Finite Group Databasebeta

← Group #72231094

Character table — Group #72231094

Order 2400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11222444444444888888888888888888888888888888881515151525253030505050505050506060606060606060100100100100100150150150150
order122365561010101010105510101010101015151515151530303030303030303030303030303030303044442244244446620202020202020206121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-11-1-1ii−i−i-1-11111-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111111111111-1-1-1-11-1-1−i−iii-1-11111-1-1-1-1-1−i−iii−i−iii
χ51111111111111111111111111111111111111111111111-1-111-1-1-11-1ii−i−i-1-1-1-1-1-11111-1ii−i−i−i−iii
χ61111111111111111111111111111111111111111111111-1-111-1-1-11-1−i−iii-1-1-1-1-1-11111-1−i−iiiii−i−i
χ71111111111111111111111111111111111111111111111-1-1-1-111-1-11111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ81111111111111111111111111111111111111111111111-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11111
χ911-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11-11111-1-111-1-1-11-11-11-11-1
χ1011-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-111111-1-111-1-1-1-11-11-11-11
χ1111-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111i−i−ii-1-111-1-1-1-1111i−i−iii−i−ii
χ1211-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111−iii−i-1-111-1-1-1-1111−iii−i−iii−i
χ1311-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11i−i−ii-1-1-1-11111-1-11i−i−ii−iii−i
χ1411-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11−iii−i-1-1-1-11111-1-11−iii−ii−i−ii
χ1511-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-111-1-111-1-111-11-11-1-11-11
χ1611-11111-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1111-1-111-1-111-1-11-111-11-1
χ17222-1-122-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000220022222-1-100000000-1-1-1-1-10000
χ18222-1-122-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022002-2-2-2-2-1-100000000-111110000
χ19222-1-122-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-200-22i2i−2i−2i11000000001−i−iii0000
χ20222-1-122-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-200-2−2i−2i2i2i11000000001ii−i−i0000
χ2122-2-1-1221-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100002200-22-22-2-1-1000000001-11-110000
χ2222-2-1-1221-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100002200-2-22-22-1-10000000011-11-10000
χ2322-2-1-1221-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000-2-20022i−2i−2i2i1100000000-1−iii−i0000
χ2422-2-1-1221-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111110000-2-2002−2i2i2i−2i1100000000-1i−i−ii0000
χ252-202-22200000-2-222-2-20000222222-2-2-2-2-2-20000000000002i−2i2i−2i2-200000002-22i−2i002i−2i00000000000
χ262-202-22200000-2-222-2-20000222222-2-2-2-2-2-20000000000002i−2i−2i2i-220000000-222i−2i00−2i2i00000000000
χ272-202-22200000-2-222-2-20000222222-2-2-2-2-2-2000000000000−2i2i2i−2i-220000000-22−2i2i002i−2i00000000000
χ282-202-22200000-2-222-2-20000222222-2-2-2-2-2-2000000000000−2i2i−2i2i2-200000002-2−2i2i00−2i2i00000000000
χ29444444-1444-1-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-10044000400000000000-1-1-1-1000000000
χ30444444-1444-1-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-100-4-4000-4000000000001111000000000
χ3144444-144-1-144-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1440000400000000-1-1-1-10000000000000
χ3244444-144-1-144-14-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-4-40000-40000000011110000000000000
χ3344-4444-1-4-4-4114-1-1-1-1-111114-1-1-1-1-14-1-1-1-1-1-4-411111111110044000-400000000000-1-111000000000
χ3444-4444-1-4-4-4114-1-1-1-1-111114-1-1-1-1-14-1-1-1-1-1-4-4111111111100-4-400040000000000011-1-1000000000
