Finite Group Databasebeta

← Group #13165637

Character table — Group #13165637

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order1222366633666666336666662442466666666666612121212121212128812122424242424661212488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1111-1-1
χ3111111111111111111111111111-11-1-111-1-111-1-1-1-111111111-1-111-1-1-1-11-111-1-11-1-1
χ4111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111
χ5111111111111111111111111-1111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-111-1-1-111
χ7111111111111111111111111-111-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-11-1-111-111
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
χ92222222222222222222222222-2-2000022002200000000000000-2-20000000000-200
χ10222222222222222222222222-2-2-20000-2-200-2-200000000000000-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-1002200-1-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-2-1-1002200-1-1-1-111-2-21111-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-221100-2-2001111-1-122-1-1-1-1-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-21100-2-200111111-2-2111122-1-1-1-1-1-1000000000
χ152-2-222-2-22222-22-2-2-2222-22-2-2-202-200000000000000000000002i−2i2-22i2i−2i−2i000000000
χ162-2-222-2-22222-22-2-2-2222-22-2-2-202-20000000000000000000000−2i2i2-2−2i−2i2i2i000000000
χ172-2-222-2-22222-22-2-2-2222-22-2-2-20-22000000000000000000000000-22000000000002-2
χ182-2-222-2-22222-22-2-2-2222-22-2-2-20-22000000000000000000000000-2200000000000-22
χ192-2-22-111-1222-22-2-2-2-1-1-11-111102-200−i3i3000000−i3−i3i3i33−30033−3−32i−2i-11−i−iii000000000
χ202-2-22-111-1222-22-2-2-2-1-1-11-111102-200−i3i3000000−i3−i3i3i3−3300−3−333−2i2i-11ii−i−i000000000
χ212-2-22-111-1222-22-2-2-2-1-1-11-111102-200i3−i3000000i3i3−i3−i33−30033−3−3−2i2i-11ii−i−i000000000
χ222-2-22-111-1222-22-2-2-2-1-1-11-111102-200i3−i3000000i3i3−i3−i3−3300−3−3332i−2i-11−i−iii000000000
χ23444444441-211-2-2-21-21-2-2111-2400202211-1-1-2-2-1-1-1-100000000000000000200-1-1000
χ24444444441-211-2-2-21-21-2-2111-2400-20-2-21111-2-2111100000000000000000-20011000
χ25444444441-211-2-2-21-21-2-2111-2-4002022-1-1-1-122-1-1-1-100000000000000000-20011000
χ26444444441-211-2-2-21-21-2-2111-2-400-20-2-2-1-11122111100000000000000000200-1-1000
χ2744444444-21-2-2111-21-211-2-2-214000200-2-20011000022-1-1-1-1-1-10000000020-1-100000
χ2844444444-21-2-2111-21-211-2-2-214000-200-2-200110000-2-211111100000000-201100000
χ2944444444-21-2-2111-21-211-2-2-21-40002002200-1-1000022-1-1-1-1-1-100000000-201100000
χ3044444444-21-2-2111-21-211-2-2-21-4000-2002200-1-10000-2-21111110000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-44-44-444-44-4-44-444-4-4-44-44000000000000000000000000000000000000000000
χ3344-4-44-44-4-212-2-1-1121-2-1-12-221000000000003-3000000−i3i3−i3i3−i3i30000000000−i3i300000
χ3444-4-44-44-4-212-2-1-1121-2-1-12-221000000000003-3000000i3−i3i3−i3i3−i30000000000i3−i300000
χ3544-4-44-44-4-212-2-1-1121-2-1-12-22100000000000-33000000−i3i3−i3i3−i3i30000000000i3−i300000
χ3644-4-44-44-4-212-2-1-1121-2-1-12-22100000000000-33000000i3−i3i3−i3i3−i30000000000−i3i300000
χ3744-4-4-22-2244-44-4-44-4-2-2222-22-200000000000000000000000000000i6−i6i6−i6000000000
χ3844-4-4-22-2244-44-4-44-4-2-2222-22-200000000000000000000000000000−i6i6−i6i6000000000
χ394-44-444-4-41-2-1-12-221-212-2-1-11200000003-3−i3i300−i3i3−i3i300000000000000000000−i3i3000
χ404-44-444-4-41-2-1-12-221-212-2-1-11200000003-3i3−i300i3−i3i3−i300000000000000000000i3−i3000
χ414-44-444-4-41-2-1-12-221-212-2-1-1120000000-33−i3i300−i3i3−i3i300000000000000000000i3−i3000
χ424-44-444-4-41-2-1-12-221-212-2-1-1120000000-33i3−i300i3−i3i3−i300000000000000000000−i3i3000
χ434-44-444-4-444-4-4-44-4444-44-4-44-4000000000000000000000000000000000000000000
χ444-44-4-2-22244-4-4-44-44-2-22-222-22000000000000000000000000000006−6−66000000000
χ454-44-4-2-22244-4-4-44-44-2-22-222-2200000000000000000000000000000−666−6000000000
χ464-4-44-222-2444-44-4-4-4-2-2-22-22220-440000000000000000000000002-20000000000000
χ478888-4-4-4-42-422-4-4-422-122-1-1-1200040-2-200-2-20011110000000000000000000000000
χ488888-4-4-4-42-422-4-4-422-122-1-1-12000-4022002200-1-1-1-10000000000000000000000000
χ498888-4-4-4-4-42-4-4222-4-12-1-1222-100004000000000000-2-2-2-2111100000000000000000
χ508888-4-4-4-4-42-4-4222-4-12-1-1222-10000-40000000000002222-1-1-1-100000000000000000
χ5188-8-88-88-82-4-2244-4-2-4244-22-2-4000000000000000000000000000000000000000000
χ5288-8-8-44-442-4-2244-4-22-1-2-21-11200000000000003-3-330000000000000000000000000
χ5388-8-8-44-442-4-2244-4-22-1-2-21-1120000000000000-333-30000000000000000000000000
χ5488-8-8-44-44-424-4-2-224-1211-22-2-10000000000000000000−2i32i3i3−i3i3−i300000000000000000
χ5588-8-8-44-44-424-4-2-224-1211-22-2-100000000000000000002i3−2i3−i3i3−i3i300000000000000000
χ568-88-888-8-8-4244-22-2-42-4-2244-4-2000000000000000000000000000000000000000000
χ578-88-8-4-4442-4-2-24-4422-1-2211-1-2000000000−2i32i300i3−i3i3−i30000000000000000000000000
χ588-88-8-4-4442-4-2-24-4422-1-2211-1-20000000002i3−2i300−i3i3−i3i30000000000000000000000000
χ598-88-8-4-444-4244-22-2-4-121-1-2-2210000000000000000000003i−3i−3i3i00000000000000000
χ608-88-8-4-444-4244-22-2-4-121-1-2-221000000000000000000000−3i3i3i−3i00000000000000000
χ618-8-888-8-882-42-2-444-2-42-442-2-24000000000000000000000000000000000000000000
χ628-8-888-8-88-42-442-2-242-42-2-444-2000000000000000000000000000000000000000000
χ638-8-88-444-42-42-2-444-22-12-2-111-200000−2i32i3000000i3i3−i3−i30000000000000000000000000
χ648-8-88-444-42-42-2-444-22-12-2-111-2000002i3−2i3000000−i3−i3i3i30000000000000000000000000
χ658-8-88-444-4-42-442-2-24-12-112-2-210000000000000000023−2300−3−33300000000000000000
χ668-8-88-444-4-42-442-2-24-12-112-2-2100000000000000000−23230033−3−300000000000000000

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