Finite Group Databasebeta

← Group #13165541

Character table — Group #13165541

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order1222366633666666336666662444446666121212121212121212121212121212122288121224242424442666688
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-11111-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111-111-1-1-1-1
χ31111111111111111111111111-1-1111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111-1-1
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
χ6111111111111111111111111-11111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-11111
χ7111111111111111111111111-1-1-1111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-111-1-111
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
χ9222222222222222222222222200-2-20222200000000000000000000-2-20000-2-20000000
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
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-2000011-1-122-2-2-1-1-1-1111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-22220000-1-111-2-2221111-1-1-1-100-2-2-1-11111000000000
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
χ1522-2-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000002−20022−2−22i−2i00000−i2i2
χ1622-2-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000002−20022−2−2−2i2i00000i2−i2
χ1722-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000−2200−2−2222i−2i00000i2−i2
χ1822-2-222-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000−2200−2−222−2i2i00000−i2i2
χ192-2-222-2-2222-2-22-22-222-2-22-22-20002-20000000000000000000002-200-2200000002-20000
χ202-2-222-2-2222-2-22-22-222-2-22-22-20002-2000000000000000000000-2200-220000000-220000
χ212-2-222-2-2222-2-22-22-222-2-22-22-202-2-2200000002-22-20022-2-2000000002-20000000000000
χ222-2-222-2-2222-2-22-22-222-2-22-22-20-22-220000000-22-2200-2-222000000002-20000000000000
χ232-2-22-111-122-2-22-22-2-1-111-11-1102-2-22000003−3-112-200-1-11133−3−30000-113−33−3000000000
χ242-2-22-111-122-2-22-22-2-1-111-11-1102-2-2200000−33-112-200-1-111−3−3330000-11−33−33000000000
χ252-2-22-111-122-2-22-22-2-1-111-11-110-22-22000003−31-1-220011-1-133−3−30000-11−33−33000000000
χ262-2-22-111-122-2-22-22-2-1-111-11-110-22-2200000−331-1-220011-1-1−3−3330000-113−33−3000000000
χ27444444441-21-21-2-211-21-21-2-2140000211-2-2220000-1-10000-1-1-1-1000000000000200-1-100
χ28444444441-21-21-2-211-21-21-2-2140000-211-2-2-2-200001100001111000000000000-2001100
χ29444444441-21-21-2-211-21-21-2-21-400002-1-122220000-1-10000-1-1-1-1000000000000-2001100
χ30444444441-21-21-2-211-21-21-2-21-40000-2-1-122-2-200001100001111000000000000200-1-100
χ3144444444-21-21-211-2-21-21-211-2422000-2-2110022-1-100-1-1-1-100002200000000000-1-10000
χ3244444444-21-21-211-2-21-21-211-24-2-2000-2-21100-2-2110011110000-2-200000000000110000
χ3344444444-21-21-211-2-21-21-211-2-42200022-1-10022-1-100-1-1-1-10000-2-200000000000110000
χ3444444444-21-21-211-2-21-21-211-2-4-2-200022-1-100-2-21100111100002200000000000-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-4-2-2224444-4-4-4-4-2-2-2-22222000000000000000000000000000022−2200−2−222000000000
χ3744-4-4-2-2224444-4-4-4-4-2-2-2-222220000000000000000000000000000−22220022−2−2000000000
χ384-44-44-44-41-2-12-1-2211-2-12-1-2210000003-300000000−i3i30000−i3i3−i3i3000000000000000−i3i300
χ394-44-44-44-41-2-12-1-2211-2-12-1-2210000003-300000000i3−i30000i3−i3i3−i3000000000000000i3−i300
χ404-44-44-44-41-2-12-1-2211-2-12-1-221000000-3300000000−i3i30000−i3i3−i3i3000000000000000i3−i300
χ414-44-44-44-41-2-12-1-2211-2-12-1-221000000-3300000000i3−i30000i3−i3i3−i3000000000000000−i3i300
χ424-44-44-44-444-4-4-44-4444-4-4-44-44000000000000000000000000000000000000000000000
χ434-44-4-22-2244-4-4-44-44-2-2222-22-2000000000000000000000000000000006−6−66000000000
χ444-44-4-22-2244-4-4-44-44-2-2222-22-200000000000000000000000000000000−666−6000000000
χ454-4-444-4-44-212-1-2-112-212-1-2-11202-2000003-3002-2-1100-1-11100002-200000000000-110000
χ464-4-444-4-44-212-1-2-112-212-1-2-11202-200000-33002-2-1100-1-1110000-22000000000001-10000
χ474-4-444-4-44-212-1-2-112-212-1-2-1120-22000003-300-221-10011-1-10000-22000000000001-10000
χ484-4-444-4-44-212-1-2-112-212-1-2-1120-2200000-3300-221-10011-1-100002-200000000000-110000
χ494-4-44-222-244-4-44-44-4-2-222-22-220004-400000000000000000000000002-20000000000000
χ508888-4-4-4-42-42-42-4-42-12-12-122-10000040000-2-20000-2-2000011110000000000000000000
χ518888-4-4-4-42-42-42-4-42-12-12-122-100000-40000220000220000-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-42-422-42-12-12-1-12044000000000-2-2-2-200111100000000000000000000000
χ538888-4-4-4-4-42-42-422-42-12-12-1-120-4-4000000000222200-1-1-1-100000000000000000000000
χ5488-8-888-8-82-42-4-244-22-42-4-244-2000000000000000000000000000000000000000000000
χ5588-8-888-8-8-42-424-2-24-42-424-2-24000000000000000000000000000000000000000000000
χ5688-8-8-4-4442-42-4-244-2-12-121-2-2100000000000000000000003i−3i−3i3i0000000000000000000
χ5788-8-8-4-4442-42-4-244-2-12-121-2-210000000000000000000000−3i3i3i−3i0000000000000000000
χ5888-8-8-4-444-42-424-2-242-12-1-211-20000000000000000003i−3i3i−3i00000000000000000000000
χ5988-8-8-4-444-42-424-2-242-12-1-211-2000000000000000000−3i3i−3i3i00000000000000000000000
χ608-88-88-88-8-424-242-2-4-424-242-2-4000000000000000000000000000000000000000000000
χ618-88-8-44-442-4-24-2-442-121-212-2-10000000000000000−2i32i30000i3−i3i3−i30000000000000000000
χ628-88-8-44-442-4-24-2-442-121-212-2-100000000000000002i3−2i30000−i3i3−i3i30000000000000000000
χ638-88-8-44-44-424-242-2-42-1-21-2-1120000000000000000003i−3i−3i3i00000000000000000000000
χ648-88-8-44-44-424-242-2-42-1-21-2-112000000000000000000−3i3i3i−3i00000000000000000000000
χ658-8-888-8-882-4-2424-4-22-4-2424-4-2000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-2424-4-2-121-2-1-221000000000023−230000000000−3−3330000000000000000000
χ678-8-88-444-42-4-2424-4-2-121-2-1-2210000000000−2323000000000033−3−30000000000000000000
χ688-8-88-444-4-424-2-4-2242-1-2121-1-204-4000000000-22-220011-1-100000000000000000000000
χ698-8-88-444-4-424-2-4-2242-1-2121-1-20-440000000002-22-200-1-11100000000000000000000000

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