Finite Group Databasebeta

← Group #72220327

Character table — Group #72220327

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size114444444488888888999916161616181818181818181836363636363636363636363636363636363636363636363672727272727272728181162162162162
order123333666633336666222233662222444466666666666666661212121212121212666612121212224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111
χ8111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1
χ91-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1i−ii−i11-1-111-1-111-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i1-1i−ii−i
χ101-11111-1-1-1-11111-1-1-1-111-1-111-1-11-11-1−ii−ii11-1-111-1-111-1-111-1-1−i−iii−i−iii1-11-1−ii−ii1-1−ii−ii
χ111-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11-11i−ii−i11-1-111-1-1-1-111-1-111ii−i−iii−i−i-11-11i−ii−i1-1−ii−ii
χ121-11111-1-1-1-11111-1-1-1-111-1-111-1-1-11-11−ii−ii11-1-111-1-1-1-111-1-111−i−iii−i−iii-11-11−ii−ii1-1i−ii−i
χ131-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-11i−i−ii-1-111-1-11111-1-1-1-111ii−i−i−i−iii1-1-11i−i−ii1-1i−i−ii
χ141-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-1-11−iii−i-1-111-1-11111-1-1-1-111−i−iiiii−i−i1-1-11−iii−i1-1−iii−i
χ151-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1i−i−ii-1-111-1-111-1-11111-1-1ii−i−i−i−iii-111-1i−i−ii1-1−iii−i
χ161-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1−iii−i-1-111-1-111-1-11111-1-1−i−iiiii−i−i-111-1−iii−i1-1i−i−ii
χ172222222222222222222-22-22222000000002-22-22-22-2000000000000000000000000-2-20000
χ18222222222222222222-22-22222200000000-22-22-22-22000000000000000000000000-2-20000
χ192-22222-2-2-2-22222-2-2-2-22-2-2222-2-2000000002-2-222-2-22000000000000000000000000-220000
χ202-22222-2-2-2-22222-2-2-2-2-222-222-2-200000000-222-2-222-2000000000000000000000000-220000
χ2144144-24-21411-2-2-2-21104041-21-20000222201010-20-2000000002-12-12-12-10000-1-1-1-1000000
χ2244144-24-21411-2-2-2-21104041-21-20000-2-2-2-201010-20-200000000-21-21-21-2100001111000000
χ2344144-24-21411-2-2-2-2110-40-41-21-2000022-2-20-10-10202000000002-12-1-21-210000-1-111000000
χ2444144-24-21411-2-2-2-2110-40-41-21-20000-2-2220-10-1020200000000-21-212-12-1000011-1-1000000
χ254441-24-244111-2-2-2-2114040-21-21000022221010-20-2000000000-12-12-12-120000-1-1-1-1000000
χ264441-24-244111-2-2-2-2114040-21-210000-2-2-2-21010-20-20000000001-21-21-21-200001111000000
χ274441-24-244111-2-2-2-211-40-40-21-21000022-2-2-10-10202000000000-12-121-21-20000-1-111000000
χ284441-24-244111-2-2-2-211-40-40-21-210000-2-222-10-102020000000001-21-2-12-12000011-1-1000000
χ29444-214144-2-2-21111-2-240401-21-222220000-20-201010-12-12-12-1200000000-1-1-1-10000000000
χ30444-214144-2-2-21111-2-240401-21-2-2-2-2-20000-20-2010101-21-21-21-20000000011110000000000
χ31444-214144-2-2-21111-2-2-40-401-21-222-2-200002020-10-10-12-121-21-200000000-1-1110000000000
χ32444-214144-2-2-21111-2-2-40-401-21-2-2-22200002020-10-101-21-2-12-120000000011-1-10000000000
χ3344-244141-24-2-21111-2-20404-21-21222200000-20-201012-12-12-12-100000000-1-1-1-10000000000
χ3444-244141-24-2-21111-2-20404-21-21-2-2-2-200000-20-20101-21-21-21-210000000011110000000000
χ3544-244141-24-2-21111-2-20-40-4-21-2122-2-2000002020-10-12-12-1-21-2100000000-1-1110000000000
χ3644-244141-24-2-21111-2-20-40-4-21-21-2-222000002020-10-1-21-212-12-10000000011-1-10000000000
χ374-4144-2-42-1-411-2-222-1-1040-41-2-1200002i−2i2i−2i010-10-202000000002i−i−2ii2i−i−2ii0000−ii−ii000000
