Finite Group Databasebeta

← Group #13165576

Character table — Group #13165576

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666224442666666666666666612121212448812122424242444266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111-1-111-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111-11111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111
χ5111111111111111111111111-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-111
χ7111111111111111111111111-1-1-1111-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111
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
χ9222222222222222222222222002-2-20000000000000000022220000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-200000000000000000-2-2-2-20000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-1-1-12222-1-1-1-1-1-1-1-100000022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-2-1-11122-2-2-1-1-1-11111000000-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022211-1-1-2-2221111-1-1-1-1000000-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-21111-2-2-2-21111111100000022-1-1-1-1-1-1000000000
χ152-22-22-2-222222-2-2-2-22222-2-2-2-20002-20000000000000000000002i−2i002-20000000002i−2i00
χ162-22-22-2-222222-2-2-2-22222-2-2-2-20002-2000000000000000000000−2i2i002-2000000000−2i2i00
χ172-22-22-2-222222-2-2-2-22222-2-2-2-22-20-2202-2002-20022-2-2000000000000-220000000000000
χ182-22-22-2-222222-2-2-2-22222-2-2-2-2-220-220-2200-2200-2-222000000000000-220000000000000
χ192-22-2-111-12222-2-2-2-2-1-1-1-111112-20-220-11−i3i32-200-1-111−i3−i3i3i3000000001-1−i3−i3i3i3000000000
χ202-22-2-111-12222-2-2-2-2-1-1-1-111112-20-220-11i3−i32-200-1-111i3i3−i3−i3000000001-1i3i3−i3−i3000000000
χ212-22-2-111-12222-2-2-2-2-1-1-1-11111-220-2201-1−i3i3-220011-1-1−i3−i3i3i3000000001-1i3i3−i3−i3000000000
χ222-22-2-111-12222-2-2-2-2-1-1-1-11111-220-2201-1i3−i3-220011-1-1i3i3−i3−i3000000001-1−i3−i3i3i3000000000
χ232-2-2222-2-222-2-22-2-2222-2-222-2-200000000000000000000000000002−2002−22−22-2000002−2
χ242-2-2222-2-222-2-22-2-2222-2-222-2-200000000000000000000000000002−2002−22−2-2200000−22
χ252-2-2222-2-222-2-22-2-2222-2-222-2-20000000000000000000000000000−2200−22−222-200000−22
χ262-2-2222-2-222-2-22-2-2222-2-222-2-20000000000000000000000000000−2200−22−22-22000002−2
χ27444444441-21-2-21-211-21-21-21-22240002200-1-100-1-1-1-1000011-2-2220000000000000-1-100
χ28444444441-21-2-21-211-21-21-21-222-40002200-1-100-1-1-1-10000-1-122-2-200000000000001100
χ29444444441-21-2-21-211-21-21-21-2-2-24000-2-20011001111000011-2-2-2-200000000000001100
χ30444444441-21-2-21-211-21-21-21-2-2-2-4000-2-200110011110000-1-122220000000000000-1-100
χ3144444444-21-211-21-2-21-21-21-21004002002200-1-10000-1-1-1-1-2-2110000000000002-1-10000
χ3244444444-21-211-21-2-21-21-21-2100400-200-2-2001100001111-2-211000000000000-2110000
χ3344444444-21-211-21-2-21-21-21-2100-4002002200-1-10000-1-1-1-122-1-1000000000000-2110000
χ3444444444-21-211-21-2-21-21-21-2100-400-200-2-200110000111122-1-10000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-44-444-4-4-444-444-4-4-4-444000000000000000000000000000000000000000000000
