Finite Group Databasebeta

← Group #13166013

Character table — Group #13166013

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222223344444466666888888121212121212121212161616161616161616161616161616363636484848484848727272727272108108108108
order1233466223612121212466663336664661212121212123336661212121212121212124121212121212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1111-1-1111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111-1111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ522222222222222222222-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000000
χ622222222222222222222-1-1-1-1-1-1-2222-2-2222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111110000000000
χ72222-2222222-2-2-2-2-22222222222022-200-2-2-2222222-2-2-2-2-2-2-2-2-20000000000000000000
χ82222-2222222-2-2-2-2-22222-1-1-1-1-1-1022-200-2-2-2-1-1-1-1-1-1111111111000−i3−i3−i3i3i3i30000000000
χ92222-2222222-2-2-2-2-22222-1-1-1-1-1-1022-200-2-2-2-1-1-1-1-1-1111111111000i3i3i3−i3−i3−i30000000000
χ10222-122-122-1-12-1-1-1222-1-12222220-1-1200-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-100000000022-1-1-1-10000
χ11222-122-122-1-12-1-1-1222-1-12222220-1-1200-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1000000000-2-211110000
χ12222-1-22-122-1-1-2111-222-1-12222220-1-1-200111-1-1-1-1-1-1-2-2-211111100000000000−i3i3−i3i30000
χ13222-1-22-122-1-1-2111-222-1-12222220-1-1-200111-1-1-1-1-1-1-2-2-211111100000000000i3−i3i3−i30000
χ1422-122-1222-1-1-12-1-12-1-1222-1-12-1-12-1-1-1-1-12-1-12-1-12-1-12-1-122-1-1-1-12-1-12-1-12-1-10000000000
χ1522-122-1222-1-1-12-1-12-1-1222-1-12-1-1-2-1-1-1112-1-12-1-12-1-12-1-122-1-1-1-1-211-211-2110000000000
χ1622-122-1222-1-1-12-1-12-1-122-12-1-12-12-1-1-1-1-12-1-1-12-1-12-1-12-1-1-122-1-12-1-1-12-1-12-10000000000
χ1722-122-1222-1-1-12-1-12-1-122-12-1-12-1-2-1-1-1112-1-1-12-1-12-1-12-1-1-122-1-1-2111-211-210000000000
χ1822-122-1222-1-1-12-1-12-1-122-1-12-1-122-1-1-1-1-12-1-1-1-12-1-12-1-12-1-1-1-1222-1-1-1-12-1-120000000000
χ1922-122-1222-1-1-12-1-12-1-122-1-12-1-12-2-1-1-1112-1-1-1-12-1-12-1-12-1-1-1-122-21111-211-20000000000
χ2022-12-2-1222-1-11-211-2-1-1222-1-12-1-10-1-11−i3i3-2112-1-12-1-1-211-2-211110−i3i30−i3i30i3−i30000000000
χ2122-12-2-1222-1-11-211-2-1-1222-1-12-1-10-1-11i3−i3-2112-1-12-1-1-211-2-211110i3−i30i3−i30−i3i30000000000
χ2222-12-2-1222-1-11-211-2-1-122-12-1-12-10-1-11−i3i3-211-12-1-12-11-2111-2-2110−i3i3i30−i3−i30i30000000000
χ2322-12-2-1222-1-11-211-2-1-122-12-1-12-10-1-11i3−i3-211-12-1-12-11-2111-2-2110i3−i3−i30i3i30−i30000000000
χ2422-12-2-1222-1-11-211-2-1-122-1-12-1-120-1-11−i3i3-211-1-12-1-1211-21111-2-20−i3i3−i3i30i3−i300000000000
χ2522-12-2-1222-1-11-211-2-1-122-1-12-1-120-1-11i3−i3-211-1-12-1-1211-21111-2-20i3−i3i3−i30−i3i300000000000
χ262-2220-2-22-22-2000002-22-2222-2-2-202-2000000222-2-2-20000000000000000000000002−22−2
χ272-2220-2-22-22-2000002-22-2222-2-2-202-2000000222-2-2-2000000000000000000000000−22−22
χ283333333-1-1333333-1-1-1-1-10000003-1-1-133-1-1-1000000000000000-1-1-10000001-111-1-111-1-1
χ293333333-1-1333333-1-1-1-1-10000003-1-1-133-1-1-1000000000000000-1-1-1000000-11-1-111-1-111
χ303333333-1-1333333-1-1-1-1-1000000-3-1-1-1-3-3-1-1-10000000000000001110000001-111-1-1-1-111
χ313333333-1-1333333-1-1-1-1-1000000-3-1-1-1-3-3-1-1-1000000000000000111000000-11-1-11111-1-1
χ32444-244-244-2-24-2-2-2444-2-2-2-2-2-2-2-20-2-2400-2-2-2111111-2-2-21111110000000000000000000
