Finite Group Databasebeta

← Group #13138993

Character table — Group #13138993

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222222244444446666666666661212121212121212121212121212121212121212121212121212363636363636363636363636727272727272727272727272
order12234466688812122424242433661212121224242424366666121212121212242424242424242424242424242424668812122424242444881212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-11-111-1-111-1-1
χ6111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-11-11-1-111-1-111
χ7111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1111-1-1-1-111
χ8111111111-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-1-11111-1-1
χ92222222222222222222-12-1-1-122-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ102222222222222222222-12-1-1-122-1-1-1-1-12-1-1-1-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ11222222222222222222-12-1222-1-12222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000220000-1-1-1-1
χ12222222222222222222-12-1222-1-12222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000000000-2-200001111
χ13222222222-2-2-222-2-2-2-22-12-1-1-1221111-12-1-1-1-1-1-1-12-1-111-2-2-2-21111111122-1-1-2-2-1-11111000000000000
χ14222222222-2-2-222-2-2-2-22-12-1-1-1221111-12-1-1-1-1-1-1-12-1-111-2-2-2-211111111-2-2112211-1-1-1-1000000000000
χ15222222222-2-2-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-12-1-1-12-1-1-1-1-1-2-2111111111111000000000000002-20000-1-111
χ16222222222-2-2-222-2-2-2-2-12-1222-1-1-2-2-2-2-1-12-1-1-12-1-1-1-1-1-2-211111111111100000000000000-22000011-1-1
χ172222-2-2222000-2-200002222-2-2-2-20000222222-2-2-2-2-2-20000000000000000002i−2i002i2i−2i−2i000000000000
χ182222-2-2222000-2-200002222-2-2-2-20000222222-2-2-2-2-2-2000000000000000000−2i2i00−2i−2i2i2i000000000000
χ192222-2-2222000-2-200002-12-111-2-233−3−3-12-1-1-1-1111-2113−300003333−3−3−3−300−i3i32i−2i−i3i3−i−iii000000000000
χ202222-2-2222000-2-200002-12-111-2-233−3−3-12-1-1-1-1111-2113−300003333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i000000000000
χ212222-2-2222000-2-200002-12-111-2-2−3−333-12-1-1-1-1111-211−330000−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i000000000000
χ222222-2-2222000-2-200002-12-111-2-2−3−333-12-1-1-1-1111-211−330000−3−3−3−3333300i3−i32i−2ii3−i3−i−iii000000000000
χ2322-222-2-2-2222-2-2222-2-2222222-2-222222-2-2-2-22-2-2-2222-2-222-2-222-2-222-2-2000000000000000000000000
χ2422-222-2-2-2222-2-2222-2-22-12-1-1-1-2-2-1-1-1-1-1-2111-11112-1-11122-2-2-1-111-1-11100−i3i300i3−i3−i3i3−i3i3000000000000
χ2522-222-2-2-2222-2-2222-2-22-12-1-1-1-2-2-1-1-1-1-1-2111-11112-1-11122-2-2-1-111-1-11100i3−i300−i3i3i3−i3i3−i3000000000000
χ2622-222-2-2-2222-2-2222-2-2-12-1222112222-11-211-1-211-1-1-1-2-2-1-111-1-111-1-111000000000000000000003−33−3
χ2722-222-2-2-2222-2-2222-2-2-12-1222112222-11-211-1-211-1-1-1-2-2-1-111-1-111-1-11100000000000000000000−33−33
χ2822-222-2-2-22-2-22-22-2-222222222-2-2-2-2-2-22-2-2-2-22-2-2-222222-2-222-2-222-2-222000000000000000000000000
χ2922-222-2-2-22-2-22-22-2-2222-12-1-1-1-2-21111-1-2111-11112-1-1-1-1-2-22211-1-111-1-100−i3i300i3−i3i3−i3i3−i3000000000000
χ3022-222-2-2-22-2-22-22-2-2222-12-1-1-1-2-21111-1-2111-11112-1-1-1-1-2-22211-1-111-1-100i3−i300−i3i3−i3i3−i3i3000000000000
χ3122-222-2-2-22-2-22-22-2-222-12-122211-2-2-2-2-11-211-1-211-1-1-12211-1-111-1-111-1-1000000000000000000003−3−33
