Finite Group Databasebeta

← Group #13165580

Character table — Group #13165580

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order12223666336666663366666644444266666666121212121212121212121212448812122424242444266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111-1111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111-1-111
χ5111111111111111111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-111
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
χ9222222222222222222222222002-2-20000000000000222200000000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-20000000000000-2-2-2-200000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-122-1-1-1-1-1-1220000-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-211-2-21111-1-1220000-1-1-1-100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-20222-1-122-1-1-1-111-2-20000111100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-211-2-2111111-2-2000011110022-1-1-1-1-1-1000000000
χ1522-2-22-2-2222-22-22-2-222-2-22-2-220002-20000000000000000000002i−2i002-20000000002i−2i00
χ1622-2-22-2-2222-22-22-2-222-2-22-2-220002-2000000000000000000000−2i2i002-2000000000−2i2i00
χ1722-2-22-2-2222-22-22-2-222-2-22-2-222-20-220000000002-22-2000022-2-20000-220000000000000
χ1822-2-22-2-2222-22-22-2-222-2-22-2-22-220-22000000000-22-220000-2-2220000-220000000000000
χ1922-2-2-111-122-22-22-2-2-1-111-111-12-20-220−i3i300−i3−i3i3i3-112-20000-1-11100001-1−i3−i3i3i3000000000
χ2022-2-2-111-122-22-22-2-2-1-111-111-12-20-220i3−i300i3i3−i3−i3-112-20000-1-11100001-1i3i3−i3−i3000000000
χ2122-2-2-111-122-22-22-2-2-1-111-111-1-220-220−i3i300−i3−i3i3i31-1-22000011-1-100001-1i3i3−i3−i3000000000
χ2222-2-2-111-122-22-22-2-2-1-111-111-1-220-220i3−i300i3i3−i3−i31-1-22000011-1-100001-1−i3−i3i3i3000000000
χ232-2-2222-2-2222-22-2-2-2222-2-22-2-20000000000000000000000000000−i2i200−i2i2−i2i22-200000−i2i2
χ242-2-2222-2-2222-22-2-2-2222-2-22-2-20000000000000000000000000000−i2i200−i2i2−i2i2-2200000i2−i2
χ252-2-2222-2-2222-22-2-2-2222-2-22-2-20000000000000000000000000000i2−i200i2−i2i2−i22-200000i2−i2
χ262-2-2222-2-2222-22-2-2-2222-2-22-2-20000000000000000000000000000i2−i200i2−i2i2−i2-2200000−i2i2
χ27444444441-21-2-21-211-211-2-2-212240000000000022-1-1-2-211-1-1-1-1220000000000000-1-100
χ28444444441-21-2-21-211-211-2-2-2122-40000000000022-1-122-1-1-1-1-1-1-2-200000000000001100
χ29444444441-21-2-21-211-211-2-2-21-2-2400000000000-2-211-2-2111111-2-200000000000001100
χ30444444441-21-2-21-211-211-2-2-21-2-2-400000000000-2-21122-1-11111220000000000000-1-100
χ3144444444-21-211-21-2-21-2-2111-200400222-1-1-1-1-1-1000011-2-200000000000000002-1-10000
χ3244444444-21-211-21-2-21-2-2111-200400-2-2-2111111000011-2-20000000000000000-2110000
χ3344444444-21-211-21-2-21-2-2111-200-400222-1-1-1-1-1-10000-1-1220000000000000000-2110000
χ3444444444-21-211-21-2-21-2-2111-200-400-2-2-21111110000-1-12200000000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-4-441-2-1-2212-11-2-1-1-22212-20000000000002-2-11003i−3i-1-1112i−2i0000000000000−ii00
