Finite Group Databasebeta

← Group #13165674

Character table — Group #13165674

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666444444121212121212121212121212121212121212121244881212242424244441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1111111-1-1111111-1-1-1-111-1-111-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111-1111111111-1-111-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111
χ5111111111111111111111111-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ7111111111111111111111111-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11111
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
χ9222222222222222222222222002-2-20000000220022000000000000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-20000000-2-200-2-2000000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-1-1-122002200-1-1-1-1-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-211-1-12200-2-200-1-1-1-1111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-20222-1-111-2-20022001111-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-21111-2-200-2-200111111110022-1-1-1-1-1-1000000000
χ1522-2-22-2-22222-22-2-2-2222-2-2-22-2000-220000000000000000000002i−2i00-220000000002i−2i00
χ1622-2-22-2-22222-22-2-2-2222-2-2-22-2000-22000000000000000000000−2i2i00-22000000000−2i2i00
χ1722-2-22-2-22222-22-2-2-2222-2-2-22-22-202-20002-22-200000022-2-2000000002-20000000000000
χ1822-2-22-2-22222-22-2-2-2222-2-2-22-2-2202-2000-22-22000000-2-222000000002-20000000000000
χ1922-2-2-111-1222-22-2-2-2-1-1-1111-112-202-203−3-112-2000000-1-11133−3−30000-1133−3−3000000000
χ2022-2-2-111-1222-22-2-2-2-1-1-1111-112-202-20−33-112-2000000-1-111−3−3330000-11−3−333000000000
χ2122-2-2-111-1222-22-2-2-2-1-1-1111-11-2202-203−31-1-2200000011-1-133−3−30000-11−3−333000000000
χ2222-2-2-111-1222-22-2-2-2-1-1-1111-11-2202-20−331-1-2200000011-1-1−3−3330000-1133−3−3000000000
χ232-22-22-22-222-2-2-22-2222-22-2-2-220000000000000000000000000000−i2i200−i2i2−i2i22i−2i000002−2
χ242-22-22-22-222-2-2-22-2222-22-2-2-220000000000000000000000000000−i2i200−i2i2−i2i2−2i2i00000−22
χ252-22-22-22-222-2-2-22-2222-22-2-2-220000000000000000000000000000i2−i200i2−i2i2−i22i−2i00000−22
χ262-22-22-22-222-2-2-22-2222-22-2-2-220000000000000000000000000000i2−i200i2−i2i2−i2−2i2i000002−2
χ27444444441-21-2-211-21-21-21-2-2100400222000011-1-1-2-20000-1-1-1-10000000000002-1-10000
χ28444444441-21-2-211-21-21-21-2-2100400-2-2-200001111-2-200001111000000000000-2110000
χ29444444441-21-2-211-21-21-21-2-2100-4002220000-1-1-1-1220000-1-1-1-1000000000000-2110000
χ30444444441-21-2-211-21-21-21-2-2100-400-2-2-20000-1-11122000011110000000000002-1-10000
χ3144444444-21-211-2-21-21-21-211-22240000022-1-1-2-20011-1-1-1-10000220000000000000-1-100
χ3244444444-21-211-2-21-21-21-211-222-40000022-1-12200-1-1-1-1-1-10000-2-200000000000001100
χ3344444444-21-211-2-21-21-21-211-2-2-2400000-2-211-2-2001111110000-2-200000000000001100
χ3444444444-21-211-2-21-21-21-211-2-2-2-400000-2-2112200-1-111110000220000000000000-1-100
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-4-44-21-2-1122-1-21-2-12-1122-20000002-2-1100003i−3i-1-11100002i−2i0000000000000−ii00
