Finite Group Databasebeta

← Group #13165636

Character table — Group #13165636

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122224444444488888888121818242424242424242424242424242424242424242424243636363636363636727272727272108108108
order12223666336666663366666644422666666666666666612121212881212242424244412121212288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-111-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11-111-1-11-1-1
χ3111111111111111111111111111-11-1-111-1-111-1-1-1-111111111-1-111-1-1-1-1-11-1-1111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1111
χ5111111111111111111111111-111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-111-111
χ7111111111111111111111111-111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-111-1-1-111
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
χ92222222222222222222222222-2-2000000000000000000222200-2-20000000000-200
χ10222222222222222222222222-2-2-2000000000000000000-2-2-2-200-2-20000000000200
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-102222-1-1-1-12222-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-10222-2-1-11122-2-2-1-1-1-111110000-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2211-1-1-2-2221111-1-1-1-10000-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-1022-2-21111-2-2-2-211111111000022-1-1-1-1-1-1000000000
χ1522-2-22-2-2222-2-222-2-22222-2-2-2-202-20000000000000000000000002-2000000000002i−2i
χ1622-2-22-2-2222-2-222-2-22222-2-2-2-202-20000000000000000000000002-200000000000−2i2i
χ1722-2-22-2-2222-2-222-2-22222-2-2-2-20-2200000000000000000000002-2-2222-2-2000000000
χ1822-2-22-2-2222-2-222-2-22222-2-2-2-20-220000000000000000000000-22-22-2-222000000000
χ1922-2-2-111-122-2-222-2-2-1-1-1-111110-2200−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i300002-21-1-1-111000000000
χ2022-2-2-111-122-2-222-2-2-1-1-1-111110-2200−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i30000-221-111-1-1000000000
χ2122-2-2-111-122-2-222-2-2-1-1-1-111110-2200i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i30000-221-111-1-1000000000
χ2222-2-2-111-122-2-222-2-2-1-1-1-111110-2200i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i300002-21-1-1-111000000000
χ23444444441-21-21-21-21-21-211-2-240002002200-1-10000-1-1-1-111-2-2000000000200-1-1000
χ24444444441-21-21-21-21-21-211-2-24000-200-2-200110000111111-2-2000000000-20011000
χ25444444441-21-21-21-21-21-211-2-2-40002002200-1-10000-1-1-1-1-1-122000000000-20011000
χ26444444441-21-21-21-21-21-211-2-2-4000-200-2-2001100001111-1-122000000000200-1-1000
χ2744444444-21-21-21-21-21-21-2-211400202200-1-100-1-1-1-10000-2-2110000000020-1-100000
χ2844444444-21-21-21-21-21-21-2-211400-20-2-200110011110000-2-21100000000-201100000
χ2944444444-21-21-21-21-21-21-2-211-400202200-1-100-1-1-1-1000022-1-100000000-201100000
χ3044444444-21-21-21-21-21-21-2-211-400-20-2-20011001111000022-1-10000000020-1-100000
χ314444-2-2-2-244444444-2-2-2-2-2-2-2-20-4-4000000000000000000000000220000000000000
χ3244-4-4-222-244-4-444-4-4-2-2-2-2222204-4000000000000000000000000-220000000000000
χ334-44-444-4-41-212-12-1-21-2-121-12-200000000000−i3i30000−i3i3−i3i33i−3i000000000000003−3000
χ344-44-444-4-41-212-12-1-21-2-121-12-200000000000−i3i30000−i3i3−i3i3−3i3i00000000000000−33000
χ354-44-444-4-41-212-12-1-21-2-121-12-200000000000i3−i30000i3−i3i3−i33i−3i00000000000000−33000
χ364-44-444-4-41-212-12-1-21-2-121-12-200000000000i3−i30000i3−i3i3−i3−3i3i000000000000003−3000
χ374-44-444-4-4444-4-4-4-4444-4-44-4-44000000000000000000000000000000000000000000
χ384-44-4-2-222444-4-4-4-44-2-222-222-200000000000000000000000000000i6−i6i6−i6000000000
χ394-44-4-2-222444-4-4-4-44-2-222-222-200000000000000000000000000000−i6i6−i6i6000000000
χ404-4-444-44-444-44-4-44-444-4-4-444-4000000000000000000000000000000000000000000
χ414-4-444-44-4-21212-1-2-1-212-12-21-1000000000−i3i300−i3i3−i3i30000003i−3i00000000003−300000
χ424-4-444-44-4-21212-1-2-1-212-12-21-1000000000−i3i300−i3i3−i3i3000000−3i3i0000000000−3300000
χ434-4-444-44-4-21212-1-2-1-212-12-21-1000000000i3−i300i3−i3i3−i30000003i−3i0000000000−3300000
χ444-4-444-44-4-21212-1-2-1-212-12-21-1000000000i3−i300i3−i3i3−i3000000−3i3i00000000003−300000
χ454-4-44-22-2244-44-4-44-4-2-2222-2-2200000000000000000000000000000i6−i6−i6i6000000000
χ464-4-44-22-2244-44-4-44-4-2-2222-2-2200000000000000000000000000000−i6i6i6−i6000000000
χ478888-4-4-4-42-42-42-42-4-12-12-1-1220000400-2-200-2-200001111000000000000000000000
χ488888-4-4-4-42-42-42-42-4-12-12-1-1220000-4002200220000-1-1-1-1000000000000000000000
χ498888-4-4-4-4-42-42-42-422-12-122-1-100040-2-200-2-20011110000000000000000000000000
χ508888-4-4-4-4-42-42-42-422-12-122-1-1000-4022002200-1-1-1-10000000000000000000000000
χ5188-8-88-8-882-4-242-4-242-42-4-2-244000000000000000000000000000000000000000000
χ5288-8-88-8-88-424-2-424-2-42-4244-2-2000000000000000000000000000000000000000000
χ5388-8-8-444-42-4-242-4-24-12-1211-2-20000000−2i32i300000000i3i3−i3−i3000000000000000000000
χ5488-8-8-444-42-4-242-4-24-12-1211-2-200000002i3−2i300000000−i3−i3i3i3000000000000000000000
χ5588-8-8-444-4-424-2-424-22-12-1-2-21100000−2i32i3000000i3i3−i3−i30000000000000000000000000
χ5688-8-8-444-4-424-2-424-22-12-1-2-211000002i3−2i3000000−i3−i3i3i30000000000000000000000000
χ578-88-888-8-8-42-4-24-242-424-2-44-22000000000000000000000000000000000000000000
χ588-88-8-4-4442-424-24-2-4-121-2-11-2200000000000−2i32i30000i3−i3i3−i3000000000000000000000
χ598-88-8-4-4442-424-24-2-4-121-2-11-22000000000002i3−2i30000−i3i3−i3i3000000000000000000000
χ608-88-8-4-444-42-4-24-2422-1-212-21-100000000000003-3-330000000000000000000000000
χ618-88-8-4-444-42-4-24-2422-1-212-21-10000000000000-333-30000000000000000000000000
χ628-8-888-88-82-4-2-4-24242-4-24-22-44000000000000000000000000000000000000000000
χ638-8-88-44-442-4-2-4-2424-121-21-12-2000000000000000003-3-33000000000000000000000
χ648-8-88-44-442-4-2-4-2424-121-21-12-200000000000000000-333-3000000000000000000000
χ658-8-88-44-44-42424-2-4-22-1-21-22-11000000000−2i32i300i3−i3i3−i30000000000000000000000000
χ668-8-88-44-44-42424-2-4-22-1-21-22-110000000002i3−2i300−i3i3−i3i30000000000000000000000000

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