Finite Group Databasebeta

← Group #13165600

Character table — Group #13165600

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order1222366633666666336666664444426666666612121212121212121212121244881212242424244441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-111-1-1
χ31111111111111111111111111-1-111111111111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-111
χ5111111111111111111111111-1111111111111111-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-11111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1111-1-111
χ7111111111111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11111
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
χ9222222222222222222222222200-2-20000000000022002200000000-2-20000-2-20000000
χ10222222222222222222222222-200-2-200000000000-2-200-2-200000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1022222-1-122-1-1-1-1-1-1002200-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-211-2-21111-1-1002200-1-1-1-100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-2222-1-122-1-1-1-11100-2-200111100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222-211-2-211111100-2-20011110022-1-1-1-1-1-1000000000
χ1522-2-222-2-222-2-2-22-22222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i22i−2i000002−2
χ1622-2-222-2-222-2-2-22-22222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i2−2i2i00000−22
χ1722-2-222-2-222-2-2-22-22222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i22i−2i00000−22
χ1822-2-222-2-222-2-2-22-22222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i2−2i2i000002−2
χ192-2-222-2-2222-2-22-22-222-2-2-22-220002-20000000000000000000002i−2i002-20000000002i−2i00
χ202-2-222-2-2222-2-22-22-222-2-2-22-220002-2000000000000000000000−2i2i002-2000000000−2i2i00
χ212-2-222-2-2222-2-22-22-222-2-2-22-2202-2-220000000002-2002-20022-2-20000-220000000000000
χ222-2-222-2-2222-2-22-22-222-2-2-22-220-22-22000000000-2200-2200-2-2220000-220000000000000
χ232-2-22-111-122-2-22-22-2-1-1111-11-102-2-220−i3i300−i3−i3i3i3-11002-200-1-11100001-1−i3i3−i3i3000000000
χ242-2-22-111-122-2-22-22-2-1-1111-11-102-2-220i3−i300i3i3−i3−i3-11002-200-1-11100001-1i3−i3i3−i3000000000
χ252-2-22-111-122-2-22-22-2-1-1111-11-10-22-220−i3i300−i3−i3i3i31-100-220011-1-100001-1i3−i3i3−i3000000000
χ262-2-22-111-122-2-22-22-2-1-1111-11-10-22-220i3−i300i3i3−i3−i31-100-220011-1-100001-1−i3i3−i3i3000000000
χ27444444441-21-21-2-211-211-2-2-214220000000000022-2-2-1-111-1-1-1-1220000000000000-1-100
χ28444444441-21-21-2-211-211-2-2-214-2-200000000000-2-2-2-211111111-2-200000000000001100
χ29444444441-21-21-2-211-211-2-2-21-422000000000002222-1-1-1-1-1-1-1-1-2-200000000000001100
χ30444444441-21-21-2-211-211-2-2-21-4-2-200000000000-2-22211-1-11111220000000000000-1-100
χ3144444444-21-21-211-2-21-2-2111-240000222-1-1-1-1-1-1001100-2-200000000000000002-1-10000
χ3244444444-21-21-211-2-21-2-2111-240000-2-2-2111111001100-2-20000000000000000-2110000
χ3344444444-21-21-211-2-21-2-2111-2-40000222-1-1-1-1-1-100-1-100220000000000000000-2110000
χ3444444444-21-21-211-2-21-2-2111-2-40000-2-2-211111100-1-1002200000000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-4-2-22244-4-4-44-44-2-2-22-22220000000000000000000000000000−2i22i200i2i2−i2−i2000000000
