Finite Group Databasebeta

← Group #13165564

Character table — Group #13165564

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1122244444448888888121212121212121212121216181818182424242424242424242424242436363648487272727272727272108216
order122363366666336666622444661212121264412126666612121212121212122412612468121212242428
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-111-1-1-1-111111111111-1-11-1-1-1-111111-11-11-1-1-1-11-1
χ311111111111111111111-1111-1-11111111111-1-11-111111111-1-1111-1-11-1-1-111-1-1
χ411111111111111111111-11-1-1-1-1-1-1-1-1111111-1-11-11-1-11-1-1-1-1-1-11111-1-1-111-1-1-11
χ51111111111111111111-11-11111111111111-111-11-111-11111-1-11-1-11-1-1-111-1-11-1
χ61111111111111111111-11-1-1-111-1-1-1-111111-111-11-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-11111
χ71111111111111111111-1-1-111-1-1111111111-1-1-1-1-1-111-11111111-1-1-11-11-1-1-1-1-11
χ81111111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1-1
χ92222222222222222222020002200002-2-2-2-2022020000000000-20000000000-20
χ1022222222222222222220-2000-2-200002-2-2-2-20-2-20-20000000000-2000000000020
χ11222-1-1222-1222-1-12-1-1-1-12022200-1-1-1-1-122-1-1-10020-1222-1-1-1-100-1-1-1002000-1-100
χ12222-1-1222-1222-1-12-1-1-1-1202-2-2001111-122-1-1-10020-1-2-22111100-1-1-100-20001100
χ13222-1-1222-1222-1-12-1-1-1-1-20-22200-1-1-1-1-122-1-1100-20122-2-1-1-1-100-11100-20001100
χ14222-1-1222-1222-1-12-1-1-1-1-20-2-2-2001111-122-1-1100-201-2-2-2111100-111002000-1-100
χ1522-22222-2-2-22222-22-22-200000000000-22-22200000000000002-2-200020-2000000
χ1622-22222-2-2-22222-22-22-200000000000-22-2220000000000000-22-2000-202000000
χ1722-22222-2-2-22222-22-22-220-200000000-2-22-2-220020-200-200000022-20000000000
χ1822-22222-2-2-22222-22-22-2-20200000000-2-22-2-2-200-2020020000002-220000000000
χ1922-2-1-122-21-222-1-1-2-11-1120-2000033−3−31-2211-10020100-233−3−300-1-110000003−300
χ2022-2-1-122-21-222-1-1-2-11-1120-20000−3−3331-2211-10020100-2−3−33300-1-11000000−3300
χ2122-2-1-122-21-222-1-1-2-11-11-202000033−3−31-2211100-20-100233−3−300-11-1000000−3300
χ2222-2-1-122-21-222-1-1-2-11-11-2020000−3−3331-2211100-20-1002−3−33300-11-10000003−300
χ23444441-2141-211-2-211-2104022-2-22222-200000110-20-1-10-1-1-1-1000002000-1-10000
χ24444441-2141-211-2-211-21040-2-2-2-2-2-2-2-2-200000110-20110111100000-2000110000
χ25444441-2141-211-2-211-210-4022222222-200000-1-1020-1-10-1-1-1-100000-2000110000
χ26444441-2141-211-2-211-210-40-2-222-2-2-2-2-200000-1-10201101111000002000-1-10000
χ2744444-21-24-21-2-211-2-21-224200110000100002-2-2-11200-10000220-1-10-10-1000000
χ2844444-21-24-21-2-211-2-21-22-4200-1-1000010000222-1-1200-10000-2-20-1-10101000000
χ2944444-21-24-21-2-211-2-21-2-24-20011000010000-2-2-211-20010000-2-20110101000000
χ3044444-21-24-21-2-211-2-21-2-2-4-200-1-1000010000-2221-1-20010000220110-10-1000000
χ31444-2-2444-2444-2-24-2-2-2-200000000000-2-4-4220000000000000002000000000000
χ3244-444-212-421-2-21-1-221220-200330000-10000200-1-3-20010000-220-11010-1000000
