Finite Group Databasebeta

← Group #72220737

Character table — Group #72220737

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1144444444668888888899991212121212121212121216161616242424242424242436363636363636365454545454548181108108108108108108162162162162
order123333666644333366662222121212121212121212123366121212121212121266666666444444221212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1-1-1−i−iii−i−iii
χ51111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-11111-1-1-1-1
χ61111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i-1-111ii−i−i−i−iii
χ81111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iii-1-111−i−iiiii−i−i
χ91-11111-1-1-1-1i−i1111-1-1-1-11-11-1iiii−i−i−i−ii−i11-1-1iiii−i−i−i−i11-1-111-1-1i−ii−ii−i-11i−ii−ii−i1-11-1
χ101-11111-1-1-1-1i−i1111-1-1-1-11-11-1iiii−i−i−i−ii−i11-1-1iiii−i−i−i−i11-1-111-1-1i−i−ii−ii-11i−i−ii−ii-11-11
χ111-11111-1-1-1-1i−i1111-1-1-1-11-1-11iiii−i−i−i−ii−i11-1-1iiii−i−i−i−i11-1-1-1-111−ii1-1-111-1−ii1-1-11−iii−i
χ121-11111-1-1-1-1i−i1111-1-1-1-11-1-11iiii−i−i−i−ii−i11-1-1iiii−i−i−i−i11-1-1-1-111−ii-111-11-1−ii-111-1i−i−ii
χ131-11111-1-1-1-1−ii1111-1-1-1-11-11-1−i−i−i−iiiii−ii11-1-1−i−i−i−iiiii11-1-111-1-1−iii−ii−i-11−iii−ii−i-11-11
χ141-11111-1-1-1-1−ii1111-1-1-1-11-11-1−i−i−i−iiiii−ii11-1-1−i−i−i−iiiii11-1-111-1-1−ii−ii−ii-11−ii−ii−ii1-11-1
χ151-11111-1-1-1-1−ii1111-1-1-1-11-1-11−i−i−i−iiiii−ii11-1-1−i−i−i−iiiii11-1-1-1-111i−i1-1-111-1i−i1-1-11i−i−ii
χ161-11111-1-1-1-1−ii1111-1-1-1-11-1-11−i−i−i−iiiii−ii11-1-1−i−i−i−iiiii11-1-1-1-111i−i-111-11-1i−i-111-1−iii−i
χ1722222222220022222222-2-2220000000000222200000000-2-2-2-22222000000-2-20000000000
χ1822222222220022222222-2-2-2-20000000000222200000000-2-2-2-2-2-2-2-2000000220000000000
χ192-22222-2-2-2-2002222-2-2-2-2-222-2000000000022-2-200000000-2-22222-2-20000002-20000000000
χ202-22222-2-2-2-2002222-2-2-2-2-22-22000000000022-2-200000000-2-222-2-222000000-220000000000
χ2144144-2144-200-2-2-2-2-2-2-2-20044000000000011110000000000001-2-210022220000-1-1-1-10000
χ2244144-2144-200-2-2-2-2-2-2-2-20044000000000011110000000000001-2-2100-2-2-2-2000011110000
χ2344144-2144-200-2-2-2-2-2-2-2-200-4-400000000001111000000000000-122-1002i2i−2i−2i0000−i−iii0000
χ2444144-2144-200-2-2-2-2-2-2-2-200-4-400000000001111000000000000-122-100−2i−2i2i2i0000ii−i−i0000
χ254441-2441-240011-2-211-2-2-4-400003-3003-3001-21-2003-3003-32-12-10000000000000000000000
χ264441-2441-240011-2-211-2-2-4-40000-3300-33001-21-200-3300-332-12-10000000000000000000000
χ274441-2441-244411-2-211-2-24400-2-211-2-211441-21-2-2-211-2-211-21-210000000000000000000000
χ284441-2441-24-4-411-2-211-2-2440022-1-122-1-1-4-41-21-222-1-122-1-1-21-210000000000000000000000
χ29444-2144-21400-2-211-2-211-4-4003-3003-30000-21-213-3003-300-12-120000000000000000000000
χ30444-2144-21400-2-211-2-211-4-400-3300-330000-21-21-3300-3300-12-120000000000000000000000
χ31444-2144-21444-2-211-2-211440011-2-211-2-244-21-2111-2-211-2-21-21-20000000000000000000000
χ32444-2144-214-4-4-2-211-2-2114400-1-122-1-122-4-4-21-21-1-122-1-1221-21-20000000000000000000000
χ3344-2441-24412211111111004422222222-1-1-2-2-2-2-1-1-1-1-1-1-1-10000-211-222000000-1-100000000
χ3444-2441-2441221111111100-4-422222222-1-1-2-2-2-2-1-1-1-1-1-1-1-100002-1-12-2-20000001100000000
χ3544-2441-2441-2-2111111110044-2-2-2-2-2-2-2-211-2-2-2-2111111110000-211-2-2-20000001100000000
χ3644-2441-2441-2-21111111100-4-4-2-2-2-2-2-2-2-211-2-2-2-21111111100002-1-1222000000-1-100000000
χ374-4144-2-1-4-4200-2-2-2-22222004-4000000000011-1-10000000000001-22-1002i−2i2i−2i0000−ii−ii0000
χ384-4144-2-1-4-4200-2-2-2-22222004-4000000000011-1-10000000000001-22-100−2i2i−2i2i0000i−ii−i0000