χ3744-4-44-4-44-21-2-1122-1-21-2-12-1122-20000002-2-110000−3i3i-1-1110000−2i2i0000000000000i−i00
χ3844-4-44-4-44-21-2-1122-1-21-2-12-112-22000000-221-100003i−3i11-1-10000−2i2i0000000000000i−i00
χ3944-4-44-4-44-21-2-1122-1-21-2-12-112-22000000-221-10000−3i3i11-1-100002i−2i0000000000000−ii00
χ4044-4-4-222-2444-44-4-4-4-2-2-2222-22000-4400000000000000000000000002-20000000000000
χ414-44-4-22-2244-4-4-44-44-2-22-2222-20000000000000000000000000000−2i22i200i2−i2i2−i2000000000
χ424-44-4-22-2244-4-4-44-44-2-22-2222-200000000000000000000000000002i2−2i200−i2i2−i2i2000000000
χ434-4-4444-4-41-2-1-22-1121-2-121-22-10000000000003i−3i3−30000003−33−30000000000000−i3i30000
χ444-4-4444-4-41-2-1-22-1121-2-121-22-10000000000003i−3i−33000000−33−330000000000000i3−i30000
χ454-4-4444-4-41-2-1-22-1121-2-121-22-1000000000000−3i3i3−30000003−33−30000000000000i3−i30000
χ464-4-4444-4-41-2-1-22-1121-2-121-22-1000000000000−3i3i−33000000−33−330000000000000−i3i30000
χ474-4-4444-4-444-44-4-44-444-4-444-4-4000000000000000000000000000000000000000000000
χ484-4-44-2-22244-44-4-44-4-2-222-2-22200000000000000000000000000000000i6−i6−i6i6000000000
χ494-4-44-2-22244-44-4-44-4-2-222-2-22200000000000000000000000000000000−i6i6i6−i6000000000
χ508888-4-4-4-42-42-4-422-4-12-12-122-1000004-2-2000000-2-200000011110000000000000000000
χ518888-4-4-4-42-42-4-422-4-12-12-122-100000-42200000022000000-1-1-1-10000000000000000000
χ528888-4-4-4-4-42-422-4-422-12-12-1-1244000000-2-2-2-2000000111100000000000000000000000
χ538888-4-4-4-4-42-422-4-422-12-12-1-12-4-40000002222000000-1-1-1-100000000000000000000000
χ5488-8-88-8-882-424-4-2-242-424-24-4-2000000000000000000000000000000000000000000000
χ5588-8-8-444-42-424-4-2-24-12-1-21-22100000023−2300000000000000−3−3330000000000000000000
χ5688-8-8-444-42-424-4-2-24-12-1-21-221000000−23230000000000000033−3−30000000000000000000
χ5788-8-8-444-4-42-4-2244-22-121-21-1-24-4000000-22-2200000011-1-100000000000000000000000
χ5888-8-8-444-4-42-4-2244-22-121-21-1-2-440000002-22-2000000-1-11100000000000000000000000
χ598-88-88-88-82-4-2442-2-42-4-2-4-2442000000000000000000000000000000000000000000000
χ608-88-88-88-8-424-2-2-442-42424-2-2-4000000000000000000000000000000000000000000000
χ618-88-8-44-442-4-2442-2-4-12121-2-2-100000000000000000000003-3-330000000000000000000
χ628-88-8-44-442-4-2442-2-4-12121-2-2-10000000000000000000000-333-30000000000000000000
χ638-88-8-44-44-424-2-2-4422-1-2-1-21120000000000000000003i−3i3i−3i00000000000000000000000
χ648-88-8-44-44-424-2-2-4422-1-2-1-2112000000000000000000−3i3i−3i3i00000000000000000000000
χ658-8-8888-8-8-4242-24-4-2-424-2-42-24000000000000000000000000000000000000000000000
χ668-8-88-4-4442-4-2-44-224-121-2-12-210000000000000023−23000000−33−330000000000000000000
χ678-8-88-4-4442-4-2-44-224-121-2-12-2100000000000000−23230000003−33−30000000000000000000
χ688-8-88-4-444-4242-24-4-22-1-212-11-20000000000000000003i−3i−3i3i00000000000000000000000
χ698-8-88-4-444-4242-24-4-22-1-212-11-2000000000000000000−3i3i3i−3i00000000000000000000000

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