Finite Group Databasebeta

← Group #13140927

Character table — Group #13140927

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222224444466666688121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order1223446446121233666612123666612121212121212121212121212121212224444666612121212121212122668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111-1-1111111111-1-1111111111-1-1-1-1-1-111-1-1-1-11-11-11111-1-1111111-1-1-1-1-11-111-1-1
χ61111111-1-1111111111-1-1111111111-1-1-1-1-1-111-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1111-11-1-111
χ71111111-1-1111111111-1-1111111111-1-1-1-1-1-111-1-1-1-1-11-1111-1-1111111-1-111-1-1-1-11-1-111
χ81111111-1-1111111111-1-1111111111-1-1-1-1-1-111-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1111111-111-1-1
χ92222222222222-1222-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222200-1-1-1-10000-1-1-1-1000000000
χ102222222222222-1222-122-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-200111100001111000000000
χ11222222222222-12-1-1-1222-12-1-1-1-1-1222222-1-1-1-1-1-1-1-10000220000-1-1-1-100002-1-1000000
χ12222222222222-12-1-1-1222-12-1-1-1-1-1222222-1-1-1-1-1-1-1-10000-2-2000011110000-211000000
χ132222222-2-22222-1222-1-2-2-1-1-1-1-122-1-11111-2-2-1-111112-22-200-1-1110000-1-111000000000
χ142222222-2-22222-1222-1-2-2-1-1-1-1-122-1-11111-2-2-1-11111-22-220011-1-1000011-1-1000000000
χ152222222-2-2222-12-1-1-12-2-2-12-1-1-1-1-122-2-2-2-211-1-111110000220000-1-1-1-10000-211000000
χ162222222-2-2222-12-1-1-12-2-2-12-1-1-1-1-122-2-2-2-211-1-111110000-2-20000111100002-1-1000000
χ172222-2-222-22-2-22222222-222222-2-2-2-222-2-22-2-2-222-2-2000000000000000000000000000
χ182222-2-222-22-2-22-1222-12-2-1-1-1-1-1-2-211-1-1112-211-1-111000000−i3i3−i3i30000−i3i3−i3i3000000000
χ192222-2-222-22-2-22-1222-12-2-1-1-1-1-1-2-211-1-1112-211-1-111000000i3−i3i3−i30000i3−i3i3−i3000000000
χ202222-2-222-22-2-2-12-1-1-122-2-12-1-1-111-2-222-2-2-1111-1-1110000000000−i3−i3i3i300000−i3i3000000
χ212222-2-222-22-2-2-12-1-1-122-2-12-1-1-111-2-222-2-2-1111-1-1110000000000i3i3−i3−i300000i3−i3000000
χ222222-2-22-222-2-2222222-2222222-2-2-2-2-2-222-22-2-2-2-222000000000000000000000000000
χ232222-2-22-222-2-22-1222-1-22-1-1-1-1-1-2-21111-1-1-221111-1-1000000−i3i3i3−i30000−i3i3i3−i3000000000
χ242222-2-22-222-2-22-1222-1-22-1-1-1-1-1-2-21111-1-1-221111-1-1000000i3−i3−i3i30000i3−i3−i3i3000000000
χ252222-2-22-222-2-2-12-1-1-12-22-12-1-1-111-2-2-2-2221-11111-1-10000000000−i3−i3i3i300000i3−i3000000
χ262222-2-22-222-2-2-12-1-1-12-22-12-1-1-111-2-2-2-2221-11111-1-10000000000i3i3−i3−i300000−i3i3000000
χ2722-222-2200-22-2222-2-22002-2-2-222-22-20000002-20000020-2000022000000-2-2000000000
χ2822-222-2200-22-2222-2-22002-2-2-222-22-20000002-200000-2020000-2-200000022000000000
χ2922-222-2200-22-22-12-2-2-100-1111-12-2-11−i3i3−i3i300-11−i3i3−i3i3020-200−i3i3-1-10000i3−i311000000000
χ3022-222-2200-22-22-12-2-2-100-1111-12-2-11−i3i3−i3i300-11−i3i3−i3i30-20200i3−i3110000−i3i3-1-1000000000
χ3122-222-2200-22-22-12-2-2-100-1111-12-2-11i3−i3i3−i300-11i3−i3i3−i3020-200i3−i3-1-10000−i3i311000000000
χ3222-222-2200-22-22-12-2-2-100-1111-12-2-11i3−i3i3−i300-11i3−i3i3−i30-20200−i3i3110000i3−i3-1-1000000000
χ3322-22-22200-2-22222-2-22002-2-2-22-22-22000000-22000020-200022000000-2-200000000000
