Finite Group Databasebeta

← Group #13137473

Character table — Group #13137473

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222244466666688812121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order12222366663366664121236666666666121212121212121222244444121212124466612121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1111-1-11111-1-1-11-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-11-11-1-1111-1-1-1-1
χ411111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-11-1-11-1-1-11-111
χ51111111111111111-1-1-111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1
χ61111111111111111-1-1-111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-111-11-1-111-1111
χ71111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1111-11111-111-1-11-1-1-1-111
χ81111111111111111-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-111-1111111-1-1-11-1111-1-1-1
χ922222222222-122-12222-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10020000200000200-1000-10-1-1
χ1022222222222-122-12222-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100-20000-200000-20010001011
χ1122222222222-122-12-2-2-2-122-1-1-1-1-1-1-1-1-2-21111110020000200000-200-1000-1011
χ1222222222222-122-12-2-2-2-122-1-1-1-1-1-1-1-1-2-211111100-20000-200000200100010-1-1
χ132222222222-12-1-12-1222-1-1-12-12-1-12-1-1-1-122-1-1-1-120022200-1-1-1-1000-100000-100
χ142222222222-12-1-12-1222-1-1-12-12-1-12-1-1-1-122-1-1-1-1-200-2-2-2001111000100000100
χ152222222222-12-1-12-1-2-2-2-1-1-12-12-1-12-1-111-2-211112002-2-2001111000-100000-100
χ162222222222-12-1-12-1-2-2-2-1-1-12-12-1-12-1-111-2-21111-200-22200-1-1-1-1000100000100
χ17222-2-222-22-22222220002-2-2-22222-2-2-200000000200-200000000000200000-200
χ18222-2-222-22-22222220002-2-2-22222-2-2-200000000-200200000000000-200000200
χ19222-2-222-22-2-12-1-12-1000-111-2-12-1-1-211−i3i300−i3−i3i3i3200-20000−i3−i3i3i3000-100000100
χ20222-2-222-22-2-12-1-12-1000-111-2-12-1-1-211−i3i300−i3−i3i3i3-20020000i3i3−i3−i3000100000-100
χ21222-2-222-22-2-12-1-12-1000-111-2-12-1-1-211i3−i300i3i3−i3−i3200-20000i3i3−i3−i3000-100000100
χ22222-2-222-22-2-12-1-12-1000-111-2-12-1-1-211i3−i300i3i3−i3−i3-20020000−i3−i3i3i3000100000-100
χ2322-22-2222-2-222-2-22200022-2-22-2-2-222-200000000020000-20000000200-2000000
χ2422-22-2222-2-222-2-22200022-2-22-2-2-222-2000000000-2000020000000-2002000000
χ2522-2-2222-2-2222-2-2220002-2222-2-2-2-2-22000000000020000-2000000002000-2000
χ2622-2-2222-2-2222-2-2220002-2222-2-2-2-2-220000000000-20000200000000-20002000
χ2722-2-2222-2-222-1-2-2-12000-1-22-1-111111-1003−33−33−30020000-200000000-1000103−3
χ2822-2-2222-2-222-1-2-2-12000-1-22-1-111111-1003−33−33−300-200002000000001000-10−33
χ2922-2-2222-2-222-1-2-2-12000-1-22-1-111111-100−33−33−330020000-200000000-100010−33
χ3022-2-2222-2-222-1-2-2-12000-1-22-1-111111-100−33−33−3300-200002000000001000-103−3
χ314444444444-2-2-2-2-2-24441-2-2-21-211-211-2-2-2-21111000000000000000000000000
χ324444444444-2-2-2-2-2-2-4-4-41-2-2-21-211-2112222-1-1-1-1000000000000000000000000
χ33444-4-444-44-44-244-24000-2-4-42-2-2-2-222200000000000000000000000000000000
χ34444-4-444-44-4-2-2-2-2-2-200012221-2112-1-1−2i32i300i3i3−i3−i3000000000000000000000000
χ35444-4-444-44-4-2-2-2-2-2-200012221-2112-1-12i3−2i300−i3−i3i3i3000000000000000000000000
χ3644-44-4444-4-44-2-4-4-24000-24-42-2222-2-2200000000000000000000000000000000
χ3744-44-4444-4-4-24224-2000-2-22-4-2-4224-2200000000000000000000000000000000
χ3844-44-4444-4-4-2-222-2-20001-22212-1-1-21-100003i−3i−3i3i000000000000000000000000
χ3944-44-4444-4-4-2-222-2-20001-22212-1-1-21-10000−3i3i3i−3i000000000000000000000000
χ4044-4-4444-4-44-24224-2000-22-24-2-422-42-200000000000000000000000000000000
χ4144-4-4444-4-44-2-222-2-200012-2-212-1-12-110023−23−33−33000000000000000000000000
χ4244-4-4444-4-44-2-222-2-200012-2-212-1-12-1100−23233−33−3000000000000000000000000
χ434-40004-40004400-4-40004000-40000000000000000002i−2i002i−2i2i−2i000000000000
χ444-40004-40004400-4-40004000-4000000000000000000−2i2i00−2i2i−2i2i000000000000
χ454-40004-4000-24−2i32i3-42000-200020−2i32i30000000000000002i−2i002ζ11−2ζ112ζ7−2ζ7000000000000
χ464-40004-4000-24−2i32i3-42000-200020−2i32i3000000000000000−2i2i00−2ζ112ζ11−2ζ72ζ7000000000000
χ474-40004-4000-242i3−2i3-42000-2000202i3−2i30000000000000002i−2i002ζ7−2ζ72ζ11−2ζ11000000000000
χ484-40004-4000-242i3−2i3-42000-2000202i3−2i3000000000000000−2i2i00−2ζ72ζ7−2ζ112ζ11000000000000
χ4966666-3-3-3-3-30000006-3-3000000000000000000002000020000020-100-1-1-10000
χ5066666-3-3-3-3-30000006-3-300000000000000000000-20000-200000-201001110000
χ5166666-3-3-3-3-3000000-6330000000000000000000020000200000-20-100-1110000
χ5266666-3-3-3-3-3000000-63300000000000000000000-20000-200000201001-1-10000
χ5366-66-6-3-3-333000000033−330000000000000000000020000-20000000-10013−30000
χ5466-66-6-3-3-333000000033−3300000000000000000000-2000020000000100-1−330000
χ5566-66-6-3-3-3330000000−33330000000000000000000020000-20000000-1001−330000
χ5666-66-6-3-3-3330000000−333300000000000000000000-2000020000000100-13−30000
χ578-80008-80008-4004-8000-4000400000000000000000000000000000000000000
χ588-80008-8000-4-4−4i34i3440002000-202i3−2i300000000000000000000000000000000000
χ598-80008-8000-4-44i3−4i3440002000-20−2i32i300000000000000000000000000000000000
χ60121212-12-12-6-66-660000000000000000000000000000000000000000000000000000
χ611212-12-1212-6-666-60000000000000000000000000000000000000000000000000000
χ6224-24000-12120000000000000000000000000000000000000000000000000000000

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