Finite Group Databasebeta

← Group #13140999

Character table — Group #13140999

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222224466668881212121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order122344666121233664121236666612121212121212121212121212122222444412121212666688121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-11-1-1-1-1-1-1-1-1-11-11-11-111-1-1
χ411111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-1-1-1-11-11-11-1-111
χ5111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ6111111111111111-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ7111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-11-11-1111111-1-11-1-111-1-1-111
χ8111111111111111-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-11-11111111-1-1-111-1-1111-1-1
χ9222222222222-12-1222-12-1-1-1-12-12-122-1-1-1-1-1-1-1-1000202000000000-1020-100-1-1
χ10222222222222-12-1222-12-1-1-1-12-12-122-1-1-1-1-1-1-1-1000-20-200000000010-2010011
χ11222222222222-12-1-2-2-2-12-1-1-1-12-12-1-2-211-1-11111000202000000000-10-20-10011
χ12222222222222-12-1-2-2-2-12-1-1-1-12-12-1-2-211-1-11111000-20-20000000001020100-1-1
χ1322222222222-12-12222-1-12-1-1-1-12-12-1-122-1-1-1-1-1-100202000000000-1020-10-1-100
χ1422222222222-12-12222-1-12-1-1-1-12-12-1-122-1-1-1-1-1-100-20-200000000010-20101100
χ1522222222222-12-12-2-2-2-1-12-1-1-1-12-1211-2-2-1-1111100202000000000-10-20-101100
χ1622222222222-12-12-2-2-2-1-12-1-1-1-12-1211-2-2-1-1111100-20-2000000000102010-1-100
χ172222-2-2222-2-22222000222222-2-2-2-20000-2-200002-200000000002-20000000000
χ182222-2-2222-2-22222000222222-2-2-2-20000-2-20000-220000000000-220000000000
χ1922-222-22-2-22-222220002-2-2-2-222-2-2200002-2000000020-20000000002000-20000
χ2022-222-22-2-22-222220002-2-2-2-222-2-2200002-20000000-202000000000-200020000
χ2122-222-22-2-22-22-12-1000-1-2111-121-2-100−i3i3-11−i3−i3i3i300020-2000000000-1000100−i3i3
χ2222-222-22-2-22-22-12-1000-1-2111-121-2-100−i3i3-11−i3−i3i3i3000-2020000000001000-100i3−i3
χ2322-222-22-2-22-22-12-1000-1-2111-121-2-100i3−i3-11i3i3−i3−i300020-2000000000-1000100i3−i3
χ2422-222-22-2-22-22-12-1000-1-2111-121-2-100i3−i3-11i3i3−i3−i3000-2020000000001000-100−i3i3
χ2522-22-222-2-2-2222220002-2-2-2-22-222-20000-2200000020-20000000002000-200000
χ2622-22-222-2-2-2222220002-2-2-2-22-222-20000-22000000-202000000000-2000200000
χ2722-22-222-2-2-22-12-12000-11-211-112-1-2−i3i3001-1−i3i3−i3i30020-2000000000-100010−i3i300
χ2822-22-222-2-2-22-12-12000-11-211-112-1-2−i3i3001-1−i3i3−i3i300-2020000000001000-10i3−i300
χ2922-22-222-2-2-22-12-12000-11-211-112-1-2i3−i3001-1i3−i3i3−i30020-2000000000-100010i3−i300
χ3022-22-222-2-2-22-12-12000-11-211-112-1-2i3−i3001-1i3−i3i3−i300-2020000000001000-10−i3i300
χ3144444444444-2-2-2-24441-2-2111-2-2-2-2-2-2-2-2111111000000000000000000000000
χ3244444444444-2-2-2-2-4-4-41-2-2111-2-2-2-2222211-1-1-1-1000000000000000000000000
χ334444-4-4444-4-44-24-2000-24-2-2-2-2-42-420000220000000000000000000000000000
χ344444-4-4444-4-4-24-24000-2-24-2-2-22-42-40000220000000000000000000000000000
χ354444-4-4444-4-4-2-2-2-20001-2-211122220000-1-13-3-33000000000000000000000000
χ364444-4-4444-4-4-2-2-2-20001-2-211122220000-1-1-333-3000000000000000000000000
χ3744-444-44-4-44-4-24-24000-22-422-2-2-4240000-220000000000000000000000000000
χ3844-444-44-4-44-4-2-2-2-2000122-1-11-222-200−2i32i31-1i3i3−i3−i3000000000000000000000000
χ3944-444-44-4-44-4-2-2-2-2000122-1-11-222-2002i3−2i31-1−i3−i3i3i3000000000000000000000000
χ4044-44-444-4-4-444-24-2000-2-4222-2-4-24200002-20000000000000000000000000000
χ4144-44-444-4-4-44-2-2-2-2000122-1-112-2-22−2i32i300-11i3−i3i3−i3000000000000000000000000
χ4244-44-444-4-4-44-2-2-2-2000122-1-112-2-222i3−2i300-11−i3i3−i3i3000000000000000000000000
χ434-40400-4000044-4-400040000-4000000000000000000002i−2i2i2i−2i−2i000000000000
χ444-40400-4000044-4-400040000-400000000000000000000−2i2i−2i−2i2i2i000000000000
χ45666-366-3-3-3-3-300006-3-30000000000000000000022000022-1-1-1-1-1-10000000000
χ46666-366-3-3-3-3-300006-3-300000000000000000000-2-20000-2-21111110000000000
χ47666-366-3-3-3-3-30000-63300000000000000000000220000-2-21111-1-10000000000
χ48666-366-3-3-3-3-30000-63300000000000000000000-2-2000022-1-1-1-1110000000000
χ49666-3-6-6-3-3-33300000−3i33i3000000000000000000002-2000000−i3i3−i3i3-110000000000
χ50666-3-6-6-3-3-33300000−3i33i300000000000000000000-22000000i3−i3i3−i31-10000000000
χ51666-3-6-6-3-3-333000003i3−3i3000000000000000000002-2000000i3−i3i3−i3-110000000000
χ52666-3-6-6-3-3-333000003i3−3i300000000000000000000-22000000−i3i3−i3i31-10000000000
χ538-80800-800008-4-84000-40000400000000000000000000000000000000000000
χ548-80800-80000-484-8000-40000400000000000000000000000000000000000000
χ558-80800-80000-4-4440002006-6-200000000000000000000000000000000000000
χ568-80800-80000-4-444000200-66-200000000000000000000000000000000000000
χ571212-12-612-12-666-66000000000000000000000000000000000000000000000000000
χ581212-12-6-1212-6666-6000000000000000000000000000000000000000000000000000
χ5912-120-6006−6i36i3000000000000000000000000000000000002i−2i2ζ72ζ11−2ζ7−2ζ11000000000000
χ6012-120-6006−6i36i300000000000000000000000000000000000−2i2i−2ζ7−2ζ112ζ72ζ11000000000000
χ6112-120-60066i3−6i3000000000000000000000000000000000002i−2i2ζ112ζ7−2ζ11−2ζ7000000000000
χ6212-120-60066i3−6i300000000000000000000000000000000000−2i2i−2ζ11−2ζ72ζ112ζ7000000000000

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