Finite Group Databasebeta

← Group #13137474

Character table — Group #13137474

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222224466668881212121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order12222366666336641212366666666666121212121212121222244444121212124466612121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1111-1-11111-1-11-1-11-1-1-1-1-1-1
χ311111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-11-1-11-1-11-111-1-1
χ411111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-11-1-11-1-11-1-111
χ5111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1111-1-11-1-11111
χ7111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1111-11111-11-11-1-11-1-1-111
χ8111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11-111-1111111-1-1-11-1-1111-1-1
χ9222222222222-12-1222-12-1-12-1-1-12-1-1-122-1-1-1-1-1-10020000200000200-100-100-1-1
χ10222222222222-12-1222-12-1-12-1-1-12-1-1-122-1-1-1-1-1-100-20000-200000-20010010011
χ11222222222222-12-1-2-2-2-12-1-12-1-1-12-1-1-1-2-21111110020000200000-200-100-10011
χ12222222222222-12-1-2-2-2-12-1-12-1-1-12-1-1-1-2-211111100-20000-200000200100100-1-1
χ1322222222222-12-12222-1-12-1-12-1-1-12-1-1-1-122-1-1-1-1020000200000200-100-10-1-100
χ1422222222222-12-12222-1-12-1-12-1-1-12-1-1-1-122-1-1-1-10-20000-200000-200100101100
χ1522222222222-12-12-2-2-2-1-12-1-12-1-1-12-1-111-2-21111020000200000-200-100-101100
χ1622222222222-12-12-2-2-2-1-12-1-12-1-1-12-1-111-2-211110-20000-20000020010010-1-100
χ17222-2-22222-2-222220002-2-222222-2-2-2-200000000200-20000000000200-2000000
χ18222-2-22222-2-222220002-2-222222-2-2-2-200000000-20020000000000-2002000000
χ1922-22-22-2-222-2222200022-22-2-2-2-2-222-200000000020000-200000000200-200000
χ2022-22-22-2-222-2222200022-22-2-2-2-2-222-2000000000-20000200000000-200200000
χ2122-22-22-2-222-2-12-12000-1-1-2-11-21112-113−30033−3−3020000-200000000-100103−300
χ2222-22-22-2-222-2-12-12000-1-1-2-11-21112-113−30033−3−30-20000200000000100-10−3300
χ2322-22-22-2-222-2-12-12000-1-1-2-11-21112-11−3300−3−333020000-200000000-10010−3300
χ2422-22-22-2-222-2-12-12000-1-1-2-11-21112-11−3300−3−3330-20000200000000100-103−300
χ2522-2-222-2-22-2222220002-222-2-2-2-22-2-22000000000020000-200000000200-20000
χ2622-2-222-2-22-2222220002-222-2-2-2-22-2-220000000000-20000200000000-20020000
χ2722-2-222-2-22-222-12-1000-1-2-1-1-2111211-1003−33−33−30020000-200000000-1001003−3
χ2822-2-222-2-22-222-12-1000-1-2-1-1-2111211-1003−33−33−300-20000200000000100-100−33
χ2922-2-222-2-22-222-12-1000-1-2-1-1-2111211-100−33−33−330020000-200000000-100100−33
χ3022-2-222-2-22-222-12-1000-1-2-1-1-2111211-100−33−33−3300-20000200000000100-1003−3
χ3144444444444-2-2-2-24441-2-21-2-211-2-211-2-2-2-21111000000000000000000000000
χ3244444444444-2-2-2-2-4-4-41-2-21-2-211-2-2112222-1-1-1-1000000000000000000000000
χ33444-4-44444-4-44-24-2000-2-42-24-2-2-2-422200000000000000000000000000000000
χ34444-4-44444-4-4-24-24000-22-4-2-24-2-22-42200000000000000000000000000000000
χ35444-4-44444-4-4-2-2-2-20001221-2-21122-1-100003-3-33000000000000000000000000
χ36444-4-44444-4-4-2-2-2-20001221-2-21122-1-10000-333-3000000000000000000000000
χ3744-44-44-4-444-44-24-2000-242-2-4222-4-2-2200000000000000000000000000000000
χ3844-44-44-4-444-4-2-2-2-20001-22122-1-12-21-123−2300−3−333000000000000000000000000
χ3944-44-44-4-444-4-2-2-2-20001-22122-1-12-21-1−23230033−3−3000000000000000000000000
χ4044-4-444-4-44-44-24-24000-224-22-422-2-42-200000000000000000000000000000000
χ4144-4-444-4-44-44-2-2-2-200012-2122-1-1-22-110023−23−33−33000000000000000000000000
χ4244-4-444-4-44-44-2-2-2-200012-2122-1-1-22-1100−23233−33−3000000000000000000000000
χ434-4000400-40044-4-4000400-4000000000000000000002i−2i002i2i−2i−2i000000000000
χ444-4000400-40044-4-4000400-400000000000000000000−2i2i00−2i−2i2i2i000000000000
χ4566666-3-3-3-3-3-300006-3-30000000000000000000020022200-1-1-1-100-100-1000000
χ4666666-3-3-3-3-3-300006-3-300000000000000000000-200-2-2-2001111001001000000
χ4766666-3-3-3-3-3-30000-633000000000000000000002002-2-200111100-100-1000000
χ4866666-3-3-3-3-3-30000-63300000000000000000000-200-22200-1-1-1-1001001000000
χ49666-6-6-3-3-3-33300000−3i33i300000000000000000000200-20000−i3i3−i3i300-1001000000
χ50666-6-6-3-3-3-33300000−3i33i300000000000000000000-20020000i3−i3i3−i300100-1000000
χ51666-6-6-3-3-3-333000003i3−3i300000000000000000000200-20000i3−i3i3−i300-1001000000
χ52666-6-6-3-3-3-333000003i3−3i300000000000000000000-20020000−i3i3−i3i300100-1000000
χ538-8000800-8008-4-84000-40040000000000000000000000000000000000000000
χ548-8000800-800-484-8000-40040000000000000000000000000000000000000000
χ558-8000800-800-4-444000200-2006-6000000000000000000000000000000000000
χ568-8000800-800-4-444000200-200-66000000000000000000000000000000000000
χ571212-1212-12-666-6-66000000000000000000000000000000000000000000000000000
χ581212-12-1212-666-66-6000000000000000000000000000000000000000000000000000
χ5912-12000-6−6i36i360000000000000000000000000000000002i−2i002ζ112ζ7−2ζ11−2ζ7000000000000
χ6012-12000-6−6i36i36000000000000000000000000000000000−2i2i00−2ζ11−2ζ72ζ112ζ7000000000000
χ6112-12000-66i3−6i360000000000000000000000000000000002i−2i002ζ72ζ11−2ζ7−2ζ11000000000000
χ6212-12000-66i3−6i36000000000000000000000000000000000−2i2i00−2ζ7−2ζ112ζ72ζ11000000000000

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