Finite Group Databasebeta

← Group #13165554

Character table — Group #13165554

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666244444666612121212121212121212121212121212228812122424242444466121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1111111-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-111-1-1-1-1
χ31111111111111111111111111-1-11111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111-1-1
χ41111111111111111111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ5111111111111111111111111-111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-11111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111
χ7111111111111111111111111-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1
χ9222222222222222222222222200-2-20222200000000000000000000-2-20000-2-20000000
χ10222222222222222222222222-200-2-20-2-2-2-200000000000000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-10222220000-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-20000-1-11122-2-2-1-1-1-1111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-2222000011-1-1-2-2221111-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222-200001111-2-2-2-2111111110022-1-1-1-1-1-1000000000
χ152-22-222-2-222-22-2-2-222222-2-2-2-200000000000000000000000000002−20022−2−22i−2i00000−i2i2
χ162-22-222-2-222-22-2-2-222222-2-2-2-200000000000000000000000000002−20022−2−2−2i2i00000i2−i2
χ172-22-222-2-222-22-2-2-222222-2-2-2-20000000000000000000000000000−2200−2−2222i−2i00000i2−i2
χ182-22-222-2-222-22-2-2-222222-2-2-2-20000000000000000000000000000−2200−2−222−2i2i00000−i2i2
χ192-2-222-2-2222-2-2-222-222-2-2-2-222000-220000000000000000000002-2002-200000002-20000
χ202-2-222-2-2222-2-2-222-222-2-2-2-222000-22000000000000000000000-22002-20000000-220000
χ212-2-222-2-2222-2-2-222-222-2-2-2-22202-22-2000002-2002-20022-2-200000000-220000000000000
χ222-2-222-2-2222-2-2-222-222-2-2-2-2220-222-200000-2200-2200-2-22200000000-220000000000000
χ232-2-22-111-122-2-2-222-2-1-11111-1-102-22-200000-11−i3i32-200-1-111−i3−i3i3i300001-1−i3i3−i3i3000000000
χ242-2-22-111-122-2-2-222-2-1-11111-1-102-22-200000-11i3−i32-200-1-111i3i3−i3−i300001-1i3−i3i3−i3000000000
χ252-2-22-111-122-2-2-222-2-1-11111-1-10-222-2000001-1−i3i3-220011-1-1−i3−i3i3i300001-1i3−i3i3−i3000000000
χ262-2-22-111-122-2-2-222-2-1-11111-1-10-222-2000001-1i3−i3-220011-1-1i3i3−i3−i300001-1−i3i3−i3i3000000000
χ27444444441-21-2-21-211-21-21-21-240000211-2-2002200-1-10000-1-1-1-1000000000000200-1-100
χ28444444441-21-2-21-211-21-21-21-240000-211-2-200-2-2001100001111000000000000-2001100
χ29444444441-21-2-21-211-21-21-21-2-400002-1-122002200-1-10000-1-1-1-1000000000000-2001100
χ30444444441-21-2-21-211-21-21-21-2-40000-2-1-12200-2-2001100001111000000000000200-1-100
χ3144444444-21-211-21-2-21-21-21-21422000-2-2112200-1-100-1-1-1-100002200000000000-1-10000
χ3244444444-21-211-21-2-21-21-21-214-2-2000-2-211-2-200110011110000-2-200000000000110000
χ3344444444-21-211-21-2-21-21-21-21-42200022-1-12200-1-100-1-1-1-10000-2-200000000000110000
χ3444444444-21-211-21-2-21-21-21-21-4-2-200022-1-1-2-2001100111100002200000000000-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-44-41-212-2-12-11-2-121-2-120000003-3000000003−300003−33−30000000000000003−300