χ3222-222-2-2-22-2-22-22-2-222-12-122211-2-2-2-2-11-211-1-211-1-1-12211-1-111-1-111-1-100000000000000000000−333−3
χ3322-22-22-2-220002-200002222-2-22200002-2-2-2-22222-2-2-2000000000000002-22200-2-20000000000000000
χ3422-22-22-2-220002-200002222-2-22200002-2-2-2-22222-2-2-200000000000000-22-2-200220000000000000000
χ3522-22-22-2-220002-200002-12-1112233−3−3-1-2111-1-1-1-1-211−33000033−3−3−3−3332-2-1-100113−3−33000000000000
χ3622-22-22-2-220002-200002-12-1112233−3−3-1-2111-1-1-1-1-211−33000033−3−3−3−333-221100-1-1−333−3000000000000
χ3722-22-22-2-220002-200002-12-11122−3−333-1-2111-1-1-1-1-2113−30000−3−33333−3−32-2-1-10011−333−3000000000000
χ3822-22-22-2-220002-200002-12-11122−3−333-1-2111-1-1-1-1-2113−30000−3−33333−3−3-221100-1-13−3−33000000000000
χ39444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2111-211-211-2-2-2-2-2-211111111000000000000000000000000
χ40444444444-4-4-444-4-4-4-4-2-2-2-2-2-2-2-222221-2-2111-211-211222222-1-1-1-1-1-1-1-1000000000000000000000000
χ414444-4-4444000-4-40000-24-24-4-4220000-2-24-2-2-2-42222200000000000000000000000000000000000000
χ424444-4-4444000-4-40000-2-2-2-222222323−23−231-2-21112-1-12-1-123−230000−3−3−3−33333000000000000000000000000
χ434444-4-4444000-4-40000-2-2-2-22222−23−2323231-2-21112-1-12-1-1−232300003333−3−3−3−3000000000000000000000000
χ4444-444-4-4-4444-4-4444-4-4-2-2-2-2-2-222-2-2-2-2122-1-112-1-1-21122-2-22211-1-111-1-1000000000000000000000000
χ4544-444-4-4-44-4-44-44-4-444-2-2-2-2-2-2222222122-1-112-1-1-211-2-222-2-2-1-111-1-111000000000000000000000000
χ4644-44-44-4-440004-40000-24-24-4-4-2-20000-22-422-24-2-222200000000000000000000000000000000000000
χ4744-44-44-4-440004-40000-2-2-2-222-2-22323−23−23122-1-11-2112-1-1−23230000−3−33333−3−3000000000000000000000000
χ4844-44-44-4-440004-40000-2-2-2-222-2-2−23−232323122-1-11-2112-1-123−23000033−3−3−3−333000000000000000000000000
χ494-4040000-422−2200022−220044-4-4000022−2222−2240000-40000000022−220022−220022−2200000000000000000000000000
χ504-4040000-422−2200022−22004-2-4223−23002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23-200002000023−230022−22002ζ5−2ζ7−2ζ5+2ζ7002ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000
χ514-4040000-422−2200022−22004-2-42−2323002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7-2000020000−23230022−22002ζ13−2ζ23−2ζ13+2ζ23002ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000
χ524-4040000-422−2200022−2200-242-40023−2322−2222−22-200002023−2300000−226−6−226−6−226−6000000000000000000000000
χ534-4040000-422−2200022−2200-242-400−232322−2222−22-2000020−232300000−22−66−22−66−22−66000000000000000000000000
χ544-4040000-422−2200022−2200-2-22223−2323−232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ231003-3-10−330−3300−226−6−ζ5+ζ7ζ5−ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23−ζ13+ζ23ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000
χ554-4040000-422−2200022−2200-2-22223−23−23232ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ23100-33-103−30−3300−22−66−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23−ζ13+ζ23ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000
χ564-4040000-422−2200022−2200-2-222−232323−232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ7100-33-10−3303−300−226−6−ζ13+ζ23ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000
