Finite Group Databasebeta

← Group #13165588

Character table — Group #13165588

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666444444121212121212121212121212121212121212121244881212242424244441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111-1-1111111-1-11111-1-1-1-111-1-111-1-1-1-111-111-1-1-1-1
χ31111111111111111111111111-1-1111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111-1-1
χ41111111111111111111111111-1-111-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ5111111111111111111111111-1111111111-1-111-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-11111-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111
χ7111111111111111111111111-1-1-1111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-111
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
χ9222222222222222222222222200-2-20000022002200000000000000-2-20000-2-20000000
χ10222222222222222222222222-200-2-200000-2-200-2-200000000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1022222-1-1-1-100220022-1-1-1-1-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-2-1-111002200-2-2-1-1-1-1111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222211-1-100-2-200221111-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222-2111100-2-200-2-2111111110022-1-1-1-1-1-1000000000
χ152-22-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000002−20022−2−22-2000002−2
χ162-22-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000002−20022−2−2-2200000−22
χ172-22-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000−2200−2−2222-200000−22
χ182-22-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000−2200−2−222-22000002−2
χ192-2-222-2-2222-2-22-22-222-2-2-2-2220002-20000000000000000000002i−2i002-200000002i−2i0000
χ202-2-222-2-2222-2-22-22-222-2-2-2-2220002-2000000000000000000000−2i2i002-20000000−2i2i0000
χ212-2-222-2-2222-2-22-22-222-2-2-2-22202-2-2202-200002-2000022-2-200000000-220000000000000
χ222-2-222-2-2222-2-22-22-222-2-2-2-2220-22-220-220000-220000-2-22200000000-220000000000000
χ232-2-22-111-122-2-22-22-2-1-11111-1-102-2-220-11−i3i3002-20000-1-111−i3−i3i3i300001-1−i3i3−i3i3000000000
χ242-2-22-111-122-2-22-22-2-1-11111-1-102-2-220-11i3−i3002-20000-1-111i3i3−i3−i300001-1i3−i3i3−i3000000000
χ252-2-22-111-122-2-22-22-2-1-11111-1-10-22-2201-1−i3i300-22000011-1-1−i3−i3i3i300001-1i3−i3i3−i3000000000
χ262-2-22-111-122-2-22-22-2-1-11111-1-10-22-2201-1i3−i300-22000011-1-1i3i3−i3−i300001-1−i3i3−i3i3000000000
χ27444444441-21-21-2-211-21-21-21-24220002200-2-2-1-11100-1-1-1-100002200000000000-1-10000
χ28444444441-21-21-2-211-21-21-21-24-2-2000-2-200-2-211110011110000-2-200000000000110000
χ29444444441-21-21-2-211-21-21-21-2-422000220022-1-1-1-100-1-1-1-10000-2-200000000000110000
χ30444444441-21-21-2-211-21-21-21-2-4-2-2000-2-2002211-1-100111100002200000000000-1-10000
χ3144444444-21-21-211-2-21-21-21-2140000200221100-2-2-1-10000-1-1-1-1000000000000200-1-100
χ3244444444-21-21-211-2-21-21-21-2140000-200-2-21100-2-21100001111000000000000-2001100
χ3344444444-21-21-211-2-21-21-21-21-4000020022-1-10022-1-10000-1-1-1-1000000000000-2001100
χ3444444444-21-21-211-2-21-21-21-21-40000-200-2-2-1-100221100001111000000000000200-1-100
