Finite Group Databasebeta

← Group #13165552

Character table — Group #13165552

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666222444666666666666121212121212121244881212242424244441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-111-1-1-1-1
χ311111111111111111111111111-111111-1-111-1-1111111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111
χ5111111111111111111111111-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-111-1-1
χ6111111111111111111111111-1-1111-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ7111111111111111111111111-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-111-1-111
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
χ9222222222222222222222222002-2-20002200220000000000000000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-2000-2-200-2-20000000000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-1002200-1-1-1-1-1-122-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-2-1-1002200-1-1-1-111-2-2111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-202221100-2-2001111-1-122-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-21100-2-200111111-2-211110022-1-1-1-1-1-1000000000
χ152-22-222-2-222-22-2-22-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i22i−2i000002−2
χ162-22-222-2-222-22-2-22-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i2−2i2i00000−22
χ172-22-222-2-222-22-2-22-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i22i−2i00000−22
χ182-22-222-2-222-22-2-22-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i2−2i2i000002−2
χ192-2-222-2-2222-2-2-22-2222-2-2-22-22000-220000000000000000000002-2002-200000002-20000
χ202-2-222-2-2222-2-2-22-2222-2-2-22-22000-22000000000000000000000-22002-20000000-220000
χ212-2-222-2-2222-2-2-22-2222-2-2-22-222-202-202-2002-20022-2-2000000000000-220000000000000
χ222-2-222-2-2222-2-2-22-2222-2-2-22-22-2202-20-2200-2200-2-222000000000000-220000000000000
χ232-2-22-111-122-2-2-22-22-1-1111-11-12-202-20-11002-200-1-111−i3i300−i3−i3i3i300001-1−i3i3−i3i3000000000
χ242-2-22-111-122-2-2-22-22-1-1111-11-12-202-20-11002-200-1-111i3−i300i3i3−i3−i300001-1i3−i3i3−i3000000000
χ252-2-22-111-122-2-2-22-22-1-1111-11-1-2202-201-100-220011-1-1−i3i300−i3−i3i3i300001-1i3−i3i3−i3000000000
χ262-2-22-111-122-2-2-22-22-1-1111-11-1-2202-201-100-220011-1-1i3−i300i3i3−i3−i300001-1−i3i3−i3i3000000000
χ27444444441-21-2-211-21-211-2-2-21004002001100-2-2000022-1-1-1-1-1-1000000000000200-1-100
χ28444444441-21-2-211-21-211-2-2-2100400-2001100-2-20000-2-2111111000000000000-2001100
χ29444444441-21-2-211-21-211-2-2-2100-400200-1-10022000022-1-1-1-1-1-1000000000000-2001100
χ30444444441-21-2-211-21-211-2-2-2100-400-200-1-100220000-2-2111111000000000000200-1-100
χ3144444444-21-211-2-21-21-2-2111-222400022-2-2-1-111-1-1-1-1000000002200000000000-1-10000
χ3244444444-21-211-2-21-21-2-2111-222-40002222-1-1-1-1-1-1-1-100000000-2-200000000000110000
χ3344444444-21-211-2-21-21-2-2111-2-2-24000-2-2-2-21111111100000000-2-200000000000110000
χ3444444444-21-211-2-21-21-2-2111-2-2-2-4000-2-22211-1-11111000000002200000000000-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-44-41-212-2-1-121-2-1122-2-1000000003-300000000003−33−33−30000000000000003−300
χ3744-4-44-44-41-212-2-1-121-2-1122-2-1000000003-30000000000−33−33−33000000000000000−3300
χ3844-4-44-44-41-212-2-1-121-2-1122-2-100000000-3300000000003−33−33−3000000000000000−3300
χ3944-4-44-44-41-212-2-1-121-2-1122-2-100000000-330000000000−33−33−330000000000000003−300
χ4044-4-44-44-4444-44-4-4-444-44-4-44-4000000000000000000000000000000000000000000000
χ4144-4-4-22-22444-44-4-4-4-2-22-222-22000000000000000000000000000000006−6−66000000000
χ4244-4-4-22-22444-44-4-4-4-2-22-222-2200000000000000000000000000000000−666−6000000000
χ434-44-4-2-22244-44-4-44-4-2-2-22-22220000000000000000000000000000−2i22i200i2i2−i2−i2000000000
χ444-44-4-2-22244-44-4-44-4-2-2-22-222200000000000000000000000000002i2−2i200−i2−i2i2i2000000000
χ454-4-444-4-44-212-1-1-221-2122-11-1-22-200002-200-113-3-1-111000000002-200000000000-110000
χ464-4-444-4-44-212-1-1-221-2122-11-1-22-200002-200-11-33-1-11100000000-22000000000001-10000
χ474-4-444-4-44-212-1-1-221-2122-11-1-2-220000-22001-13-311-1-100000000-22000000000001-10000
χ484-4-444-4-44-212-1-1-221-2122-11-1-2-220000-22001-1-3311-1-1000000002-200000000000-110000
χ494-4-44-222-244-4-4-44-44-2-2222-22-2000-440000000000000000000000000-220000000000000
χ508888-4-4-4-42-42-4-422-4-12-1-1222-1000004000000000000-2-2-2-211110000000000000000000
χ518888-4-4-4-42-42-4-422-4-12-1-1222-100000-40000000000002222-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-422-4-422-122-1-1-12440000-2-200-2-2001111000000000000000000000000000
χ538888-4-4-4-4-42-422-4-422-122-1-1-12-4-4000022002200-1-1-1-1000000000000000000000000000
χ5488-8-88-88-8-42-4-2244-2-424-4-2-224000000000000000000000000000000000000000000000
χ5588-8-8-44-442-424-4-2-24-121-1-2-2210000000000000000000023−23−33−330000000000000000000
χ5688-8-8-44-442-424-4-2-24-121-1-2-22100000000000000000000−23233−33−30000000000000000000
χ5788-8-8-44-44-42-4-2244-22-1-2211-1-2000000000000003-33-3000000000000000000000000000
χ5888-8-8-44-44-42-4-2244-22-1-2211-1-200000000000000-33-33000000000000000000000000000
χ598-88-888-8-82-4-2-44-2242-42-2-444-2000000000000000000000000000000000000000000000
χ608-88-888-8-8-4242-24-4-2-42-442-2-24000000000000000000000000000000000000000000000
χ618-88-8-4-4442-4-2-44-224-12-112-2-2100000000000000000000003i−3i−3i3i0000000000000000000
χ628-88-8-4-4442-4-2-44-224-12-112-2-210000000000000000000000−3i3i3i−3i0000000000000000000
χ638-88-8-4-444-4242-24-4-22-12-2-111-2000000000000003-3-33000000000000000000000000000
χ648-88-8-4-444-4242-24-4-22-12-2-111-200000000000000-333-3000000000000000000000000000
χ658-8-888-8-882-4-2442-2-42-4-2-24-442000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-2442-2-4-1211-22-2-1000000000000000000−2i32i300i3i3−i3−i30000000000000000000
χ678-8-88-444-42-4-2442-2-4-1211-22-2-10000000000000000002i3−2i300−i3−i3i3i30000000000000000000
χ688-8-88-444-4-424-2-2-4422-1-2-21-1124-40000-2200-220011-1-1000000000000000000000000000
χ698-8-88-444-4-424-2-2-4422-1-2-21-112-4400002-2002-200-1-111000000000000000000000000000

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