χ574-4040000-422−2200022−2200-2-222−2323−23232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ71003-3-103−303−300−22−66−ζ13+ζ23ζ13−ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000
χ584-4040000-4−2222000−22220044-4-40000−2222−222240000-400000000−222200−222200−222200000000000000000000000000
χ594-4040000-4−2222000−2222004-2-4223−2300−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23-200002000023−2300−222200−2ζ5+2ζ72ζ5−2ζ700−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000
χ604-4040000-4−2222000−2222004-2-42−232300−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7-2000020000−232300−222200−2ζ13+2ζ232ζ13−2ζ2300−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000
χ614-4040000-4−2222000−222200-242-40023−23−2222−2222-200002023−23000002−2−662−2−662−2−66000000000000000000000000
χ624-4040000-4−2222000−222200-242-400−2323−2222−2222-2000020−2323000002−26−62−26−62−26−6000000000000000000000000
χ634-4040000-4−2222000−222200-2-22223−2323−23−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ231003-3-10−330−33002−2−66ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23ζ13−ζ23−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23000000000000000000000000
χ644-4040000-4−2222000−222200-2-22223−23−2323−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23100-33-103−30−33002−26−6ζ5−ζ7−ζ5+ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23ζ13−ζ23−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23000000000000000000000000
χ654-4040000-4−2222000−222200-2-222−232323−23−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7100-33-10−3303−3002−2−66ζ13−ζ23−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23−2ζ5+2ζ7−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−2ζ13+2ζ23ζ5−ζ7+2ζ13−2ζ23000000000000000000000000
χ664-4040000-4−2222000−222200-2-222−2323−2323−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ71003-3-103−303−3002−26−6ζ13−ζ23−ζ13+ζ23−2ζ5+2ζ7−ζ13+ζ232ζ5−2ζ7+ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7+2ζ13−2ζ23−ζ5+ζ7−2ζ13+2ζ23000000000000000000000000
χ67666-366-3-3-3666-3-3-3-3-3-3000000000000000000000000000000000000000000000000002200-1-1-1-10000
χ68666-366-3-3-3666-3-3-3-3-3-300000000000000000000000000000000000000000000000000-2-20011110000
χ69666-366-3-3-3-6-6-6-3-33333000000000000000000000000000000000000000000000000002-200-1-1110000
χ70666-366-3-3-3-6-6-6-3-3333300000000000000000000000000000000000000000000000000-220011-1-10000
χ7166-6-36-633-366-63-3-3-333000000000000000000000000000000000000000000000000000000−i3i3−i3i30000
χ7266-6-36-633-366-63-3-3-333000000000000000000000000000000000000000000000000000000i3−i3i3−i30000
χ7366-6-36-633-3-6-663-333-3-3000000000000000000000000000000000000000000000000000000−i3i3i3−i30000
χ7466-6-36-633-3-6-663-333-3-3000000000000000000000000000000000000000000000000000000i3−i3−i3i30000
χ75121212-6-12-12-6-6-600066000000000000000000000000000000000000000000000000000000000000000000
χ761212-12-6-121266-6000-66000000000000000000000000000000000000000000000000000000000000000000
χ7712-120-600−6i36i3662−62000−32323i6−3i600000000000000000000000000000000000000000000000000000000000000
χ7812-120-600−6i36i36−626200032−32−3i63i600000000000000000000000000000000000000000000000000000000000000
χ7912-120-6006i3−6i3662−62000−3232−3i63i600000000000000000000000000000000000000000000000000000000000000
χ8012-120-6006i3−6i36−626200032−323i6−3i600000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.