χ3744-4-4-2-22244-4-4-44-44-2-2-22-222200000000000000000000000000002i2−2i200−i2−i2i2i2000000000
χ384-44-44-44-44444-4-4-4-444-44-4-44-4000000000000000000000000000000000000000000000
χ394-44-44-44-4-21-212-1-12-212-2-1-11200000000−i3i3−i3i3−i3i3003i−3i0000000000000000000003−30000
χ404-44-44-44-4-21-212-1-12-212-2-1-11200000000−i3i3−i3i3−i3i300−3i3i000000000000000000000−330000
χ414-44-44-44-4-21-212-1-12-212-2-1-11200000000i3−i3i3−i3i3−i3003i−3i000000000000000000000−330000
χ424-44-44-44-4-21-212-1-12-212-2-1-11200000000i3−i3i3−i3i3−i300−3i3i0000000000000000000003−30000
χ434-44-4-22-224444-4-4-4-4-2-22-222-22000000000000000000000000000000006−6−66000000000
χ444-44-4-22-224444-4-4-4-4-2-22-222-2200000000000000000000000000000000−666−6000000000
χ454-4-444-4-441-2-1212-2-11-2-1-12-22102-2000000000002-200-113i−3i-1-1112i−2i0000000000000−ii00
χ464-4-444-4-441-2-1212-2-11-2-1-12-22102-2000000000002-200-11−3i3i-1-111−2i2i0000000000000i−i00
χ474-4-444-4-441-2-1212-2-11-2-1-12-2210-2200000000000-22001-13i−3i11-1-1−2i2i0000000000000i−i00
χ484-4-444-4-441-2-1212-2-11-2-1-12-2210-2200000000000-22001-1−3i3i11-1-12i−2i0000000000000−ii00
χ494-4-44-222-244-4-44-44-4-2-2222-22-20004-40000000000000000000000000-220000000000000
χ508888-4-4-4-42-42-42-4-42-12-1-1222-104400000000000-2-200-2-20011110000000000000000000
χ518888-4-4-4-42-42-42-4-42-12-1-1222-10-4-40000000000022002200-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-42-422-42-122-1-1-12000004-2-2-2-211110000000000000000000000000000000
χ538888-4-4-4-4-42-42-422-42-122-1-1-1200000-42222-1-1-1-10000000000000000000000000000000
χ5488-8-888-8-82-4-24-2-4422-42-2-444-2000000000000000000000000000000000000000000000
χ5588-8-888-8-8-424-242-2-4-42-442-2-24000000000000000000000000000000000000000000000
χ5688-8-8-4-4442-4-24-2-442-12-112-2-2100000000000000000000003i−3i3i−3i0000000000000000000
χ5788-8-8-4-4442-4-24-2-442-12-112-2-210000000000000000000000−3i3i−3i3i0000000000000000000
χ5888-8-8-4-444-424-242-2-42-12-2-111-200000000003-3-330000000000000000000000000000000
χ5988-8-8-4-444-424-242-2-42-12-2-111-20000000000-333-30000000000000000000000000000000
χ608-88-88-88-82-42-4-244-22-4-2244-4-2000000000000000000000000000000000000000000000
χ618-88-8-44-442-42-4-244-2-121-1-2-22100000000000000000000003i−3i−3i3i0000000000000000000
χ628-88-8-44-442-42-4-244-2-121-1-2-2210000000000000000000000−3i3i3i−3i0000000000000000000
χ638-88-8-44-44-42-424-2-242-1-2211-1-200000000−2i32i3i3−i3i3−i30000000000000000000000000000000
χ648-88-8-44-44-42-424-2-242-1-2211-1-2000000002i3−2i3−i3i3−i3i30000000000000000000000000000000
χ658-8-888-8-88-424-2-4-224-4244-22-2-4000000000000000000000000000000000000000000000
χ668-8-88-444-42-4-2424-4-2-1211-22-2-104-400000000000-2200-220011-1-10000000000000000000
χ678-8-88-444-42-4-2424-4-2-1211-22-2-10-44000000000002-2002-200-1-1110000000000000000000
χ688-8-88-444-4-424-2-4-2242-1-2-21-112000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ698-8-88-444-4-424-2-4-2242-1-2-21-1120000002i3−2i300−i3−i3i3i30000000000000000000000000000000

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