χ3544-444-14-411-4-4-14-1-1-1-11111-14-1-1-1-1-14-1-1-1-111-4-411111111440000-400000000-1-1110000000000000
χ3644-444-14-411-4-4-14-1-1-1-11111-14-1-1-1-1-14-1-1-1-111-4-411111111-4-4000040000000011-1-10000000000000
χ374-404-44-1000−55-41-1-111−5−5554-1-1-1-1-1-41111100−55−5−5−5−55555004i−4i000000000000000−ii−i5i5000000000
χ384-404-44-1000−55-41-1-111−5−5554-1-1-1-1-1-41111100−55−5−5−5−5555500−4i4i000000000000000i−ii5−i5000000000
χ394-404-44-10005−5-41-1-11155−5−54-1-1-1-1-1-411111005−55555−5−5−5−5004i−4i000000000000000−iii5−i5000000000
χ404-404-44-10005−5-41-1-11155−5−54-1-1-1-1-1-411111005−55555−5−5−5−500−4i4i000000000000000i−i−i5i5000000000
χ414-404-4-140−55001-4-1-111−55−55-14-1-1-1-11-41111−5500−5−555−5−5554i−4i0000000000000−ii−i5i50000000000000
χ424-404-4-140−55001-4-1-111−55−55-14-1-1-1-11-41111−5500−5−555−5−555−4i4i0000000000000i−ii5−i50000000000000
χ434-404-4-1405−5001-4-1-1115−55−5-14-1-1-1-11-411115−50055−5−555−5−54i−4i0000000000000−iii5−i50000000000000
χ444-404-4-1405−5001-4-1-1115−55−5-14-1-1-1-11-411115−50055−5−555−5−5−4i4i0000000000000i−i−i5i50000000000000
χ454-40-224400000-4-444-4-40000-2-2-2-2-2-222222200000000000000004-40000000-2200000000000000000
χ464-40-224400000-4-444-4-40000-2-2-2-2-2-22222220000000000000000-4400000002-200000000000000000
χ4788888-2-28-2-2-2-2-2-23-23-23-2-23-2-233-2-2-2-233-2-2-2-2-2-233-2-2-2-23300000000000000000000000000000000
χ4888888-2-28-2-2-2-2-2-2-23-23-233-2-2-2-2-233-2-2-2-233-2-2-2-2-2-23333-2-200000000000000000000000000000000
χ49888-4-48-2-488-2-28-2-2-2-2-2-2-2-2-2-411111-411111-4-4111111111100000000000000000000000000000000
χ50888-4-4-28-4-2-288-28-2-2-2-2-2-2-2-21-411111-4111111-4-41111111100000000000000000000000000000000
χ51888-4-4-2-2-4-2-2-2-2-2-23-23-23-2-2311−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i151111−3−i152−3+i1521−i151+i151−i151+i15−3−i152−3+i15200000000000000000000000000000000
χ52888-4-4-2-2-4-2-2-2-2-2-23-23-23-2-2311−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i151111−3+i152−3−i1521+i151−i151+i151−i15−3+i152−3−i15200000000000000000000000000000000
χ53888-4-4-2-2-4-2-2-2-2-2-2-23-23-233-2111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i15211111−i151+i15−3+i152−3−i152−3+i152−3−i1521−i151+i1500000000000000000000000000000000
χ54888-4-4-2-2-4-2-2-2-2-2-2-23-23-233-2111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i15211111+i151−i15−3−i152−3+i152−3−i152−3+i1521+i151−i1500000000000000000000000000000000
χ5588-888-2-2-82222-2-23-23-2-322-3-2-233-2-2-2-233-2-22222-3-32222-3-300000000000000000000000000000000
χ5688-888-2-2-82222-2-2-23-232-3-32-2-2-2-233-2-2-2-233222222-3-3-3-32200000000000000000000000000000000
χ5788-8-4-48-24-8-8228-2-2-2-2-22222-411111-41111144-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5888-8-4-4-28422-8-8-28-2-2-2-222221-411111-41111-1-144-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5988-8-4-4-2-242222-2-23-23-2-322-311−3−i152−3+i1521−i151+i1511−3−i152−3+i1521−i151+i15-1-1-1-13+i1523−i152−1+i15−1−i15−1+i15−1−i153+i1523−i15200000000000000000000000000000000
χ6088-8-4-4-2-242222-2-23-23-2-322-311−3+i152−3−i1521+i151−i1511−3+i152−3−i1521+i151−i15-1-1-1-13−i1523+i152−1−i15−1+i15−1−i15−1+i153−i1523+i15200000000000000000000000000000000
χ6188-8-4-4-2-242222-2-2-23-232-3-32111−i151+i15−3+i152−3−i152111−i151+i15−3+i152−3−i152-1-1-1-1−1+i15−1−i153−i1523+i1523−i1523+i152−1+i15−1−i1500000000000000000000000000000000
χ6288-8-4-4-2-242222-2-2-23-232-3-32111+i151−i15−3−i152−3+i152111+i151−i15−3−i152−3+i152-1-1-1-1−1−i15−1+i153+i1523−i1523+i1523−i152−1−i15−1+i1500000000000000000000000000000000