χ3422-22-22200-2-22222-2-22002-2-2-22-22-22000000-220000-202000-2-20000002200000000000
χ3522-22-22200-2-222-12-2-2-100-1111-1-221-1−i3i3i3−i3001-1−i3i3i3−i320-2000-1-1−i3i3000011i3−i3000000000
χ3622-22-22200-2-222-12-2-2-100-1111-1-221-1−i3i3i3−i3001-1−i3i3i3−i3-20200011i3−i30000-1-1−i3i3000000000
χ3722-22-22200-2-222-12-2-2-100-1111-1-221-1i3−i3−i3i3001-1i3−i3−i3i320-2000-1-1i3−i3000011−i3i3000000000
χ3822-22-22200-2-222-12-2-2-100-1111-1-221-1i3−i3−i3i3001-1i3−i3−i3i3-20200011−i3i30000-1-1i3−i3000000000
χ39444444444444-2-2-2-2-2-2441-2111-2-2-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ404444444-4-4444-2-2-2-2-2-2-4-41-2111-2-2-2-222222211-1-1-1-1000000000000000000000000000
χ414444-4-444-44-4-4-2-2-2-2-2-24-41-21112222-2-222-22-1-111-1-1000000000000000000000000000
χ424444-4-44-444-4-4-2-2-2-2-2-2-441-2111222222-2-22-2-1-1-1-111000000000000000000000000000
χ4344-444-4400-44-4-24-222400-2-422-2-224-4000000-220000000000000000000000000000000
χ4444-444-4400-44-4-2-2-222-20012-1-11-22-22−2i32i3−2i32i3001-1i3−i3i3−i3000000000000000000000000000
χ4544-444-4400-44-4-2-2-222-20012-1-11-22-222i3−2i32i3−2i3001-1−i3i3−i3i3000000000000000000000000000
χ4644-44-44400-4-44-24-222400-2-422-22-2-440000002-20000000000000000000000000000000
χ4744-44-44400-4-44-2-2-222-20012-1-112-22-2−2i32i32i3−2i300-11i3−i3−i3i3000000000000000000000000000
χ4844-44-44400-4-44-2-2-222-20012-1-112-22-22i3−2i3−2i32i300-11−i3i3i3−i3000000000000000000000000000
χ494-40400-40000044-400-4004000-4000000000000000000002i−2i00002i−2i2i−2i0000000000000
χ504-40400-40000044-400-4004000-400000000000000000000−2i2i0000−2i2i−2i2i0000000000000
χ514-40400-400000-242−2i32i3-400-20−2i32i32000000000000000000002i−2i00002ζ7−2ζ72ζ11−2ζ110000000000000
χ524-40400-400000-242−2i32i3-400-20−2i32i3200000000000000000000−2i2i0000−2ζ72ζ7−2ζ112ζ110000000000000
χ534-40400-400000-2422i3−2i3-400-202i3−2i32000000000000000000002i−2i00002ζ11−2ζ112ζ7−2ζ70000000000000
χ544-40400-400000-2422i3−2i3-400-202i3−2i3200000000000000000000−2i2i0000−2ζ112ζ11−2ζ72ζ70000000000000
χ55666-366-366-3-3-3000000-3-300000000000000000000000000000000000000000022-1-1-1-1
χ56666-366-366-3-3-3000000-3-3000000000000000000000000000000000000000000-2-21111
χ57666-366-3-6-6-3-3-3000000330000000000000000000000000000000000000000002-2-1-111
χ58666-366-3-6-6-3-3-300000033000000000000000000000000000000000000000000-2211-1-1
χ59666-3-6-6-36-6-333000000-33000000000000000000000000000000000000000000003−33−3
χ60666-3-6-6-36-6-333000000-3300000000000000000000000000000000000000000000−33−33
χ61666-3-6-6-3-66-3330000003-3000000000000000000000000000000000000000000003−3−33
χ62666-3-6-6-3-66-3330000003-300000000000000000000000000000000000000000000−333−3
χ638-80800-8000008-4-800400-400040000000000000000000000000000000000000000000
χ648-80800-800000-4-44−4i34i3400202i3−2i3-20000000000000000000000000000000000000000000
χ658-80800-800000-4-444i3−4i340020−2i32i3-20000000000000000000000000000000000000000000
χ661212-12-612-12-6006-6600000000000000000000000000000000000000000000000000000000
χ671212-12-6-1212-60066-600000000000000000000000000000000000000000000000000000000
χ6824-240-1200120000000000000000000000000000000000000000000000000000000000000

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