Finite Group Databasebeta

← Group #13135213

Character table — Group #13135213

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size112224444446666668812121212121212121224242424242424242424363636363636727272727272727272727272727272
order12236444612123366661212366661212121212121212121212121212441212121226688882424242424242424
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111-1-11-1-11111111-11111111-1-11-1-1-111-1-1-1-1111111-1-1-1i−ii−iii−i−iii−i−i
χ6111111-1-11-1-11111111-11111111-1-11-1-1-111-1-1-1-1111111-1-1-1−ii−ii−i−iii−i−iii
χ7111111-1-11-1-11111111-11111111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1111i−i−iiii−i−i−i−iii
χ8111111-1-11-1-11111111-11111111-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1111−iii−i−i−iiiii−i−i
χ9222222222222-12-1-1-122-12-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12-1-1000000000000
χ10222222222222-12-1-1-122-12-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-21111-211000000000000
χ1122222222222-12-122222-1-1-1-1-122-1-1-1-122-1-1-1-1-1-100000000000220000-1-1-1-1
χ1222222222222-12-122222-1-1-1-1-122-1-1-1-122-1-1-1-1-1-100000000000-2-200001111
χ13222222-2-22-2-22-12-1-1-12-2-12-1-1-1-1-1-2-22-211-1-1111122-1-1-1-1-211000000000000
χ14222222-2-22-2-22-12-1-1-12-2-12-1-1-1-1-1-2-22-211-1-11111-2-211112-1-1000000000000
χ15222222-2-22-2-2-12-12222-2-1-1-1-1-12211-11-2-2-1-11111000000000002i−2i0000−i−iii
χ16222222-2-22-2-2-12-12222-2-1-1-1-1-12211-11-2-2-1-1111100000000000−2i2i0000ii−i−i
χ1722222-22-2222222222-2-222222-2-2-2-2-222-2-2-222-2-2000000000000000000000
χ1822222-22-22222-12-1-1-1-2-2-12-1-1-111-2-2-22-1111-1-11100−i3−i3i3i30−i3i3000000000000
χ1922222-22-22222-12-1-1-1-2-2-12-1-1-111-2-2-22-1111-1-11100i3i3−i3−i30i3−i3000000000000
χ2022222-22-2222-12-1222-2-2-1-1-1-1-1-2-2111-12-211-1-111000000000000000003−33−3
χ2122222-22-2222-12-1222-2-2-1-1-1-1-1-2-2111-12-211-1-11100000000000000000−33−33
χ2222222-2-222-2-2222222-2222222-2-222-2-2-22-2-2-2-222000000000000000000000
χ2322222-2-222-2-22-12-1-1-1-22-12-1-1-11122-2-21-11111-1-100−i3−i3i3i30i3−i3000000000000
χ2422222-2-222-2-22-12-1-1-1-22-12-1-1-11122-2-21-11111-1-100i3i3−i3−i30−i3i3000000000000
χ2522222-2-222-2-2-12-1222-22-1-1-1-1-1-2-2-1-111-221111-1-100000000000000000−i3i3i3−i3
χ2622222-2-222-2-2-12-1222-22-1-1-1-1-1-2-2-1-111-221111-1-100000000000000000i3−i3−i3i3
χ2744444444444-2-2-2-2-2-2441-2111-2-2-2-2-2-2-2-2111111000000000000000000000
χ28444444-4-44-4-4-2-2-2-2-2-24-41-2111-2-222-222211-1-1-1-1000000000000000000000
χ2944444-44-4444-2-2-2-2-2-2-4-41-211122222-2-22-1-111-1-1000000000000000000000
χ3044444-4-444-4-4-2-2-2-2-2-2-441-211122-2-2222-2-1-1-1-111000000000000000000000
χ3144-444000-4004444-4-4004-4-4-4400000000000000000000000000000000000
χ3244-444000-4004-24-22200-2-422-2−2i32i3000000−2i32i30000000000000000000000000
χ3344-444000-4004-24-22200-2-422-22i3−2i30000002i3−2i30000000000000000000000000
χ3444-444000-400-24-24-4-400-2222-200−2i32i300000000−2i32i3000000000000000000000
χ3544-444000-400-24-24-4-400-2222-2002i3−2i3000000002i3−2i3000000000000000000000
χ3644-444000-400-2-2-2-2220012-1-11−2i32i3−2i32i30000i3−i33-3i3−i3000000000000000000000
χ3744-444000-400-2-2-2-2220012-1-11−2i32i32i3−2i30000i3−i3-33−i3i3000000000000000000000
χ3844-444000-400-2-2-2-2220012-1-112i3−2i3−2i32i30000−i3i3-33i3−i3000000000000000000000
χ3944-444000-400-2-2-2-2220012-1-112i3−2i32i3−2i30000−i3i33-3−i3i3000000000000000000000
χ404-404-400000044-4-400004000-4000000000000002i−2i2i−2i2i−2i000000000000000
χ414-404-400000044-4-400004000-400000000000000−2i2i−2i2i−2i2i000000000000000
χ424-404-40000004-2-42−2i32i300-20−2i32i32000000000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000000
χ434-404-40000004-2-42−2i32i300-20−2i32i3200000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000000
χ444-404-40000004-2-422i3−2i300-202i3−2i32000000000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000000
χ454-404-40000004-2-422i3−2i300-202i3−2i3200000000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000000
χ46666-3-3666-3-3-3000000-3-300000000000000000000000000002200-1-1-1-10000
χ47666-3-3666-3-3-3000000-3-30000000000000000000000000000-2-20011110000
χ48666-3-36-6-6-333000000-3300000000000000000000000000002i−2i00−i−iii0000
χ49666-3-36-6-6-333000000-330000000000000000000000000000−2i2i00ii−i−i0000
χ50666-3-3-66-6-3-3-30000003300000000000000000000000000000000−i3i3−i3i30000
χ51666-3-3-66-6-3-3-30000003300000000000000000000000000000000i3−i3i3−i30000
χ52666-3-3-6-66-3330000003-3000000000000000000000000000000003−3−330000
χ53666-3-3-6-66-3330000003-300000000000000000000000000000000−333−30000
χ548-808-8000000-484-80000-4000400000000000000000000000000000000000
χ558-808-8000000-4-444−4i34i300202i3−2i3-200000000000000000000000000000000000
χ568-808-8000000-4-4444i3−4i30020−2i32i3-200000000000000000000000000000000000
χ571212-12-6-60006−6i36i3000000000000000000000000000000000000000000000000
χ581212-12-6-600066i3−6i3000000000000000000000000000000000000000000000000
χ5924-240-1212000000000000000000000000000000000000000000000000000000

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