χ33444-2-44-244-2-2-4222-444-2-2-2-2-2-2-2-20-2-2-400222111111222-1-1-1-1-1-10000000000000000000
χ3444-2-24-2-24411-2-2114-2-2-2-24-2-24-2-2011-200-211-211-2114-2-2-2-211110000000000000000000
χ3544-2-24-2-24411-2-2114-2-2-2-2-24-2-24-2011-200-2111-211-21-24-211-2-2110000000000000000000
χ3644-2-24-2-24411-2-2114-2-2-2-2-2-24-2-24011-200-21111-211-2-2-241111-2-20000000000000000000
χ3744-2-2-4-2-2441122-1-1-4-2-2-2-24-2-24-2-20112002-1-1-211-211-42222-1-1-1-10000000000000000000
χ3844-2-2-4-2-2441122-1-1-4-2-2-2-2-24-2-24-20112002-1-11-211-212-42-1-122-1-10000000000000000000
χ3944-2-2-4-2-2441122-1-1-4-2-2-2-2-2-24-2-240112002-1-111-211-222-4-1-1-1-1220000000000000000000
χ404-4440-4-44-44-4000004-44-4-2-2-222204-4000000-2-2-22220000000000000000000000000000
χ414-44-20-424-4-22000004-4-22444-4-4-40-22000000-2-2-22220000000000000000000000000000
χ424-44-20-424-4-22000004-4-22-2-2-22220-22000000111-1-1-10003i−3i3i−3i3i−3i0000000000000000000
χ434-44-20-424-4-22000004-4-22-2-2-22220-22000000111-1-1-1000−3i3i−3i3i−3i3i0000000000000000000
χ444-4-2402-44-4-2200000-224-44-2-2-4220-220000004-2-2-4220000000000000000000000000000
χ454-4-2402-44-4-2200000-224-4-24-22-420-22000000-24-22-420000000000000000000000000000
χ464-4-2402-44-4-2200000-224-4-2-2422-40-22000000-2-2422-40000000000000000000000000000
χ474-4-2-20224-41-1003i−3i0-22-224-2-2-42201-100003i−3i-2112-1-1000003i−3i−3i3i0000000000000000000
χ484-4-2-20224-41-1003i−3i0-22-22-24-22-4201-100003i−3i1-21-12-1000−3i3i003i−3i0000000000000000000
χ494-4-2-20224-41-1003i−3i0-22-22-2-2422-401-100003i−3i11-2-1-120003i−3i−3i3i000000000000000000000
χ504-4-2-20224-41-100−3i3i0-22-224-2-2-42201-10000−3i3i-2112-1-100000−3i3i3i−3i0000000000000000000
χ514-4-2-20224-41-100−3i3i0-22-22-24-22-4201-10000−3i3i1-21-12-10003i−3i00−3i3i0000000000000000000
χ524-4-2-20224-41-100−3i3i0-22-22-2-2422-401-10000−3i3i11-2-1-12000−3i3i3i−3i000000000000000000000
χ536666-666-2-266-6-6-6-62-2-2-2-20000000-2-22002220000000000000000000000000000000000
χ54666-366-3-2-2-3-36-3-3-3-2-2-211000000011-2001110000000000000000000000002-2-1-1110000
χ55666-366-3-2-2-3-36-3-3-3-2-2-211000000011-200111000000000000000000000000-2211-1-10000
χ56666-3-66-3-2-2-3-3-63332-2-211000000011200-1-1-100000000000000000000000000−i3i3i3−i30000
χ57666-3-66-3-2-2-3-3-63332-2-211000000011200-1-1-100000000000000000000000000i3−i3−i3i30000
χ5866-366-36-2-2-3-3-36-3-3-211-2-20000006111-3-3-211000000000000000-2110000000000000000
χ5966-366-36-2-2-3-3-36-3-3-211-2-2000000-611133-2110000000000000002-1-10000000000000000
χ6066-36-6-36-2-2-3-33-633211-2-2000000011-1−3i33i32-1-10000000000000000i3−i30000000000000000
χ6166-36-6-36-2-2-3-33-633211-2-2000000011-13i3−3i32-1-10000000000000000−i3i30000000000000000
χ626-6660-6-6-226-600000-22-220000000-220000000000000000000000000000000000002−2−22
χ636-6660-6-6-226-600000-22-220000000-22000000000000000000000000000000000000−222−2
χ641212-6-612-6-6-4-433-6-633-422220000000-1-12002-1-10000000000000000000000000000000000
χ651212-6-6-12-6-6-4-43366-3-3422220000000-1-1-200-2110000000000000000000000000000000000
χ6612-1212-60-126-44-6600000-442-200000002-20000000000000000000000000000000000000000
χ6712-12-61206-12-44-66000002-2-4400000002-20000000000000000000000000000000000000000
χ6812-12-6-6066-443-3009i−9i02-22-20000000-110000−3i3i0000000000000000000000000000000000
χ6912-12-6-6066-443-300−9i9i02-22-20000000-1100003i−3i0000000000000000000000000000000000

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