Finite Group Databasebeta

← Group #13140615

Character table — Group #13140615

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222444466668812121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order122344666221212336666366666666612121212666666121222444466661212121212121212488121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111-1-1111111-1-1111-1-1-1-11111111-1-1-1-1-1-1111-11-11111-1-1111111-1-1-11-1-1-111-1-1
χ6111111111-1-1111111-1-1111-1-1-1-11111111-1-1-1-1-1-1111-11-1-1-111-1-1-1-1-1-111-1-11-1111-1-111
χ7111111111-1-1111111-1-1111-1-1-1-11111111-1-1-1-1-1-111-11-1111-1-1111111-1-111-1-11-1-1-1-111
χ8111111111-1-1111111-1-1111-1-1-1-11111111-1-1-1-1-1-111-11-11-1-1-1-111-1-1-1-1-1-11111-11111-1-1
χ922222222222222-12-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1222200-1-1-1-10000-1-1-1-1000000000
χ1022222222222222-12-122-12-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-200111100001111000000000
χ112222222222222-12-1222-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-100000000000000000002200-1-1-1-1
χ122222222222222-12-1222-1-122222-1-1-122-1-1-1-1-1-1-1-1-1-10000000000000000000-2-2001111
χ13222222222-2-2222-12-1-2-2-12-11111-1-1-1-1-122-2-21111-1-12-22-200-1-1110000-1-111000000000
χ14222222222-2-2222-12-1-2-2-12-11111-1-1-1-1-122-2-21111-1-1-22-220011-1-1000011-1-1000000000
χ15222222222-2-222-12-12-2-2-1-12-2-2-2-2-1-1-122-1-1111111-1-100000000000000000002-200-1-111
χ16222222222-2-222-12-12-2-2-1-12-2-2-2-2-1-1-122-1-1111111-1-10000000000000000000-220011-1-1
χ172222-2-22222-2-2-222222-222222-2-2222-2-2-2-22-222-2-2-2-2000000000000000000000000000
χ182222-2-22222-2-2-22-12-12-2-12-1-1-111-1-1-111-2-22-2-1-11111000000−i3i3−i3i30000−i3i3−i3i3000000000
χ192222-2-22222-2-2-22-12-12-2-12-1-1-111-1-1-111-2-22-2-1-11111000000i3−i3i3−i30000i3−i3i3−i3000000000
χ202222-2-22222-2-2-2-12-122-2-1-1222-2-2-1-1-1-2-211-11-1-11111000000000000000000000003−33−3
χ212222-2-22222-2-2-2-12-122-2-1-1222-2-2-1-1-1-2-211-11-1-1111100000000000000000000000−33−33
χ222222-2-2222-22-2-22222-22222-2-222222-2-2-2-2-22-2-222-2-2000000000000000000000000000
χ232222-2-2222-22-2-22-12-1-22-12-111-1-1-1-1-111-2-2-2211-1-111000000−i3i3i3−i30000−i3i3i3−i3000000000
χ242222-2-2222-22-2-22-12-1-22-12-111-1-1-1-1-111-2-2-2211-1-111000000i3−i3−i3i30000i3−i3−i3i3000000000
χ252222-2-2222-22-2-2-12-12-22-1-12-2-222-1-1-1-2-2111-111-1-111000000000000000000000003−3−33
χ262222-2-2222-22-2-2-12-12-22-1-12-2-222-1-1-1-2-2111-111-1-11100000000000000000000000−333−3
χ2722-222-2-2-22002-22222002-2-20000-2-222-22-20000002-2020-2000022000000-2-2000000000
χ2822-222-2-2-22002-22222002-2-20000-2-222-22-20000002-20-2020000-2-200000022000000000
χ2922-222-2-2-22002-22-12-100-1-21−i3i3−i3i311-1-112-200−i3i3−i3i3-11020-200−i3i3-1-10000i3−i311000000000
χ3022-222-2-2-22002-22-12-100-1-21−i3i3−i3i311-1-112-200−i3i3−i3i3-110-20200i3−i3110000−i3i3-1-1000000000
χ3122-222-2-2-22002-22-12-100-1-21i3−i3i3−i311-1-112-200i3−i3i3−i3-11020-200i3−i3-1-10000−i3i311000000000
χ3222-222-2-2-22002-22-12-100-1-21i3−i3i3−i311-1-112-200i3−i3i3−i3-110-20200−i3i3110000i3−i3-1-1000000000
χ3322-22-22-2-2200-222222002-2-20000-2-22-22-22000000-2220-200022000000-2-200000000000
χ3422-22-22-2-2200-222222002-2-20000-2-22-22-22000000-22-202000-2-20000002200000000000
