Finite Group Databasebeta

← Group #13165634

Character table — Group #13165634

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order1222366633666666336666664444412121212121212121212121212121212121212128812122424242424661212288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-11-1-1111-1-1
χ3111111111111111111111111111-1111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-11-1-1
χ4111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11-111-1-1-111
χ7111111111111111111111111-111-1111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-1-111-111
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
χ92222222222222222222222222-2-2000000220022000000000000-2-20000000000-200
χ10222222222222222222222222-2-2-2000000-2-200-2-2000000000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-1-1-100220022-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-211-1-100-2-20022-1-1-1-11111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-22-1-111002200-2-21111-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-2111100-2-200-2-21111111122-1-1-1-1-1-1000000000
χ152-22-22-2-2222-2-22-22-2222-2-2-22-202-200000000000000000000002i−2i2-22i2i−2i−2i000000000
χ162-22-22-2-2222-2-22-22-2222-2-2-22-202-20000000000000000000000−2i2i2-2−2i−2i2i2i000000000
χ172-22-22-2-2222-2-22-22-2222-2-2-22-20-22000000000000000000000000-22000000000002-2
χ182-22-22-2-2222-2-22-22-2222-2-2-22-20-22000000000000000000000000-2200000000000-22
χ192-22-2-111-122-2-22-22-2-1-1-1111-1102-2003−3−i3i300000000−i3−i3i3i333−3−32i−2i-11−i−iii000000000
χ202-22-2-111-122-2-22-22-2-1-1-1111-1102-2003−3i3−i300000000i3i3−i3−i333−3−3−2i2i-11ii−i−i000000000
χ212-22-2-111-122-2-22-22-2-1-1-1111-1102-200−33−i3i300000000−i3−i3i3i3−3−333−2i2i-11ii−i−i000000000
χ222-22-2-111-122-2-22-22-2-1-1-1111-1102-200−33i3−i300000000i3i3−i3−i3−3−3332i−2i-11−i−iii000000000
χ23444444441-21-2-2-2111-2-211-21-2400200022-2-20011-1-1-1-1-1-10000000000000200-1-1000
χ24444444441-21-2-2-2111-2-211-21-2400-2000-2-2-2-200111111110000000000000-20011000
χ25444444441-21-2-2-2111-2-211-21-2-4002000222200-1-1-1-1-1-1-1-10000000000000-20011000
χ26444444441-21-2-2-2111-2-211-21-2-400-2000-2-22200-1-11111110000000000000200-1-1000
χ2744444444-21-2111-2-2-211-2-21-2140002220011-1-1-2-2000000-1-1-1-10000000020-1-100000
χ2844444444-21-2111-2-2-211-2-21-214000-2-2-2001111-2-2000000111100000000-201100000
χ2944444444-21-2111-2-2-211-2-21-21-400022200-1-1-1-122000000-1-1-1-100000000-201100000
χ3044444444-21-2111-2-2-211-2-21-21-4000-2-2-200-1-1112200000011110000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-444-4-44444-4-4-4-444-44-44-4-4000000000000000000000000000000000000000000
χ3344-4-444-4-4-21-21-1-122-21-1-2212-10000000003i−3i3−3000000003−33−30000000000−i3i300000
χ3444-4-444-4-4-21-21-1-122-21-1-2212-10000000003i−3i−3300000000−33−330000000000i3−i300000
χ3544-4-444-4-4-21-21-1-122-21-1-2212-1000000000−3i3i3−3000000003−33−30000000000i3−i300000
χ3644-4-444-4-4-21-21-1-122-21-1-2212-1000000000−3i3i−3300000000−33−330000000000−i3i300000
χ3744-4-4-2-2224444-4-4-4-4-2-22-22-22200000000000000000000000000000i6−i6i6−i6000000000
χ3844-4-4-2-2224444-4-4-4-4-2-22-22-22200000000000000000000000000000−i6i6−i6i6000000000
χ394-44-4-222-244-4-44-44-4-2-2-2222-220-440000000000000000000000002-20000000000000
χ404-4-444-44-41-2-122-2-111-22-112-1-200000000000003i−3i3−33−33−30000000000000000−i3i3000
χ414-4-444-44-41-2-122-2-111-22-112-1-200000000000003i−3i−33−33−330000000000000000i3−i3000
χ424-4-444-44-41-2-122-2-111-22-112-1-20000000000000−3i3i3−33−33−30000000000000000i3−i3000
χ434-4-444-44-41-2-122-2-111-22-112-1-20000000000000−3i3i−33−33−330000000000000000−i3i3000
χ444-4-444-44-444-4-4-44-4444-4-44-4-44000000000000000000000000000000000000000000
χ454-4-44-22-2244-4-4-44-44-2-222-222-2000000000000000000000000000006−6−66000000000
χ464-4-44-22-2244-4-4-44-44-2-222-222-200000000000000000000000000000−666−6000000000
χ478888-4-4-4-42-42-4-4-422-122-1-12-120004000-2-2000000-2-21111000000000000000000000
χ488888-4-4-4-42-42-4-4-422-122-1-12-12000-40002200000022-1-1-1-1000000000000000000000
χ498888-4-4-4-4-42-4222-4-42-1-122-12-100004-2-20000-2-200000000111100000000000000000
χ508888-4-4-4-4-42-4222-4-42-1-122-12-10000-42200002200000000-1-1-1-100000000000000000
χ5188-8-888-8-82-42-444-2-22-442-2-4-24000000000000000000000000000000000000000000
χ5288-8-8-4-4442-42-444-2-2-12-2-1121-2000000000000000003i−3i−3i3i000000000000000000000
χ5388-8-8-4-4442-42-444-2-2-12-2-1121-200000000000000000−3i3i3i−3i000000000000000000000
χ5488-8-8-4-444-42-42-2-2442-112-2-1-210000000000023−2300000000−33−3300000000000000000
χ5588-8-8-4-444-42-42-2-2442-112-2-1-2100000000000−2323000000003−33−300000000000000000
χ568-88-88-8-882-4-24-442-22-4-4-2-2424000000000000000000000000000000000000000000
χ578-88-88-8-88-424-22-2-44-42244-2-4-2000000000000000000000000000000000000000000
χ588-88-8-444-42-4-24-442-2-12211-2-1-20000000−2i32i300000000i3i3−i3−i3000000000000000000000
χ598-88-8-444-42-4-24-442-2-12211-2-1-200000002i3−2i300000000−i3−i3i3i3000000000000000000000
χ608-88-8-444-4-424-22-2-442-1-1-2-21210000023−2300000000000000−3−33300000000000000000
χ618-88-8-444-4-424-22-2-442-1-1-2-212100000−23230000000000000033−3−300000000000000000
χ628-8-888-88-8-424-2-224-4-42-24-4-242000000000000000000000000000000000000000000
χ638-8-88-44-442-4-244-4-22-12-21-1-21200000000000000023−23−33−33000000000000000000000
χ648-8-88-44-442-4-244-4-22-12-21-1-212000000000000000−23233−33−3000000000000000000000
χ658-8-88-44-44-424-2-224-42-11-221-2-10000000000000000000003-3-3300000000000000000
χ668-8-88-44-44-424-2-224-42-11-221-2-1000000000000000000000-333-300000000000000000

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