Finite Group Databasebeta

← Group #13139212

Character table — Group #13139212

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222224466668881212121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order12234461212612336682424366612121212121261224242424242424242244444412121212266668121212122424
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-11-1-1-1111111-11-1-1-1-11-1-1-1-1-1
χ311111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-11-1111-1-11-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ5111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-1
χ6111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-11111-1-1-111
χ7111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11-1-1111111-1-11-1-11-11-1-111
χ8111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-111-1-1
χ9222222222222-1-12222-12-1-1-1-12-1-12-1-122-1-1-1-1-1-102020000000020-1-1-100-10000
χ10222222222222-1-12222-12-1-1-1-12-1-12-1-122-1-1-1-1-1-10-20-200000000-201110010000
χ11222222222222-1-12-2-2-2-12-1-1-1-12-1-12-1-1-2-2111111020200000000-20-11100-10000
χ12222222222222-1-12-2-2-2-12-1-1-1-12-1-12-1-1-2-21111110-20-200000000201-1-10010000
χ1322222222222-122-1222-1-12-122-1-1-1-1-1-1-1-122-1-1-1-100002200000000000200-1-1-1-1
χ1422222222222-122-1222-1-12-122-1-1-1-1-1-1-1-122-1-1-1-10000-2-200000000000-2001111
χ1522222222222-122-1-2-2-2-1-12-122-1-1-1-1-1-111-2-2111100002200000000000-200-1-111
χ1622222222222-122-1-2-2-2-1-12-122-1-1-1-1-1-111-2-211110000-2-20000000000020011-1-1
χ172222-2-22-2-22-222220002222-2-2-2-2-2-22-20000000000002-2000000000000002-200
χ182222-2-22-2-22-222220002222-2-2-2-2-2-22-2000000000000-2200000000000000-2200
χ192222-2-22-2-22-2-122-1000-1-12-1-2-21111-113−30033−3−300002-200000000000000-113−3
χ202222-2-22-2-22-2-122-1000-1-12-1-2-21111-113−30033−3−30000-22000000000000001-1−33
χ212222-2-22-2-22-2-122-1000-1-12-1-2-21111-11−3300−3−33300002-200000000000000-11−33
χ222222-2-22-2-22-2-122-1000-1-12-1-2-21111-11−3300−3−3330000-22000000000000001-13−3
χ2322-222-2222-2-222220002-2-22-22222-2-2-200000000020-2000000000020000-20000
χ2422-222-2222-2-222220002-2-22-22222-2-2-2000000000-2020000000000-2000020000
χ2522-222-2222-2-22-1-12000-1-21-11-12-1-1-21100−i3i3−i3i3−i3i3020-20000000000-1−i3i30010000
χ2622-222-2222-2-22-1-12000-1-21-11-12-1-1-21100−i3i3−i3i3−i3i30-20200000000001i3−i300-10000
χ2722-222-2222-2-22-1-12000-1-21-11-12-1-1-21100i3−i3i3−i3i3−i3020-20000000000-1i3−i30010000
χ2822-222-2222-2-22-1-12000-1-21-11-12-1-1-21100i3−i3i3−i3i3−i30-20200000000001−i3i300-10000
χ2922-22-222-2-2-2222220002-2-222-2-2-2-22-220000000020-2000000000020000-200000
χ3022-22-222-2-2-2222220002-2-222-2-2-2-22-2200000000-2020000000000-20000200000
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
χ334444-4-44-4-44-44-2-24000-24-2-222-422-4-2200000000000000000000000000000000
χ344444-4-44-4-44-4-2-2-2-20001-2-21222-1-121-123−2300−3−333000000000000000000000000
χ354444-4-44-4-44-4-2-2-2-20001-2-21222-1-121-1−23230033−3−3000000000000000000000000
χ3644-444-4444-4-4-244-2000-22-4-2-44-2-2-222200000000000000000000000000000000
χ3744-444-4444-4-4-2-2-2-200012212-2-2112-1-100−2i32i3i3−i3i3−i3000000000000000000000000
χ3844-444-4444-4-4-2-2-2-200012212-2-2112-1-1002i3−2i3−i3i3−i3i3000000000000000000000000
χ3944-44-444-4-4-444-2-24000-2-42-2-22-42242-200000000000000000000000000000000
χ4044-44-444-4-4-44-244-2000-22-4-24-4222-22-200000000000000000000000000000000
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
χ45666-366-3-3-3-3-300006-3-30000000000000000000020200022-1-1-1-10-10000-100000
χ46666-366-3-3-3-3-300006-3-300000000000000000000-20-2000-2-21111010000100000
χ47666-366-3-3-3-3-30000-63300000000000000000000202000-2-211110-10000-100000
χ48666-366-3-3-3-3-30000-63300000000000000000000-20-200022-1-1-1-1010000100000
χ4966-6-3-66-3333-30000033−330000000000000000000020-2000003−33−30-10000100000
χ5066-6-3-66-3333-30000033−3300000000000000000000-20200000−33−33010000-100000
χ5166-6-3-66-3333-300000−33330000000000000000000020-200000−33−330-10000100000
χ5266-6-3-66-3333-300000−333300000000000000000000-202000003−33−3010000-100000
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.