2i001-1000-20002i−ii−i1-10000000000000000000000000000000000
χ766-6-33-626-2−6i6i−6i6i-31-130006000-62-23i−3i3i−3i-332i−2i002i−2i001-1000-20002−ii−ii1-10000000000000000000000000000000000
χ779999-3-3-3-333-3-3-3-3-3-3000000001133-3-300-1-13311-3-31100000000-1-11100000000000000-1-11100000011-1-1-1-1110000
χ789999-3-3-3-333-3-3-3-3-3-3000000001133-3-300-1-1-3-311331100000000-1-1110000000000000011-1-1000000-1-11111-1-10000
χ799999-3-3-3-3-3-333-3-3-3-30000000011-3-333001133-1-1-3-3110000000011-1-100000000000000-1-111000000-1-11111-1-10000
χ809999-3-3-3-3-3-333-3-3-3-30000000011-3-3330011-3-3-1-133110000000011-1-10000000000000011-1-100000011-1-1-1-1110000
χ819-99-933-3-33i−3i−3i3i-3-33300000000-113i−3i−3i3i00−ii3i−3ii−i−3i3i1-100000000−iii−i00000000000000−iii−i0000001-1-1-1111-10000
χ829-99-933-3-33i−3i−3i3i-3-33300000000-113i−3i−3i3i00−ii−3i3ii−i3i−3i1-100000000−iii−i00000000000000i−i−ii000000-1111-1-1-110000
χ839-99-933-3-3−3i3i3i−3i-3-33300000000-11−3i3i3i−3i00i−i3i−3i−ii−3i3i1-100000000i−i−ii00000000000000−iii−i000000-1111-1-1-110000
χ849-99-933-3-3−3i3i3i−3i-3-33300000000-11−3i3i3i−3i00i−i−3i3i−ii3i−3i1-100000000i−i−ii00000000000000i−i−ii0000001-1-1-1111-10000
χ851212-6-612-412-40000-622-6000-6000-6-4-40000330000000022000200020000-1-10000000000000000000000000000000000
χ8612-12-66-12412-40000-62-26000-600064-400003-3000000002-20002000-20000-110000000000000000000000000000000000
χ871818-9-9-6-6-6-666-6-633330000000022-3-33300-2-2002200-1-10000000011-1-1000000000000000000000000000000000000
χ881818-9-9-6-6-6-6-6-6663333000000002233-3-3002200-2-200-1-100000000-1-111000000000000000000000000000000000000
χ8918-18-9966-6-66i−6i−6i6i33-3-300000000-22−3i3i3i−3i00−2i2i002i−2i00-1100000000i−i−ii000000000000000000000000000000000000
χ9018-18-9966-6-6−6i6i6i−6i33-3-300000000-223i−3i−3i3i002i−2i00−2i2i00-1100000000−iii−i000000000000000000000000000000000000

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