Finite Group Databasebeta

← Group #72220549

Character table — Group #72220549

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size114444444488888888999916161616181818181818181836363636363636363636363636363636363636363636363672727272727272728181162162162162
order123333666633336666222233664444444466666666121212121212121212121212121212121212121212121212224444
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
χ91-11111-1-1-1-11111-1-1-1-111-1-111-1-1i−ii−ii−ii−i1111-1-1-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i-111-11-1
χ101-11111-1-1-1-11111-1-1-1-111-1-111-1-1i−ii−i−ii−ii1111-1-1-1-1ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii-11-11-11
χ111-11111-1-1-1-11111-1-1-1-111-1-111-1-1−ii−iii−ii−i1111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i-11-11-11
χ121-11111-1-1-1-11111-1-1-1-111-1-111-1-1−ii−ii−ii−ii1111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii-111-11-1
χ131-11111-1-1-1-11111-1-1-1-1-1-11111-1-1i−i−iii−i−ii-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiii−i−iii−i−ii-111-1-11
χ141-11111-1-1-1-11111-1-1-1-1-1-11111-1-1i−i−ii−iii−i-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i-11-111-1
χ151-11111-1-1-1-11111-1-1-1-1-1-11111-1-1−iii−ii−i−ii-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii-11-111-1
χ161-11111-1-1-1-11111-1-1-1-1-1-11111-1-1−iii−i−iii−i-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−iii−i−iii−i-111-1-11
χ172222222222222222222-22-222220000000022-2-222-2-2000000000000000000000000-2-20000
χ18222222222222222222-22-22222200000000-2-222-2-222000000000000000000000000-2-20000
χ192-22222-2-2-2-22222-2-2-2-22-2-2222-2-20000000022-2-2-2-2220000000000000000000000002-20000
χ202-22222-2-2-2-22222-2-2-2-2-222-222-2-200000000-2-22222-2-20000000000000000000000002-20000
χ2144144-2144-211-2-211-2-204041-21-200002222001-2001-2000000002-12-12-12-10000-1-1-1-1000000
χ2244144-2144-211-2-211-2-204041-21-20000-2-2-2-2001-2001-200000000-21-21-21-2100001111000000
χ2344144-2144-211-2-211-2-20-40-41-21-2000022-2-200-1200-12000000002-12-1-21-210000-1-111000000
χ2444144-2144-211-2-211-2-20-40-41-21-20000-2-22200-1200-1200000000-21-212-12-1000011-1-1000000
χ254441-2441-2411-2-211-2-24040-21-21000022221-2001-20000000000-12-12-12-120000-1-1-1-1000000
χ264441-2441-2411-2-211-2-24040-21-210000-2-2-2-21-2001-200000000001-21-21-21-200001111000000
χ274441-2441-2411-2-211-2-2-40-40-21-21000022-2-2-1200-120000000000-12-121-21-20000-1-111000000
χ284441-2441-2411-2-211-2-2-40-40-21-210000-2-222-1200-1200000000001-21-2-12-12000011-1-1000000
χ29444-2144-214-2-211-2-21140401-21-222220000-2100-2100-12-12-12-1200000000-1-1-1-10000000000
χ30444-2144-214-2-211-2-21140401-21-2-2-2-2-20000-2100-21001-21-21-21-20000000011110000000000
χ31444-2144-214-2-211-2-211-40-401-21-222-2-200002-1002-100-12-121-21-200000000-1-1110000000000
χ32444-2144-214-2-211-2-211-40-401-21-2-2-22200002-1002-1001-21-2-12-120000000011-1-10000000000
χ3344-2441-2441-2-211-2-2110404-21-212222000000-2100-212-12-12-12-100000000-1-1-1-10000000000
χ3444-2441-2441-2-211-2-2110404-21-21-2-2-2-2000000-2100-21-21-21-21-210000000011110000000000
χ3544-2441-2441-2-211-2-2110-40-4-21-2122-2-20000002-1002-12-12-1-21-2100000000-1-1110000000000
χ3644-2441-2441-2-211-2-2110-40-4-21-21-2-2220000002-1002-1-21-212-12-10000000011-1-10000000000