χ3344-444-212-421-2-21-1-221220-200-3-30000-10000200-13-200100002-20-110-101000000
χ3444-444-212-421-2-21-1-2212-20200330000-10000-2001-3200-100002-201-10-101000000
χ3544-444-212-421-2-21-1-2212-20200-3-30000-10000-20013200-10000-2201-1010-1000000
χ3644-4-2-244-42-444-2-2-4-22-220000000000024-4-2-20000000000000002000000000000
χ374-404-41-2-3032-11-20-1-3230002i−2i−2i32i32i−2i2i−2i000000−i3i3000i−i0i−ii−i0000000003−30000
χ384-404-41-2-3032-11-20-1-3230002i−2i2i3−2i32i−2i2i−2i000000i3−i3000i−i0i−ii−i000000000−330000
χ394-404-41-2-3032-11-20-1-323000−2i2i−2i32i3−2i2i−2i2i000000−i3i3000−ii0−ii−ii000000000−330000
χ404-404-41-2-3032-11-20-1-323000−2i2i2i3−2i3−2i2i−2i2i000000i3−i3000−ii0−ii−ii0000000003−30000
χ414-404-444000-4-4440-40-400002i−2i002i−2i2i−2i00000000000−2i2i0−2i2i−2i2i000000000000000
χ424-404-444000-4-4440-40-40000−2i2i00−2i2i−2i2i000000000002i−2i02i−2i2i−2i000000000000000
χ434-40-2244000-4-4-2-2020200002i−2i00−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100023−23000000−2i2i0ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000
χ444-40-2244000-4-4-2-2020200002i−2i00ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000−2323000000−2i2i0−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000
χ454-40-2244000-4-4-2-202020000−2i2i00−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000−23230000002i−2i0ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000
χ464-40-2244000-4-4-2-202020000−2i2i00ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100023−230000002i−2i0−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000
χ47888-4-42-42-42-42-12-4-1-12-10004400-2-2-2-220000000000-2-201111000000000000000
χ48888-4-42-42-42-42-12-4-1-12-1000-4-400222220000000000220-1-1-1-1000000000000000
χ49888-4-4-42-4-4-42-42-1222-1240400000000-10000-200-20-200-20000000110000000000
χ50888-4-4-42-4-4-42-42-1222-12-40-400000000-100002002020020000000-1-10000000000
χ5188-8882-4-2-8-2-422-442-2-4-200000000000400000000000000000000000000000000
χ5288-8-4-42-4-24-2-42-124-112100000002323−23−23-20000000000000−3−333000000000000000
χ5388-8-4-42-4-24-2-42-124-11210000000−23−232323-2000000000000033−3−3000000000000000
χ5488-8-4-4-424442-42-1-22-2-1-240-40000000010000-200-20200200000001-10000000000
χ5588-8-4-4-424442-42-1-22-2-1-2-404000000001000020020-200-20000000-110000000000
χ568-808-82-460-64-22-40-264-600000000000000000000000000000000000000000000
χ578-808-8-42000-24-42040-2000000−2i32i300000000002i3−2i30000000000000000000000000
χ588-808-8-42000-24-42040-20000002i3−2i30000000000−2i32i30000000000000000000000000
χ598-80-442-460-64-2-1201-3-230000000−2i32i32i3−2i300000000000000−i3i3i3−i3000000000000000
χ608-80-442-460-64-2-1201-3-2300000002i3−2i3−2i32i300000000000000i3−i3−i3i3000000000000000
χ618-80-442-4-6064-2-12013-2-30004i−4i00−2i2i−2i2i000000000002i−2i0−ii−ii000000000000000
χ628-80-442-4-6064-2-12013-2-3000−4i4i002i−2i2i−2i00000000000−2i2i0i−ii−i000000000000000
χ6316-160-88-84000-484-20-402000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.