χ3522-22-22-2-2200-222-12-100-1-21−i3i3i3−i311-11-1-2200−i3i3i3−i31-120-2000-1-1−i3i3000011i3−i3000000000
χ3622-22-22-2-2200-222-12-100-1-21−i3i3i3−i311-11-1-2200−i3i3i3−i31-1-20200011i3−i30000-1-1−i3i3000000000
χ3722-22-22-2-2200-222-12-100-1-21i3−i3−i3i311-11-1-2200i3−i3−i3i31-120-2000-1-1i3−i3000011−i3i3000000000
χ3822-22-22-2-2200-222-12-100-1-21i3−i3−i3i311-11-1-2200i3−i3−i3i31-1-20200011−i3i30000-1-1i3−i3000000000
χ394444444444444-2-2-2-2441-2-2-2-2-2-2111-2-2-2-2-2-2111111000000000000000000000000000
χ40444444444-4-444-2-2-2-2-4-41-2-22222111-2-2-2-222-1-1-1-111000000000000000000000000000
χ414444-4-44444-4-4-4-2-2-2-24-41-2-2-2-2221112222-2211-1-1-1-1000000000000000000000000000
χ424444-4-4444-44-4-4-2-2-2-2-441-2-222-2-211122222-2-1-111-1-1000000000000000000000000000
χ4344-444-4-4-44004-4-24-2400-22-4000022-24-4-22000000-22000000000000000000000000000
χ4444-444-4-4-44004-4-2-2-2-200122−2i32i3−2i32i3-1-11-22-2200i3−i3i3−i31-1000000000000000000000000000
χ4544-444-4-4-44004-4-2-2-2-2001222i3−2i32i3−2i3-1-11-22-2200−i3i3−i3i31-1000000000000000000000000000
χ4644-44-44-4-4400-44-24-2400-22-4000022-2-442-20000002-2000000000000000000000000000
χ4744-44-44-4-4400-44-2-2-2-200122−2i32i32i3−2i3-1-112-22-200i3−i3−i3i3-11000000000000000000000000000
χ4844-44-44-4-4400-44-2-2-2-2001222i3−2i3−2i32i3-1-112-22-200−i3i3i3−i3-11000000000000000000000000000
χ494-4040000-4000044-4-400400000000-400000000000000002i−2i00002i2i−2i−2i0000000000000
χ504-4040000-4000044-4-400400000000-40000000000000000−2i2i0000−2i−2i2i2i0000000000000
χ51666-366-3-3-366-3-30000-3-300000000000000000000000000220000-1-1-1-10000200-1-10000
χ52666-366-3-3-366-3-30000-3-300000000000000000000000000-2-2000011110000-200110000
χ53666-366-3-3-3-6-6-3-300003300000000000000000000000000220000-1-1-1-10000-200110000
χ54666-366-3-3-3-6-6-3-300003300000000000000000000000000-2-2000011110000200-1-10000
χ55666-3-6-6-3-3-36-6330000-3300000000000000000000000000000000−i3i3−i3i30000000−i3i30000
χ56666-3-6-6-3-3-36-6330000-3300000000000000000000000000000000i3−i3i3−i30000000i3−i30000
χ57666-3-6-6-3-3-3-663300003-300000000000000000000000000000000−i3i3−i3i30000000i3−i30000
χ58666-3-6-6-3-3-3-663300003-300000000000000000000000000000000i3−i3i3−i30000000−i3i30000
χ598-8080000-800008-4-8400-4000000004000000000000000000000000000000000000000
χ608-8080000-80000-484-800-4000000004000000000000000000000000000000000000000
χ618-8080000-80000-4-4440020000006-6-2000000000000000000000000000000000000000
χ628-8080000-80000-4-444002000000-66-2000000000000000000000000000000000000000
χ631212-12-612-1266-600-660000000000000000000000000000000000000000000000000000000
χ641212-12-6-121266-6006-60000000000000000000000000000000000000000000000000000000
χ6512-120-600−6i36i360000000000000000000000000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ110000000000000
χ6612-120-600−6i36i36000000000000000000000000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ110000000000000
χ6712-120-6006i3−6i360000000000000000000000000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ70000000000000
χ6812-120-6006i3−6i36000000000000000000000000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ70000000000000

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