χ3744-4-44-4-441-2-1-2212-11-2-1-1-22212-20000000000002-2-1100−3i3i-1-111−2i2i0000000000000i−i00
χ3844-4-44-4-441-2-1-2212-11-2-1-1-2221-22000000000000-221-1003i−3i11-1-1−2i2i0000000000000i−i00
χ3944-4-44-4-441-2-1-2212-11-2-1-1-2221-22000000000000-221-100−3i3i11-1-12i−2i0000000000000−ii00
χ4044-4-4-222-244-44-44-4-4-2-222-222-20004-40000000000000000000000000-220000000000000
χ414-44-44-44-444-4-4-4-44444-44-4-44-4000000000000000000000000000000000000000000000
χ424-44-44-44-4-212-1-121-2-212-2-1-11200000000−i3i3−i3i3−i3i300003-30000000000000000000−i3i30000
χ434-44-44-44-4-212-1-121-2-212-2-1-11200000000−i3i3−i3i3−i3i30000-330000000000000000000i3−i30000
χ444-44-44-44-4-212-1-121-2-212-2-1-11200000000i3−i3i3−i3i3−i300003-30000000000000000000i3−i30000
χ454-44-44-44-4-212-1-121-2-212-2-1-11200000000i3−i3i3−i3i3−i30000-330000000000000000000−i3i30000
χ464-44-4-22-2244-4-4-4-444-2-22-222-22000000000000000000000000000000006−6−66000000000
χ474-44-4-22-2244-4-4-4-444-2-22-222-2200000000000000000000000000000000−666−6000000000
χ484-4-44-2-222444-44-4-4-4-2-2-222-2220000000000000000000000000000−2i22i200i2−i2i2−i2000000000
χ494-4-44-2-222444-44-4-4-4-2-2-222-22200000000000000000000000000002i2−2i200−i2i2−i2i2000000000
χ508888-4-4-4-42-42-4-42-42-12-1-1222-144000000000000-2-2-2-2000011110000000000000000000
χ518888-4-4-4-42-42-4-42-42-12-1-1222-1-4-400000000000022220000-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-422-42-42-122-1-1-12000004-2-2-2-211110000000000000000000000000000000
χ538888-4-4-4-4-42-422-42-42-122-1-1-1200000-42222-1-1-1-10000000000000000000000000000000
χ5488-8-88-8-88-4242-2-4-24-42442-2-2-4000000000000000000000000000000000000000000000
χ5588-8-8-444-42-4-2-4424-2-12112-2-2-14-4000000000000-22-22000011-1-10000000000000000000
χ5688-8-8-444-42-4-2-4424-2-12112-2-2-1-440000000000002-22-20000-1-1110000000000000000000
χ5788-8-8-444-4-4242-2-4-242-1-2-2-1112000000−2i32i300i3i3−i3−i30000000000000000000000000000000
χ5888-8-8-444-4-4242-2-4-242-1-2-2-11120000002i3−2i300−i3−i3i3i30000000000000000000000000000000
χ598-88-88-88-82-4-244-2-422-4-2244-4-2000000000000000000000000000000000000000000000
χ608-88-8-44-442-4-244-2-42-121-1-2-22100000000000000000000003i−3i3i−3i0000000000000000000
χ618-88-8-44-442-4-244-2-42-121-1-2-2210000000000000000000000−3i3i−3i3i0000000000000000000
χ628-88-8-44-44-424-2-242-42-1-2211-1-200000000−2i32i3i3−i3i3−i30000000000000000000000000000000
χ638-88-8-44-44-424-2-242-42-1-2211-1-2000000002i3−2i3−i3i3−i3i30000000000000000000000000000000
χ648-8-8888-8-82-424-4-24-22-42-24-44-2000000000000000000000000000000000000000000000
χ658-8-8888-8-8-42-4-224-24-42-44-22-24000000000000000000000000000000000000000000000
χ668-8-88-4-4442-424-4-24-2-12-11-22-2100000000000000000000003i−3i−3i3i0000000000000000000
χ678-8-88-4-4442-424-4-24-2-12-11-22-210000000000000000000000−3i3i3i−3i0000000000000000000
χ688-8-88-4-444-42-4-224-242-12-21-11-200000000003-3-330000000000000000000000000000000
χ698-8-88-4-444-42-4-224-242-12-21-11-20000000000-333-30000000000000000000000000000000

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