χ384-4144-2-42-1-411-2-222-1-1040-41-2-120000−2i2i−2i2i010-10-20200000000−2ii2i−i−2ii2i−i0000i−ii−i000000
χ394-4144-2-42-1-411-2-222-1-10-4041-2-1200002i−2i−2i2i0-101020-2000000002i−i−2ii−2ii2i−i0000−iii−i000000
χ404-4144-2-42-1-411-2-222-1-10-4041-2-120000−2i2i2i−2i0-101020-200000000−2ii2i−i2i−i−2ii0000i−i−ii000000
χ414-441-242-4-4-111-2-222-1-140-40-212-100002i−2i2i−2i10-10-202000000000−i2ii−2i−i2ii−2i0000−ii−ii000000
χ424-441-242-4-4-111-2-222-1-140-40-212-10000−2i2i−2i2i10-10-202000000000i−2i−i2ii−2i−i2i0000i−ii−i000000
χ434-441-242-4-4-111-2-222-1-1-4040-212-100002i−2i−2i2i-101020-2000000000−i2ii−2ii−2i−i2i0000−iii−i000000
χ444-441-242-4-4-111-2-222-1-1-4040-212-10000−2i2i2i−2i-101020-2000000000i−2i−i2i−i2ii−2i0000i−i−ii000000
χ454-44-214-1-4-42-2-211-1-12240-401-2-122-22-20000-202010-10-121-2-121-200000000-11-110000000000
χ464-44-214-1-4-42-2-211-1-12240-401-2-12-22-220000-202010-101-2-121-2-12000000001-11-10000000000
χ474-44-214-1-4-42-2-211-1-122-40401-2-122-2-22000020-20-1010-121-21-2-1200000000-111-10000000000
χ484-44-214-1-4-42-2-211-1-122-40401-2-12-222-2000020-20-10101-2-12-121-2000000001-1-110000000000
χ494-4-2441-4-12-4-2-211-1-122040-4-212-12-22-200000-202010-12-1-212-1-2100000000-11-110000000000
χ504-4-2441-4-12-4-2-211-1-122040-4-212-1-22-2200000-202010-1-212-1-212-1000000001-11-10000000000
χ514-4-2441-4-12-4-2-211-1-1220-404-212-12-2-220000020-20-1012-1-21-212-100000000-111-10000000000
χ524-4-2441-4-12-4-2-211-1-1220-404-212-1-222-20000020-20-101-212-12-1-21000000001-1-110000000000
χ538822-4-4-4-4225-422225-40000-1-1-1-10000004400000000000000000000-2-2-2-200000011000000
χ548822-4-4-4-4225-422225-40000-1-1-1-1000000-4-4000000000000000000002222000000-1-1000000
χ558822-4-4-4-422-452222-450000-1-1-1-1000044000000000000000000-2-2-2-2000000001100000000
χ568822-4-4-4-422-452222-450000-1-1-1-10000-4-4000000000000000000222200000000-1-100000000
χ5788-4-42222-4-4225-45-4220000-1-1-1-100440000000000000000-2-2-2-20000000000110000000000
χ5888-4-42222-4-4225-45-4220000-1-1-1-100-4-4000000000000000022220000000000-1-10000000000
χ5988-4-42222-4-422-45-45220000-1-1-1-14400000000000000-2-2-2-200000000000011000000000000
χ6088-4-42222-4-422-45-45220000-1-1-1-1-4-4000000000000002222000000000000-1-1000000000000
χ618-822-4-444-2-25-422-2-2-540000-1-1110000004i−4i00000000000000000000−2i−2i2i2i000000i−i000000
χ628-822-4-444-2-25-422-2-2-540000-1-111000000−4i4i000000000000000000002i2i−2i−2i000000−ii000000
χ638-822-4-444-2-2-4522-2-24-50000-1-11100004i−4i000000000000000000−2i−2i2i2i00000000i−i00000000
χ648-822-4-444-2-2-4522-2-24-50000-1-1110000−4i4i0000000000000000002i2i−2i−2i00000000−ii00000000
χ658-8-4-422-2-244225-4-54-2-20000-1-111004-40000000000000000-2-22200000000001-10000000000
χ668-8-4-422-2-244225-4-54-2-20000-1-11100-44000000000000000022-2-20000000000-110000000000
χ678-8-4-422-2-24422-454-5-2-20000-1-1114-400000000000000-2-2220000000000001-1000000000000
χ688-8-4-422-2-24422-454-5-2-20000-1-111-440000000000000022-2-2000000000000-11000000000000
χ6916164-84-84-84-8-2-2-2-2-2-2-2-2000014140000000000000000000000000000000000000000000000
χ701616-84-84-84-84-2-2-2-2-2-2-2-2000041410000000000000000000000000000000000000000000000
χ7116-164-84-8-48-48-2-2-2-22222000014-1-40000000000000000000000000000000000000000000000
χ7216-16-84-848-48-4-2-2-2-22222000041-4-10000000000000000000000000000000000000000000000

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