χ374-4144-2-1-4-4211-2-2-1-122040-41-2-1200002i−2i2i−2i001-200-12000000002i−i−2ii2i−i−2ii0000−ii−ii000000
χ384-4144-2-1-4-4211-2-2-1-122040-41-2-120000−2i2i−2i2i001-200-1200000000−2ii2i−i−2ii2i−i0000i−ii−i000000
χ394-4144-2-1-4-4211-2-2-1-1220-4041-2-1200002i−2i−2i2i00-12001-2000000002i−i−2ii−2ii2i−i0000−iii−i000000
χ404-4144-2-1-4-4211-2-2-1-1220-4041-2-120000−2i2i2i−2i00-12001-200000000−2ii2i−i2i−i−2ii0000i−i−ii000000
χ414-441-24-4-12-411-2-2-1-12240-40-212-100002i−2i2i−2i1-200-120000000000−i2ii−2i−i2ii−2i0000−ii−ii000000
χ424-441-24-4-12-411-2-2-1-12240-40-212-10000−2i2i−2i2i1-200-120000000000i−2i−i2ii−2i−i2i0000i−ii−i000000
χ434-441-24-4-12-411-2-2-1-122-4040-212-100002i−2i−2i2i-12001-20000000000−i2ii−2ii−2i−i2i0000−iii−i000000
χ444-441-24-4-12-411-2-2-1-122-4040-212-10000−2i2i2i−2i-12001-20000000000i−2i−i2i−i2ii−2i0000i−i−ii000000
χ454-44-214-42-1-4-2-21122-1-140-401-2-122i−2i2i−2i0000-21002-100−i2ii−2i−i2ii−2i00000000−ii−ii0000000000
χ464-44-214-42-1-4-2-21122-1-140-401-2-12−2i2i−2i2i0000-21002-100i−2i−i2ii−2i−i2i00000000i−ii−i0000000000
χ474-44-214-42-1-4-2-21122-1-1-40401-2-122i−2i−2i2i00002-100-2100−i2ii−2ii−2i−i2i00000000−iii−i0000000000
χ484-44-214-42-1-4-2-21122-1-1-40401-2-12−2i2i2i−2i00002-100-2100i−2i−i2i−i2ii−2i00000000i−i−ii0000000000
χ494-4-24412-4-4-1-2-21122-1-1040-4-212-12i−2i2i−2i000000-21002-12i−i−2ii2i−i−2ii00000000−ii−ii0000000000
χ504-4-24412-4-4-1-2-21122-1-1040-4-212-1−2i2i−2i2i000000-21002-1−2ii2i−i−2ii2i−i00000000i−ii−i0000000000
χ514-4-24412-4-4-1-2-21122-1-10-404-212-12i−2i−2i2i0000002-100-212i−i−2ii−2ii2i−i00000000−iii−i0000000000
χ524-4-24412-4-4-1-2-21122-1-10-404-212-1−2i2i2i−2i0000002-100-21−2ii2i−i2i−i−2ii00000000i−i−ii0000000000
χ538822-4-422-4-45-4225-4220000-1-1-1-10000004400000000000000000000-2-2-2-200000011000000
χ548822-4-422-4-45-4225-4220000-1-1-1-1000000-4-4000000000000000000002222000000-1-1000000
χ558822-4-422-4-4-4522-45220000-1-1-1-1000044000000000000000000-2-2-2-2000000001100000000
χ568822-4-422-4-4-4522-45220000-1-1-1-10000-4-4000000000000000000222200000000-1-100000000
χ5788-4-422-4-422225-4225-40000-1-1-1-100440000000000000000-2-2-2-20000000000110000000000
χ5888-4-422-4-422225-4225-40000-1-1-1-100-4-4000000000000000022220000000000-1-10000000000
χ5988-4-422-4-42222-4522-450000-1-1-1-14400000000000000-2-2-2-200000000000011000000000000
χ6088-4-422-4-42222-4522-450000-1-1-1-1-4-4000000000000002222000000000000-1-1000000000000
χ618-822-4-4-2-2445-422-54-2-20000-1-1110000004i−4i00000000000000000000−2i−2i2i2i000000i−i000000
χ628-822-4-4-2-2445-422-54-2-20000-1-111000000−4i4i000000000000000000002i2i−2i−2i000000−ii000000
χ638-822-4-4-2-244-45224-5-2-20000-1-11100004i−4i000000000000000000−2i−2i2i2i00000000i−i00000000
χ648-822-4-4-2-244-45224-5-2-20000-1-1110000−4i4i0000000000000000002i2i−2i−2i00000000−ii00000000
χ658-8-4-42244-2-2225-4-2-2-540000-1-111004i−4i0000000000000000−2i−2i2i2i0000000000i−i0000000000
χ668-8-4-42244-2-2225-4-2-2-540000-1-11100−4i4i00000000000000002i2i−2i−2i0000000000−ii0000000000
χ678-8-4-42244-2-222-45-2-24-50000-1-1114i−4i00000000000000−2i−2i2i2i000000000000i−i000000000000
χ688-8-4-42244-2-222-45-2-24-50000-1-111−4i4i000000000000002i2i−2i−2i000000000000−ii000000000000
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).