Finite Group Databasebeta

← Group #13140650

Character table — Group #13140650

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222244466666688812121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order1223446612123366662663666612121212666666661212224444441212121266881212121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1-1
χ311111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111
χ411111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ51111111111111111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111-1-1-1111111111-1-1-1-1-1-1-1-1111-11-1-1-11111111-1-111-1-1-1-1-111
χ71111111111111111-1-1-1111111111-1-1-1-1-1-1-1-111-11-11-1-1111111-111-1-11-1-111-1-1
χ81111111111111111-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111
χ922222222222-122-12222-1-1-1-1-1-122-122-1-1-1-1-1-1-1-10202000000000-1020-10000-1-1
χ1022222222222-122-12222-1-1-1-1-1-122-122-1-1-1-1-1-1-1-10-20-200000000010-201000011
χ1122222222222-122-12-2-2-2-1-1-1-1-1-122-1-2-2111111-1-10202000000000-10-20-1000011
χ1222222222222-122-12-2-2-2-1-1-1-1-1-122-1-2-2111111-1-10-20-2000000000102010000-1-1
χ132222222222-12-1-12-1222-12-1-1-12-1-12-1-122-1-1-1-1-1-100002222-1-1-1-1000000-1-10000
χ142222222222-12-1-12-1222-12-1-1-12-1-12-1-122-1-1-1-1-1-10000-2-2-2-21111000000110000
χ152222222222-12-1-12-1-2-2-2-12-1-1-12-1-1211-2-21111-1-1000022-2-21111000000-1-10000
χ162222222222-12-1-12-1-2-2-2-12-1-1-12-1-1211-2-21111-1-10000-2-222-1-1-1-1000000110000
χ172222-2-222-2-222222200022222-2-2-2-200000000-2-200002-20000000000002-20000
χ182222-2-222-2-222222200022222-2-2-2-200000000-2-20000-22000000000000-220000
χ192222-2-222-2-2-12-1-12-1000-12-1-1-1-211-2−i3i300−i3−i3i3i31100002-200−i3−i3i3i3000000-110000
χ202222-2-222-2-2-12-1-12-1000-12-1-1-1-211-2−i3i300−i3−i3i3i3110000-2200i3i3−i3−i30000001-10000
χ212222-2-222-2-2-12-1-12-1000-12-1-1-1-211-2i3−i300i3i3−i3−i31100002-200i3i3−i3−i3000000-110000
χ222222-2-222-2-2-12-1-12-1000-12-1-1-1-211-2i3−i300i3i3−i3−i3110000-2200−i3−i3i3i30000001-10000
χ2322-222-22-22-222-2-2220002-2-2-22-22-22000000002-2020-20000000002000-2000000
χ2422-222-22-22-222-2-2220002-2-2-22-22-22000000002-20-202000000000-20002000000
χ2522-222-22-22-22-1-2-2-12000-1111-112-2-100−i3i3−i3i3−i3i3-11020-2000000000-100010000−i3i3
χ2622-222-22-22-22-1-2-2-12000-1111-112-2-100−i3i3−i3i3−i3i3-110-2020000000001000-10000i3−i3
χ2722-222-22-22-22-1-2-2-12000-1111-112-2-100i3−i3i3−i3i3−i3-11020-2000000000-100010000i3−i3
χ2822-222-22-22-22-1-2-2-12000-1111-112-2-100i3−i3i3−i3i3−i3-110-2020000000001000-10000−i3i3
χ2922-22-222-2-2222-2-2220002-2-2-222-22-200000000-2220-20000000002000-20000000
χ3022-22-222-2-2222-2-2220002-2-2-222-22-200000000-22-202000000000-200020000000
χ314444444444-2-2-2-2-2-24441-2111-2-2-2-2-2-2-2-2111111000000000000000000000000
χ324444444444-2-2-2-2-2-2-4-4-41-2111-2-2-2-22222-1-1-1-111000000000000000000000000
χ334444-4-444-4-44-244-24000-2-2-2-2-22-4-420000000022000000000000000000000000
χ344444-4-444-4-4-2-2-2-2-2-20001-21112222−2i32i300i3i3−i3−i3-1-1000000000000000000000000
χ354444-4-444-4-4-2-2-2-2-2-20001-211122222i3−2i300−i3−i3i3i3-1-1000000000000000000000000
χ3644-444-44-44-4-24224-2000-2-422-2-4-22400000000-22000000000000000000000000
χ3744-444-44-44-4-2-222-2-200012-1-112-22-200−2i32i3i3−i3i3−i31-1000000000000000000000000
χ3844-444-44-44-4-2-222-2-200012-1-112-22-2002i3−2i3−i3i3−i3i31-1000000000000000000000000
χ3944-44-444-4-444-2-4-4-24000-2222-2-2-442000000002-2000000000000000000000000
χ4044-44-444-4-44-24224-2000-2-422-242-2-4000000002-2000000000000000000000000
χ4144-44-444-4-44-2-222-2-200012-1-11-22-2200003-3-33-11000000000000000000000000
χ4244-44-444-4-44-2-222-2-200012-1-11-22-220000-333-3-11000000000000000000000000
χ434-40400-40004400-4-40004000-4000000000000000000002i−2i2i−2i2i−2i000000000000
χ444-40400-40004400-4-40004000-400000000000000000000−2i2i−2i2i−2i2i000000000000
χ454-40400-4000-24−2i32i3-42000-20−2i32i32000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000
χ464-40400-4000-24−2i32i3-42000-20−2i32i3200000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000
χ474-40400-4000-242i3−2i3-42000-202i3−2i32000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000
χ484-40400-4000-242i3−2i3-42000-202i3−2i3200000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000
χ49666-366-3-3-3-30000006-3-30000000000000000000202000000000-1020-1000-1-100
χ50666-366-3-3-3-30000006-3-30000000000000000000-20-200000000010-2010001100
χ51666-366-3-3-3-3000000-6330000000000000000000202000000000-10-20-10001100
χ52666-366-3-3-3-3000000-6330000000000000000000-20-200000000010201000-1-100
χ5366-6-3-66-333-30000000−3i33i3000000000000000000020-2000000000-10001000−i3i300
χ5466-6-3-66-333-30000000−3i33i30000000000000000000-2020000000001000-1000i3−i300
χ5566-6-3-66-333-300000003i3−3i3000000000000000000020-2000000000-10001000i3−i300
χ5666-6-3-66-333-300000003i3−3i30000000000000000000-2020000000001000-1000−i3i300
χ578-80800-80008-4004-8000-4000400000000000000000000000000000000000000
χ588-80800-8000-4-4−4i34i344000202i3−2i3-200000000000000000000000000000000000000
χ598-80800-8000-4-44i3−4i34400020−2i32i3-200000000000000000000000000000000000000
χ60121212-6-12-12-6-6660000000000000000000000000000000000000000000000000000
χ611212-12-612-12-66-660000000000000000000000000000000000000000000000000000
χ6224-240-1200120000000000000000000000000000000000000000000000000000000

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