χ394-4144-2-1-4-4200-2-2-2-2222200-44000000000011-1-1000000000000-12-21002-2-220000-111-10000
χ404-4144-2-1-4-4200-2-2-2-2222200-44000000000011-1-1000000000000-12-2100-222-200001-1-110000
χ414-441-24-4-12-40011-2-2-1-122-4400003i−3i00−3i3i001-2-12003i−3i00−3i3i2-1-210000000000000000000000
χ424-441-24-4-12-40011-2-2-1-122-440000−3i3i003i−3i001-2-1200−3i3i003i−3i2-1-210000000000000000000000
χ434-441-24-4-12-44i−4i11-2-2-1-1224-400−2i−2iii2i2i−i−i4i−4i1-2-12−2i−2iii2i2i−i−i-212-10000000000000000000000
χ444-441-24-4-12-4−4i4i11-2-2-1-1224-4002i2i−i−i−2i−2iii−4i4i1-2-122i2i−i−i−2i−2iii-212-10000000000000000000000
χ454-44-214-42-1-400-2-21122-1-1-44003i−3i00−3i3i0000-212-13i−3i00−3i3i00-121-20000000000000000000000
χ464-44-214-42-1-400-2-21122-1-1-4400−3i3i003i−3i0000-212-1−3i3i003i−3i00-121-20000000000000000000000
χ474-44-214-42-1-44i−4i-2-21122-1-14-400ii−2i−2i−i−i2i2i4i−4i-212-1ii−2i−2i−i−i2i2i1-2-120000000000000000000000
χ484-44-214-42-1-4−4i4i-2-21122-1-14-400−i−i2i2iii−2i−2i−4i4i-212-1−i−i2i2iii−2i−2i1-2-120000000000000000000000
χ494-4-24412-4-4-12i−2i1111-1-1-1-1004-42i2i2i2i−2i−2i−2i−2i−ii-2-222−i−i−i−iiiii0000-21-122i−2i000000−ii00000000
χ504-4-24412-4-4-12i−2i1111-1-1-1-100-442i2i2i2i−2i−2i−2i−2i−ii-2-222−i−i−i−iiiii00002-11-2−2i2i000000i−i00000000
χ514-4-24412-4-4-1−2i2i1111-1-1-1-1004-4−2i−2i−2i−2i2i2i2i2ii−i-2-222iiii−i−i−i−i0000-21-12−2i2i000000i−i00000000
χ524-4-24412-4-4-1−2i2i1111-1-1-1-100-44−2i−2i−2i−2i2i2i2i2ii−i-2-222iiii−i−i−i−i00002-11-22i−2i000000−ii00000000
χ5388-42-42-42-42445-4-1-15-4-1-10000-2-24-2-2-24-2-2-2-12-1211-2111-2100000000000000000000000000
χ5488-42-42-42-4244-45-1-1-45-1-10000-2-2-24-2-2-24-2-2-12-12111-2111-200000000000000000000000000
χ5588-42-42-42-42-4-45-4-1-15-4-1-1000022-4222-4222-12-12-1-12-1-1-12-100000000000000000000000000
χ5688-42-42-42-42-4-4-45-1-1-45-1-10000222-4222-422-12-12-1-1-12-1-1-1200000000000000000000000000
χ5788-4-422-4-42244-1-15-4-1-15-400004-2-2-24-2-2-2-2-22-12-1-2111-211100000000000000000000000000
χ5888-4-422-4-42244-1-1-45-1-1-450000-24-2-2-24-2-2-2-22-12-11-2111-21100000000000000000000000000
χ5988-4-422-4-422-4-4-1-15-4-1-15-40000-4222-4222222-12-12-1-1-12-1-1-100000000000000000000000000
χ6088-4-422-4-422-4-4-1-1-45-1-1-4500002-4222-422222-12-1-12-1-1-12-1-100000000000000000000000000
χ618-8-42-424-24-24i−4i5-4-1-1-54110000−2i−2i4i−2i2i2i−4i2i−2i2i-121-2ii−2ii−i−i2i−i00000000000000000000000000
χ628-8-42-424-24-24i−4i-45-1-14-5110000−2i−2i−2i4i2i2i2i−4i−2i2i-121-2iii−2i−i−i−i2i00000000000000000000000000
χ638-8-42-424-24-2−4i4i5-4-1-1-541100002i2i−4i2i−2i−2i4i−2i2i−2i-121-2−i−i2i−iii−2ii00000000000000000000000000
χ648-8-42-424-24-2−4i4i-45-1-14-51100002i2i2i−4i−2i−2i−2i4i2i−2i-121-2−i−i−i2iiii−2i00000000000000000000000000
χ658-8-4-42244-2-24i−4i-1-15-411-5400004i−2i−2i−2i−4i2i2i2i−2i2i2-1-21−2iiii2i−i−i−i00000000000000000000000000
χ668-8-4-42244-2-24i−4i-1-1-45114-50000−2i4i−2i−2i2i−4i2i2i−2i2i2-1-21i−2iii−i2i−i−i00000000000000000000000000
χ678-8-4-42244-2-2−4i4i-1-15-411-540000−4i2i2i2i4i−2i−2i−2i2i−2i2-1-212i−i−i−i−2iiii00000000000000000000000000
χ688-8-4-42244-2-2−4i4i-1-1-45114-500002i−4i2i2i−2i4i−2i−2i2i−2i2-1-21−i2i−i−ii−2iii00000000000000000000000000
χ69161644-8-844-8-800-2-244-2-244000000000000001-21-20000000000000000000000000000000000
χ7016164-84-84-84-80044-2-244-2-200000000000000-21-210000000000000000000000000000000000
χ7116-1644-8-8-4-48800-2-24422-4-4000000000000001-2-120000000000000000000000000000000000
χ7216-164-84-8-48-480044-2-2-4-42200000000000000-212-10000000000000000000000000000000000

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