χ3744-4-44-44-41-212-2-12-11-2-121-2-120000003-300000000−330000−33−33000000000000000−3300
χ3844-4-44-44-41-212-2-12-11-2-121-2-12000000-33000000003−300003−33−3000000000000000−3300
χ3944-4-44-44-41-212-2-12-11-2-121-2-12000000-3300000000−330000−33−330000000000000003−300
χ4044-4-44-44-4444-44-4-4-444-4-444-4-4000000000000000000000000000000000000000000000
χ4144-4-4-22-22444-44-4-4-4-2-222-2-22200000000000000000000000000000000i6−i6−i6i6000000000
χ4244-4-4-22-22444-44-4-4-4-2-222-2-22200000000000000000000000000000000−i6i6i6−i6000000000
χ434-44-4-2-22244-44-4-4-44-2-2-2-22222000000000000000000000000000022−2200−2−222000000000
χ444-44-4-2-22244-44-4-4-44-2-2-2-222220000000000000000000000000000−22220022−2−2000000000
χ454-4-444-4-44-212-1-1-212-212-12-1-2102-2000003-32-200-1100-1-11100002-200000000000-110000
χ464-4-444-4-44-212-1-1-212-212-12-1-2102-200000-332-200-1100-1-1110000-22000000000001-10000
χ474-4-444-4-44-212-1-1-212-212-12-1-210-22000003-3-22001-10011-1-10000-22000000000001-10000
χ484-4-444-4-44-212-1-1-212-212-12-1-210-2200000-33-22001-10011-1-100002-200000000000-110000
χ494-4-44-222-244-4-4-444-4-2-22222-2-2000-440000000000000000000000000-220000000000000
χ508888-4-4-4-42-42-4-42-42-12-12-12-12000004000000-2-200-2-2000011110000000000000000000
χ518888-4-4-4-42-42-4-42-42-12-12-12-1200000-40000002200220000-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-422-42-42-12-12-12-10440000000-2-200-2-200111100000000000000000000000
χ538888-4-4-4-4-42-422-42-42-12-12-12-10-4-4000000022002200-1-1-1-100000000000000000000000
χ5488-8-88-88-8-42-4-224-24-424-2-424-2000000000000000000000000000000000000000000000
χ5588-8-8-44-442-424-4-24-2-121-2-121-2000000000000000023−230000−33−330000000000000000000
χ5688-8-8-44-442-424-4-24-2-121-2-121-20000000000000000−232300003−33−30000000000000000000
χ5788-8-8-44-44-42-4-224-242-1-212-1-210000000000000000003i−3i3i−3i00000000000000000000000
χ5888-8-8-44-44-42-4-224-242-1-212-1-21000000000000000000−3i3i−3i3i00000000000000000000000
χ598-88-888-8-82-4-2-44-2422-42-4-24-24000000000000000000000000000000000000000000000
χ608-88-888-8-8-4242-24-2-4-42-424-24-2000000000000000000000000000000000000000000000
χ618-88-8-4-4442-4-2-44-242-12-121-21-200000000000000000000003i−3i−3i3i0000000000000000000
χ628-88-8-4-4442-4-2-44-242-12-121-21-20000000000000000000000−3i3i3i−3i0000000000000000000
χ638-88-8-4-444-4242-24-2-42-12-1-21-210000000000000000003i−3i−3i3i00000000000000000000000
χ648-88-8-4-444-4242-24-2-42-12-1-21-21000000000000000000−3i3i3i−3i00000000000000000000000
χ658-8-888-8-882-4-2442-4-22-4-24-242-4000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-2442-4-2-121-21-2-12000000000000−2i32i300000000i3i3−i3−i30000000000000000000
χ678-8-88-444-42-4-2442-4-2-121-21-2-120000000000002i3−2i300000000−i3−i3i3i30000000000000000000
χ688-8-88-444-4-424-2-2-4242-1-21-212-104-40000000-2200-220011-1-100000000000000000000000
χ698-8-88-444-4-424-2-2-4242-1-21-212-10-4400000002-2002-200-1-11100000000000000000000000

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