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-44-444-4-4-44-4444-4-444-4-4000000000000000000000000000000000000000000000
χ3744-4-44-44-4-212-121-1-2-212-1-212-100000000003-300003−300003−33−30000000000000003−300
χ3844-4-44-44-4-212-121-1-2-212-1-212-100000000003-30000−330000−33−33000000000000000−3300
χ3944-4-44-44-4-212-121-1-2-212-1-212-10000000000-3300003−300003−33−3000000000000000−3300
χ4044-4-44-44-4-212-121-1-2-212-1-212-10000000000-330000−330000−33−330000000000000003−300
χ4144-4-4-22-2244-4-4-44-44-2-222-2-22200000000000000000000000000000000i6−i6−i6i6000000000
χ4244-4-4-22-2244-4-4-44-44-2-222-2-22200000000000000000000000000000000−i6i6i6−i6000000000
χ434-44-4-2-2224444-4-4-4-4-2-2-2-22222000000000000000000000000000022−2200−2−222000000000
χ444-44-4-2-2224444-4-4-4-4-2-2-2-222220000000000000000000000000000−22220022−2−2000000000
χ454-4-444-4-441-2-1212-2-11-2-12-121-202-20002-20000-113i−3i00-1-11100002i−2i00000000000−ii0000
χ464-4-444-4-441-2-1212-2-11-2-12-121-202-20002-20000-11−3i3i00-1-1110000−2i2i00000000000i−i0000
χ474-4-444-4-441-2-1212-2-11-2-12-121-20-22000-2200001-13i−3i0011-1-10000−2i2i00000000000i−i0000
χ484-4-444-4-441-2-1212-2-11-2-12-121-20-22000-2200001-1−3i3i0011-1-100002i−2i00000000000−ii0000
χ494-4-44-222-244-4-44-44-4-2-22222-2-20004-40000000000000000000000000-220000000000000
χ508888-4-4-4-42-42-42-4-42-12-12-12-12044000-2-20000-2-20000111100000000000000000000000
χ518888-4-4-4-42-42-42-4-42-12-12-12-120-4-4000220000220000-1-1-1-100000000000000000000000
χ528888-4-4-4-4-42-42-422-42-12-12-12-100000400-2-2000000-2-2000011110000000000000000000
χ538888-4-4-4-4-42-42-422-42-12-12-12-100000-40022000000220000-1-1-1-10000000000000000000
χ5488-8-88-88-82-4-24-2-4422-4-242-4-24000000000000000000000000000000000000000000000
χ5588-8-8-44-442-4-24-2-442-121-2-121-20000000000000000003i−3i3i−3i00000000000000000000000
χ5688-8-8-44-442-4-24-2-442-121-2-121-2000000000000000000−3i3i−3i3i00000000000000000000000
χ5788-8-8-44-44-424-242-2-42-1-212-1-21000000000000000023−230000−33−330000000000000000000
χ5888-8-8-44-44-424-242-2-42-1-212-1-210000000000000000−232300003−33−30000000000000000000
χ598-88-888-8-82-42-4-244-22-42-4-24-24000000000000000000000000000000000000000000000
χ608-88-888-8-8-42-424-2-24-42-424-24-2000000000000000000000000000000000000000000000
χ618-88-8-4-4442-42-4-244-2-12-121-21-20000000000000000003i−3i−3i3i00000000000000000000000
χ628-88-8-4-4442-42-4-244-2-12-121-21-2000000000000000000−3i3i3i−3i00000000000000000000000
χ638-88-8-4-444-42-424-2-242-12-1-21-2100000000000000000000003i−3i−3i3i0000000000000000000
χ648-88-8-4-444-42-424-2-242-12-1-21-210000000000000000000000−3i3i3i−3i0000000000000000000
χ658-8-888-8-88-424-2-4-224-424-24-2-42000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-2424-4-2-121-21-2-1204-4000-220000-22000011-1-100000000000000000000000
χ678-8-88-444-42-4-2424-4-2-121-21-2-120-440002-200002-20000-1-11100000000000000000000000
χ688-8-88-444-4-424-2-4-2242-1-21-212-100000000−2i32i3000000000000i3i3−i3−i30000000000000000000
χ698-8-88-444-4-424-2-4-2242-1-21-212-1000000002i3−2i3000000000000−i3−i3i3i30000000000000000000

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