χ3744-4-44-44-4-212-1-1-212-212-12-1-21000000000000−i3i30000−i3i3−i3i3003-30000000000000−i3i30000
χ3844-4-44-44-4-212-1-1-212-212-12-1-21000000000000−i3i30000−i3i3−i3i300-330000000000000i3−i30000
χ3944-4-44-44-4-212-1-1-212-212-12-1-21000000000000i3−i30000i3−i3i3−i3003-30000000000000i3−i30000
χ4044-4-44-44-4-212-1-1-212-212-12-1-21000000000000i3−i30000i3−i3i3−i300-330000000000000−i3i30000
χ4144-4-4-22-2244-4-4-444-4-2-22222-2-200000000000000000000000000000000i6−i6−i6i6000000000
χ4244-4-4-22-2244-4-4-444-4-2-22222-2-200000000000000000000000000000000−i6i6i6−i6000000000
χ434-44-44-4-441-21-22-12-11-21-2-12-122-200002-200-1100-1-11100003i−3i002i−2i0000000000000−ii00
χ444-44-44-4-441-21-22-12-11-21-2-12-122-200002-200-1100-1-1110000−3i3i00−2i2i0000000000000i−i00
χ454-44-44-4-441-21-22-12-11-21-2-12-12-220000-22001-10011-1-100003i−3i00−2i2i0000000000000i−i00
χ464-44-44-4-441-21-22-12-11-21-2-12-12-220000-22001-10011-1-10000−3i3i002i−2i0000000000000−ii00
χ474-44-4-222-24444-4-4-4-4-2-2-2-222220004-40000000000000000000000000-220000000000000
χ484-4-44-2-22244-4-44-4-44-2-222-2-222000000000000000000000000000022−2200−22−22000000000
χ494-4-44-2-22244-4-44-4-44-2-222-2-2220000000000000000000000000000−2222002−22−2000000000
χ508888-4-4-4-42-42-4-42-42-12-12-12-12440000-2-200-2-2001111000000000000000000000000000
χ518888-4-4-4-42-42-4-42-42-12-12-12-12-4-4000022002200-1-1-1-1000000000000000000000000000
χ528888-4-4-4-4-42-422-42-42-12-12-12-100000400-2-200-2-20000111100000000000000000000000
χ538888-4-4-4-4-42-422-42-42-12-12-12-100000-4002200220000-1-1-1-100000000000000000000000
χ5488-8-88-88-82-4-2442-4-22-4-24-242-4000000000000000000000000000000000000000000000
χ5588-8-8-44-442-4-2442-4-2-121-21-2-12000000000000003-33-3000000000000000000000000000
χ5688-8-8-44-442-4-2442-4-2-121-21-2-1200000000000000-33-33000000000000000000000000000
χ5788-8-8-44-44-424-2-2-4242-1-21-212-1000000000000−2i32i30000i3−i3i3−i300000000000000000000000
χ5888-8-8-44-44-424-2-2-4242-1-21-212-10000000000002i3−2i30000−i3i3−i3i300000000000000000000000
χ598-88-88-8-88-42-42-24-24-42-424-24-2000000000000000000000000000000000000000000000
χ608-88-8-444-42-42-44-24-2-12-121-21-24-40000-2200-220011-1-1000000000000000000000000000
χ618-88-8-444-42-42-44-24-2-12-121-21-2-4400002-2002-200-1-111000000000000000000000000000
χ628-88-8-444-4-42-42-24-242-12-1-21-2100000000−2i32i300000000i3i3−i3−i300000000000000000000000
χ638-88-8-444-4-42-42-24-242-12-1-21-21000000002i3−2i300000000−i3−i3i3i300000000000000000000000
χ648-8-8888-8-82-4-24-4-2422-4-242-4-24000000000000000000000000000000000000000000000
χ658-8-8888-8-8-424-224-2-4-424-2-424-2000000000000000000000000000000000000000000000
χ668-8-88-4-4442-4-24-4-242-121-2-121-2000000000000003-3-33000000000000000000000000000
χ678-8-88-4-4442-4-24-4-242-121-2-121-200000000000000-333-3000000000000000000000000000
χ688-8-88-4-444-424-224-2-42-1-212-1-210000000000000000003-3-3300000000000000000000000
χ698-8-88-4-444-424-224-2-42-1-212-1-21000000000000000000-333-300000000000000000000000

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