χ638-808-8-2-20−2525−2525223-2-32500−5-2-233-2-222-3-322−2525−2525550000−5−500000000000000000000000000000000
χ648-808-8-2-20−252525−2522-232-30−550-2-2-2-2332222-3-3−252525−2500−5−5550000000000000000000000000000000000
χ658-808-8-2-2025−25−252522-232-305−50-2-2-2-2332222-3-325−25−25250055−5−50000000000000000000000000000000000
χ668-808-8-2-2025−2525−25223-2-32−5005-2-233-2-222-3-32225−2525−25−5−500005500000000000000000000000000000000
χ678-80-448-2000−2525-82-2-222−25−252525-4111114-1-1-1-1-1005−55555−5−5−5−500000000000000000000000000000000
χ688-80-448-200025−25-82-2-2222525−25−25-4111114-1-1-1-1-100−55−5−5−5−5555500000000000000000000000000000000
χ698-80-44-280−2525002-8-2-222−2525−25251-41111-14-1-1-1-15−50055−5−555−5−500000000000000000000000000000000
χ708-80-44-28025−25002-8-2-22225−2525−251-41111-14-1-1-1-1−5500−5−555−5−55500000000000000000000000000000000
χ718-80-44-2-20−2525−2525223-2-32500−511−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i155−55−52ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ58−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ580000−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ583ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ5800000000000000000000000000000000
χ728-80-44-2-20−2525−2525223-2-32500−511−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i155−55−5−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ582ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ5800003ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ58−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ5800000000000000000000000000000000
χ738-80-44-2-20−252525−2522-232-30−550111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i1525−5−55003ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ58−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ58−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ582ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ580000000000000000000000000000000000
χ748-80-44-2-20−252525−2522-232-30−550111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i1525−5−5500−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ583ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ582ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ58−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ580000000000000000000000000000000000
χ758-80-44-2-2025−25−252522-232-305−50111−i151+i15−3+i152−3−i152-1-1−1+i15−1−i153−i1523+i152−555−500−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ582ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ583ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ58−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ580000000000000000000000000000000000
χ768-80-44-2-2025−25−252522-232-305−50111+i151−i15−3−i152−3+i152-1-1−1−i15−1+i153+i1523−i152−555−5002ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ58−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ58−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ583ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ580000000000000000000000000000000000
χ778-80-44-2-2025−2525−25223-2-32−500511−3−i152−3+i1521−i151+i15-1-13+i1523−i152−1+i15−1−i15−55−55−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ583ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ5800002ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ58−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ5800000000000000000000000000000000
χ788-80-44-2-2025−2525−25223-2-32−500511−3+i152−3−i1521+i151−i15-1-13−i1523+i152−1−i15−1+i15−55−553ζ2+2ζ14−2ζ22+2ζ26−3ζ34+3ζ38−3ζ46−2ζ58−2ζ2−3ζ14+3ζ22−3ζ26+2ζ34−2ζ38+2ζ46+3ζ580000−3ζ2−2ζ14+2ζ22−2ζ26+3ζ34−3ζ38+3ζ46+2ζ582ζ2+3ζ14−3ζ22+3ζ26−2ζ34+2ζ38−2ζ46−3ζ5800000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.