Finite Group Databasebeta

← Group #13139207

Character table — Group #13139207

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222224466668881212121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order12234461212612336682424366612121212121261224242424242424242222444412121212466668121212122424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111
χ311111111111111111111111111111111111111-1-11-11-1111111-11-1-1-1-11-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-11-11-1-1-1-1111-1-1
χ5111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-111-1-1-1-1
χ6111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-1-111-1-1
χ7111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1-111-11111
χ8111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-11111111-1-11-1-11-11-1-111
χ9222222222222-1-12222-12-1-12-12-1-1-1-1-122-1-1-1-1-1-1220000000000000-1-120000-1-1
χ10222222222222-1-12222-12-1-12-12-1-1-1-1-122-1-1-1-1-1-1-2-2000000000000011-2000011
χ11222222222222-1-12-2-2-2-12-1-12-12-1-1-1-1-1-2-2111111220000000000000-1-1-2000011
χ12222222222222-1-12-2-2-2-12-1-12-12-1-1-1-1-1-2-2111111-2-200000000000001120000-1-1
χ1322222222222-122-1222-1-12-1-12-1-1-12-1-1-1-122-1-1-1-100020200000020-10000-1-1-100
χ1422222222222-122-1222-1-12-1-12-1-1-12-1-1-1-122-1-1-1-1000-20-2000000-201000011100
χ1522222222222-122-1-2-2-2-1-12-1-12-1-1-12-1-111-2-21111000202000000-20-10000-11100
χ1622222222222-122-1-2-2-2-1-12-1-12-1-1-12-1-111-2-21111000-20-200000020100001-1-100
χ172222-2-22-2-22-222220002222-2-2-2-2-2-22-2000000002-200000000000002-20000000
χ182222-2-22-2-22-222220002222-2-2-2-2-2-22-200000000-220000000000000-220000000
χ192222-2-22-2-22-22-1-12000-12-1-1-21-2111-11003−333−3−32-20000000000000-11000003−3
χ202222-2-22-2-22-22-1-12000-12-1-1-21-2111-11003−333−3−3-2200000000000001-100000−33
χ212222-2-22-2-22-22-1-12000-12-1-1-21-2111-1100−33−3−3332-20000000000000-1100000−33
χ222222-2-22-2-22-22-1-12000-12-1-1-21-2111-1100−33−3−333-2200000000000001-1000003−3
χ2322-222-2222-2-222220002-2-22-22222-2-2-20000000000020-20000000020000-20000
χ2422-222-2222-2-222220002-2-22-22222-2-2-200000000000-20200000000-2000020000
χ2522-222-2222-2-2-122-1000-11-2-112-1-1-1-211−i3i300−i3i3−i3i300020-200000000-100001−i3i300
χ2622-222-2222-2-2-122-1000-11-2-112-1-1-1-211−i3i300−i3i3−i3i3000-2020000000010000-1i3−i300
χ2722-222-2222-2-2-122-1000-11-2-112-1-1-1-211i3−i300i3−i3i3−i300020-200000000-100001i3−i300
χ2822-222-2222-2-2-122-1000-11-2-112-1-1-1-211i3−i300i3−i3i3−i3000-2020000000010000-1−i3i300
χ2922-22-222-2-2-2222220002-2-222-2-2-2-22-22000000000020-20000000020000-200000
χ3022-22-222-2-2-2222220002-2-222-2-2-2-22-220000000000-20200000000-20000200000
χ3144444444444-2-2-2-24441-2-21-2-2-211-211-2-2-2-21111000000000000000000000000
χ3244444444444-2-2-2-2-4-4-41-2-21-2-2-211-2112222-1-1-1-1000000000000000000000000
χ334444-4-44-4-44-4-244-2000-2-24-22-4222-4-2200000000000000000000000000000000
χ344444-4-44-4-44-4-2-2-2-20001-2-21222-1-121-10023−23−3−333000000000000000000000000
χ354444-4-44-4-44-4-2-2-2-20001-2-21222-1-121-100−232333−3−3000000000000000000000000
χ3644-444-4444-4-44-2-24000-2-42-2-4-24-2-222200000000000000000000000000000000
χ3744-444-4444-4-4-2-2-2-200012212-2-2112-1-1−2i32i300i3−i3i3−i3000000000000000000000000
χ3844-444-4444-4-4-2-2-2-200012212-2-2112-1-12i3−2i300−i3i3−i3i3000000000000000000000000
χ3944-44-444-4-4-444-2-24000-2-42-242-422-22-200000000000000000000000000000000
χ4044-44-444-4-4-44-244-2000-22-4-2-2-422242-200000000000000000000000000000000
χ4144-44-444-4-4-44-2-2-2-20001221-222-1-1-2-1100003i−3i−3i3i000000000000000000000000
χ4244-44-444-4-4-44-2-2-2-20001221-222-1-1-2-110000−3i3i3i−3i000000000000000000000000
χ434-40400-4000044-4-4000400-400000000000000000000002i−2i2i2i−2i−2i000000000000
χ444-40400-4000044-4-4000400-40000000000000000000000−2i2i−2i−2i2i2i000000000000
χ45666-366-3-3-3-3-300006-3-30000000000000000000000202022-1-1-1-10-10000-100000
χ46666-366-3-3-3-3-300006-3-30000000000000000000000-20-20-2-21111010000100000
χ47666-366-3-3-3-3-30000-63300000000000000000000002020-2-211110-10000-100000
χ48666-366-3-3-3-3-30000-6330000000000000000000000-20-2022-1-1-1-1010000100000
χ4966-6-3-66-3333-30000033−33000000000000000000000020-20003−33−30-10000100000
χ5066-6-3-66-3333-30000033−330000000000000000000000-202000−33−33010000-100000
χ5166-6-3-66-3333-300000−3333000000000000000000000020-2000−33−330-10000100000
χ5266-6-3-66-3333-300000−33330000000000000000000000-2020003−33−3010000-100000
χ538-80800-800008-44-8000-40040000000000000000000000000000000000000000
χ548-80800-80000-48-84000-40040000000000000000000000000000000000000000
χ558-80800-80000-4-444000200-20006i−6i00000000000000000000000000000000000
χ568-80800-80000-4-444000200-2000−6i6i00000000000000000000000000000000000
χ57121212-6-12-12-666-66000000000000000000000000000000000000000000000000000
χ581212-12-612-12-6-6-666000000000000000000000000000000000000000000000000000
χ5912-120-600663−63000000000000000000000000000000000002i−2iζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11000000000000
χ6012-120-600663−6300000000000000000000000000000000000−2i2i−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11000000000000
χ6112-120-6006−6363000000000000000000000000000000000002i−2i−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11000000000000
χ6212-120-6006−636300000000000000000000000000000000000−2i2iζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11000000000000

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