Finite Group Databasebeta

← Group #13165641

Character table — Group #13165641

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order12223666336666663366666624444666612121212121212121212121212121212881212242424244412121212488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-11-1-1
χ3111111111111111111111111111-111111-1-111-1-111-1-1-1-11111-1-111-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-11-1-111-111
χ7111111111111111111111111-111-11-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-11-111-1-1-111
χ8111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1
χ92222222222222222222222222-2-2002222000000000000000000-2-20000000000-200
χ10222222222222222222222222-2-2-200-2-2-2-2000000000000000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-1022220000-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-20000-1-11122-2-2-1-1-1-11111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-22000011-1-1-2-2221111-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-200001111-2-2-2-21111111122-1-1-1-1-1-1000000000
χ152-2-222-2-2222-2-222-2-222-2-2-2-22202-20000000000000000000000002-2000000000002i−2i
χ162-2-222-2-2222-2-222-2-222-2-2-2-22202-20000000000000000000000002-200000000000−2i2i
χ172-2-222-2-2222-2-222-2-222-2-2-2-2220-2200000000000000000000002-2-2222-2-2000000000
χ182-2-222-2-2222-2-222-2-222-2-2-2-2220-220000000000000000000000-22-22-2-222000000000
χ192-2-22-111-122-2-222-2-2-1-11111-1-10-22000000−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i32-21-1-1-111000000000
χ202-2-22-111-122-2-222-2-2-1-11111-1-10-22000000−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3-221-111-1-1000000000
χ212-2-22-111-122-2-222-2-2-1-11111-1-10-22000000i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3-221-111-1-1000000000
χ222-2-22-111-122-2-222-2-2-1-11111-1-10-22000000i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i32-21-1-1-111000000000
χ23444444441-21-21-21-21-211-2-21-24000211-2-2002200-1-10000-1-1-1-1000000000200-1-1000
χ24444444441-21-21-21-21-211-2-21-24000-211-2-200-2-2001100001111000000000-20011000
χ25444444441-21-21-21-21-211-2-21-2-40002-1-122002200-1-10000-1-1-1-1000000000-20011000
χ26444444441-21-21-21-21-211-2-21-2-4000-2-1-12200-2-2001100001111000000000200-1-1000
χ2744444444-21-21-21-21-21-2-211-2140020-2-2112200-1-100-1-1-1-100000000000020-1-100000
χ2844444444-21-21-21-21-21-2-211-21400-20-2-211-2-20011001111000000000000-201100000
χ2944444444-21-21-21-21-21-2-211-21-4002022-1-12200-1-100-1-1-1-1000000000000-201100000
χ3044444444-21-21-21-21-21-2-211-21-400-2022-1-1-2-2001100111100000000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-444-4-41-212-12-1-21-21-12-2-12000003-3000000003−300003−33−30000000000003−3000
χ3344-4-444-4-41-212-12-1-21-21-12-2-12000003-300000000−330000−33−33000000000000−33000
χ3444-4-444-4-41-212-12-1-21-21-12-2-1200000-33000000003−300003−33−3000000000000−33000
χ3544-4-444-4-41-212-12-1-21-21-12-2-1200000-3300000000−330000−33−330000000000003−3000
χ3644-4-444-4-4444-4-4-4-44444-4-44-4-4000000000000000000000000000000000000000000
χ3744-4-4-2-222444-4-4-4-44-2-2-222-22200000000000000000000000000000i6−i6i6−i6000000000
χ3844-4-4-2-222444-4-4-4-44-2-2-222-22200000000000000000000000000000−i6i6−i6i6000000000
χ394-44-44-44-444-44-4-44-444-444-4-4-4000000000000000000000000000000000000000000
χ404-44-44-44-4-21212-1-2-1-212-21-12-100000003-300003−3003−33−3000000000000003−300000
χ414-44-44-44-4-21212-1-2-1-212-21-12-100000003-30000−3300−33−3300000000000000−3300000
χ424-44-44-44-4-21212-1-2-1-212-21-12-10000000-3300003−3003−33−300000000000000−3300000
χ434-44-44-44-4-21212-1-2-1-212-21-12-10000000-330000−3300−33−33000000000000003−300000
χ444-44-4-22-2244-44-4-44-4-2-22-2-222200000000000000000000000000000i6−i6−i6i6000000000
χ454-44-4-22-2244-44-4-44-4-2-22-2-222200000000000000000000000000000−i6i6i6−i6000000000
χ464-4-44-222-244-4-444-4-4-2-22222-2-204-4000000000000000000000000-220000000000000
χ478888-4-4-4-42-42-42-42-4-12-1-122-1200004000000-2-200-2-20000111100000000000000000
χ488888-4-4-4-42-42-42-42-4-12-1-122-120000-40000002200220000-1-1-1-100000000000000000
χ498888-4-4-4-4-42-42-42-422-122-1-12-1000400000-2-200-2-2001111000000000000000000000
χ508888-4-4-4-4-42-42-42-422-122-1-12-1000-40000022002200-1-1-1-1000000000000000000000
χ5188-8-888-8-8-42-4-24-242-42-44-224-2000000000000000000000000000000000000000000
χ5288-8-8-4-4442-424-24-2-4-12-11-221-200000000000000023−230000−33−3300000000000000000
χ5388-8-8-4-4442-424-24-2-4-12-11-221-2000000000000000−232300003−33−300000000000000000
χ5488-8-8-4-444-42-4-24-2422-12-21-1-21000000000000000003i−3i−3i3i000000000000000000000
χ5588-8-8-4-444-42-4-24-2422-12-21-1-2100000000000000000−3i3i3i−3i000000000000000000000
χ568-88-88-88-82-4-2-4-24242-4-22-44-24000000000000000000000000000000000000000000
χ578-88-8-44-442-4-2-4-2424-121-12-21-20000000000000000000003i−3i−3i3i00000000000000000
χ588-88-8-44-442-4-2-4-2424-121-12-21-2000000000000000000000−3i3i3i−3i00000000000000000
χ598-88-8-44-44-42424-2-4-22-1-22-11-21000000000000023−2300−33−33000000000000000000000
χ608-88-8-44-44-42424-2-4-22-1-22-11-210000000000000−2323003−33−3000000000000000000000
χ618-8-888-8-882-4-242-4-242-4-2-2442-4000000000000000000000000000000000000000000
χ628-8-888-8-88-424-2-424-2-4244-2-2-42000000000000000000000000000000000000000000
χ638-8-88-444-42-4-242-4-24-1211-2-2-1200000000000−2i32i300000000i3i3−i3−i300000000000000000
χ648-8-88-444-42-4-242-4-24-1211-2-2-12000000000002i3−2i300000000−i3−i3i3i300000000000000000
χ658-8-88-444-4-424-2-424-22-1-2-2112-1000000000−2i32i3000000i3i3−i3−i3000000000000000000000
χ668-8-88-444-4-424-2-424-22-1-2-2112-10000000002i3−2i3000000−i3−i3i3i3000000000000000000000

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