Finite Group Databasebeta

← Group #13141003

Character table — Group #13141003

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112222244466666688812121212121212121224242424242424242424363636363636363636363636727272727272727272727272
order122344661212336666412123666612121212121212121212121212122222444412121212666688121224242424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-11-1-1-1-1-1-1-11-1-1-11-11-111-1-1
χ411111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-1-11-1-1-11-11-1-111
χ51111111111111111-1-1-1111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1
χ61111111111111111-1-1-1111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111-1-1-1111111111-1-1-1-111-1-1-1-1-1-11-11-11111111-1-1-1-111-1-1-111
χ81111111111111111-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-11-11111111-11-1-11-1-1111-1-1
χ922222222222-1-1-1-12222-12-1-1-1-1-122-1-122-1-1-1-1-1-122000022-1-1-1-100-1-100000000
χ1022222222222-1-1-1-12222-12-1-1-1-1-122-1-122-1-1-1-1-1-1-2-20000-2-21111001100000000
χ1122222222222-1-1-1-12-2-2-2-12-1-1-1-1-12211-2-2-1-11111220000-2-2111100-1-100000000
χ1222222222222-1-1-1-12-2-2-2-12-1-1-1-1-12211-2-2-1-11111-2-2000022-1-1-1-1001100000000
χ132222222222-12222-1222-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10002020000000-100020-100-1-1
χ142222222222-12222-1222-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000-20-200000001000-2010011
χ152222222222-12222-1-2-2-2-1-1-1-1-122-1-1-2-211-1-111110002020000000-1000-20-10011
χ162222222222-12222-1-2-2-2-1-1-1-1-122-1-1-2-211-1-11111000-20-20000000100020100-1-1
χ172222-2-222-2-222222200022222-2-2-2-20000-2-200002-20000000000002-200000000
χ182222-2-222-2-222222200022222-2-2-2-20000-2-20000-22000000000000-2200000000
χ192222-2-222-2-22-1-1-1-12000-12-1-1-111-2-2−i3i30011−i3−i3i3i32-2000000−i3−i3i3i300-1100000000
χ202222-2-222-2-22-1-1-1-12000-12-1-1-111-2-2−i3i30011−i3−i3i3i3-22000000i3i3−i3−i3001-100000000
χ212222-2-222-2-22-1-1-1-12000-12-1-1-111-2-2i3−i30011i3i3−i3−i32-2000000i3i3−i3−i300-1100000000
χ222222-2-222-2-22-1-1-1-12000-12-1-1-111-2-2i3−i30011i3i3−i3−i3-22000000−i3−i3i3i3001-100000000
χ2322-222-22-22-2222-2-220002-2-2-222-2-2200002-2000000020-20000000200000-20000
χ2422-222-22-22-2222-2-220002-2-2-222-2-2200002-20000000-2020000000-20000020000
χ2522-222-22-22-2-122-2-2-1000-1111-12-21-100−i3i3-11−i3i3−i3i300020-20000000-100000100−i3i3
χ2622-222-22-22-2-122-2-2-1000-1111-12-21-100−i3i3-11−i3i3−i3i3000-2020000000100000-100i3−i3
χ2722-222-22-22-2-122-2-2-1000-1111-12-21-100i3−i3-11i3−i3i3−i300020-20000000-100000100i3−i3
χ2822-222-22-22-2-122-2-2-1000-1111-12-21-100i3−i3-11i3−i3i3−i3000-2020000000100000-100−i3i3
χ2922-22-222-2-22222-2-220002-2-2-22-222-20000-2200000020-20000000200000-200000
χ3022-22-222-2-22222-2-220002-2-2-22-222-20000-22000000-2020000000-200000200000
χ314444444444-2-2-2-2-2-24441-2111-2-2-2-2-2-2-2-2111111000000000000000000000000
χ324444444444-2-2-2-2-2-2-4-4-41-2111-2-2-2-2222211-1-1-1-1000000000000000000000000
χ334444-4-444-4-4-24444-2000-2-2-2-2-2-4-4220000220000000000000000000000000000
χ344444-4-444-4-4-2-2-2-2-2-20001-21112222−2i32i300-1-1i3i3−i3−i3000000000000000000000000
χ354444-4-444-4-4-2-2-2-2-2-20001-211122222i3−2i300-1-1−i3−i3i3i3000000000000000000000000
χ3644-444-44-44-44-2-2224000-2-422-2-22-440000-220000000000000000000000000000
χ3744-444-44-44-4-2-2-222-200012-1-11-222-200−2i32i31-1i3−i3i3−i3000000000000000000000000
χ3844-444-44-44-4-2-2-222-200012-1-11-222-2002i3−2i31-1−i3i3−i3i3000000000000000000000000
χ3944-44-444-4-444-2-2224000-2-422-22-24-400002-20000000000000000000000000000
χ4044-44-444-4-44-244-4-4-2000-2222-2-44-2200002-20000000000000000000000000000
χ4144-44-444-4-44-2-2-222-200012-1-112-2-220000-113-3-33000000000000000000000000
χ4244-44-444-4-44-2-2-222-200012-1-112-2-220000-11-333-3000000000000000000000000
χ434-40400-400044-400-40004000-4000000000000000000002i−2i2i−2i2i−2i000000000000
χ444-40400-400044-400-40004000-400000000000000000000−2i2i−2i2i−2i2i000000000000
χ454-40400-40004-22−2i32i3-4000-20−2i32i32000000000000000000002i−2i2ζ7−2ζ72ζ11−2ζ11000000000000
χ464-40400-40004-22−2i32i3-4000-20−2i32i3200000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000
χ474-40400-40004-222i3−2i3-4000-202i3−2i32000000000000000000002i−2i2ζ11−2ζ112ζ7−2ζ7000000000000
χ484-40400-40004-222i3−2i3-4000-202i3−2i3200000000000000000000−2i2i−2ζ112ζ11−2ζ72ζ7000000000000
χ49666-366-3-3-3-30000006-3-30000000000000000000002020000000-100020-10-1-100
χ50666-366-3-3-3-30000006-3-3000000000000000000000-20-200000001000-20101100
χ51666-366-3-3-3-3000000-6330000000000000000000002020000000-1000-20-101100
χ52666-366-3-3-3-3000000-633000000000000000000000-20-2000000010002010-1-100
χ5366-6-3-66-333-30000000−3i33i300000000000000000000020-20000000-10000010−i3i300
χ5466-6-3-66-333-30000000−3i33i3000000000000000000000-2020000000100000-10i3−i300
χ5566-6-3-66-333-300000003i3−3i300000000000000000000020-20000000-10000010i3−i300
χ5666-6-3-66-333-300000003i3−3i3000000000000000000000-2020000000100000-10−i3i300
χ578-80800-8000-48-8004000-4000400000000000000000000000000000000000000
χ588-80800-8000-4-44−4i34i34000202i3−2i3-200000000000000000000000000000000000000
χ598-80800-8000-4-444i3−4i3400020−2i32i3-200000000000000000000000000000000000000
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.