Finite Group Databasebeta

← Group #13165594

Character table — Group #13165594

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order12223666336666663366666622444466666666121212121212121212121212448812122424242444266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-111111111-1-11111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-111-1-1
χ311111111111111111111111111-11111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111
χ5111111111111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111111-1-1-1-1
χ6111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ7111111111111111111111111-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111
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
χ9222222222222222222222222002-2-20000000000022220000000000-2-20000-2-20000000
χ1022222222222222222222222200-2-2-200000000000-2-2-2-20000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1220222-1-122-1-1-1-1-1-1000022-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-122022-2-1-122-1-1-1-1110000-2-2111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022211-2-21111-1-1000022-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1-2-2022-211-2-21111110000-2-211110022-1-1-1-1-1-1000000000
χ1522-2-222-2-222-2-222-2-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i22i−2i000002−2
χ1622-2-222-2-222-2-222-2-2222-22-2-2-20000000000000000000000000000−i2i200−i2−i2i2i2−2i2i00000−22
χ1722-2-222-2-222-2-222-2-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i22i−2i00000−22
χ1822-2-222-2-222-2-222-2-2222-22-2-2-20000000000000000000000000000i2−i200i2i2−i2−i2−2i2i000002−2
χ192-22-22-2-22222-2-2-22-222-2-2-22-220002-20000000000000000000002i−2i002-20000000002i−2i00
χ202-22-22-2-22222-2-2-22-222-2-2-22-220002-2000000000000000000000−2i2i002-2000000000−2i2i00
χ212-22-22-2-22222-2-2-22-222-2-2-22-222-20-2202-22-222-2-20000000000000000-220000000000000
χ222-22-22-2-22222-2-2-22-222-2-2-22-22-220-220-22-22-2-2220000000000000000-220000000000000
χ232-22-2-111-1222-2-2-22-2-1-1111-11-12-20-220-112-2-1-111−i3i3000000−i3−i3i3i300001-1−i3i3−i3i3000000000
χ242-22-2-111-1222-2-2-22-2-1-1111-11-12-20-220-112-2-1-111i3−i3000000i3i3−i3−i300001-1i3−i3i3−i3000000000
χ252-22-2-111-1222-2-2-22-2-1-1111-11-1-220-2201-1-2211-1-1−i3i3000000−i3−i3i3i300001-1i3−i3i3−i3000000000
χ262-22-2-111-1222-2-2-22-2-1-1111-11-1-220-2201-1-2211-1-1i3−i3000000i3i3−i3−i300001-1−i3i3−i3i3000000000
χ27444444441-21-21-2-21-21-2-2111-222400022-1-1-1-1-1-10011-2-2000000220000000000000-1-100
χ28444444441-21-21-2-21-21-2-2111-222-400022-1-1-1-1-1-100-1-122000000-2-200000000000001100
χ29444444441-21-21-2-21-21-2-2111-2-2-24000-2-21111110011-2-2000000-2-200000000000001100
χ30444444441-21-21-2-21-21-2-2111-2-2-2-4000-2-211111100-1-122000000220000000000000-1-100
χ3144444444-21-21-211-21-211-2-2-210040020000000022-2-211-1-1-1-1-1-10000000000002-1-10000
χ3244444444-21-21-211-21-211-2-2-2100400-200000000-2-2-2-211111111000000000000-2110000
χ3344444444-21-21-211-21-211-2-2-2100-4002000000002222-1-1-1-1-1-1-1-1000000000000-2110000
χ3444444444-21-21-211-21-211-2-2-2100-400-200000000-2-222-1-11111110000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-4-2-22244-4-444-4-4-2-2-22-22220000000000000000000000000000−2i22i200i2i2−i2−i2000000000
χ3744-4-4-2-22244-4-444-4-4-2-2-22-222200000000000000000000000000002i2−2i200−i2−i2i2i2000000000
χ384-44-44-4-441-212-12-2-1-2122-11-1-22-200002-2-11-1-111003i−3i000000002i−2i0000000000000−ii00
χ394-44-44-4-441-212-12-2-1-2122-11-1-22-200002-2-11-1-11100−3i3i00000000−2i2i0000000000000i−i00
χ404-44-44-4-441-212-12-2-1-2122-11-1-2-220000-221-111-1-1003i−3i00000000−2i2i0000000000000i−i00
χ414-44-44-4-441-212-12-2-1-2122-11-1-2-220000-221-111-1-100−3i3i000000002i−2i0000000000000−ii00
χ424-44-4-222-2444-4-4-44-4-2-2222-22-20004-40000000000000000000000000-220000000000000
χ434-4-444-44-444-44-4-4-4444-44-4-44-4000000000000000000000000000000000000000000000
χ444-4-444-44-4-21212-1-1-21-2-1122-2-10000000000000000003i−3i3−33−33−30000000000000−i3i30000
χ454-4-444-44-4-21212-1-1-21-2-1122-2-10000000000000000003i−3i−33−33−330000000000000i3−i30000
χ464-4-444-44-4-21212-1-1-21-2-1122-2-1000000000000000000−3i3i3−33−33−30000000000000i3−i30000
χ474-4-444-44-4-21212-1-1-21-2-1122-2-1000000000000000000−3i3i−33−33−330000000000000−i3i30000
χ484-4-44-22-2244-44-4-4-44-2-22-222-22000000000000000000000000000000006−6−66000000000
χ494-4-44-22-2244-44-4-4-44-2-22-222-2200000000000000000000000000000000−666−6000000000
χ508888-4-4-4-42-42-42-4-422-122-1-1-12440000-2-2-2-211110000000000000000000000000000000
χ518888-4-4-4-42-42-42-4-422-122-1-1-12-4-400002222-1-1-1-10000000000000000000000000000000
χ528888-4-4-4-4-42-42-422-4-12-1-1222-100000400000000-2-20000-2-211110000000000000000000
χ538888-4-4-4-4-42-42-422-4-12-1-1222-100000-40000000022000022-1-1-1-10000000000000000000
χ5488-8-888-8-82-4-242-44-2-42-442-2-24000000000000000000000000000000000000000000000
χ5588-8-888-8-8-424-2-42-242-42-2-444-2000000000000000000000000000000000000000000000
χ5688-8-8-4-4442-4-242-44-22-12-2-111-200000000003-33-30000000000000000000000000000000
χ5788-8-8-4-4442-4-242-44-22-12-2-111-20000000000-33-330000000000000000000000000000000
χ5888-8-8-4-444-424-2-42-24-12-112-2-2100000000000000000000003i−3i−3i3i0000000000000000000
χ5988-8-8-4-444-424-2-42-24-12-112-2-210000000000000000000000−3i3i3i−3i0000000000000000000
χ608-88-88-8-88-42-4-24-2242-4-2-24-442000000000000000000000000000000000000000000000
χ618-88-8-444-42-424-24-4-22-1-2-21-1124-40000-22-2211-1-10000000000000000000000000000000
χ628-88-8-444-42-424-24-4-22-1-2-21-112-4400002-22-2-1-1110000000000000000000000000000000
χ638-88-8-444-4-42-4-24-224-1211-22-2-100000000000000−2i32i3000000i3i3−i3−i30000000000000000000
χ648-88-8-444-4-42-4-24-224-1211-22-2-1000000000000002i3−2i3000000−i3−i3i3i30000000000000000000
χ658-8-888-88-82-4-2-4-2442-424-4-2-224000000000000000000000000000000000000000000000
χ668-8-88-44-442-4-2-4-24422-1-2211-1-200000000003-3-330000000000000000000000000000000
χ678-8-88-44-442-4-2-4-24422-1-2211-1-20000000000-333-30000000000000000000000000000000
χ688-8-88-44-44-42424-2-2-4-121-1-2-2210000000000000000000023−23−33−330000000000000000000
χ698-8-88-44-44-42424-2-2-4-121-1-2-22100000000000000000000−23233−33−30000000000000000000

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