Finite Group Databasebeta

← Group #13140951

Character table — Group #13140951

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222222444466668812121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order1223446664412123366121236666612121212121212121212121212121212224444666612121212121212122668824242424
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
χ5111111111-1-1111111-1-111111111-1-1-1-111-1-111-1-1-1-11-11-11111-1-1111111-1-1-1-1-11-111-1-1
χ6111111111-1-1111111-1-111111111-1-1-1-111-1-111-1-1-1-11-11-1-1-111-1-1-1-1-1-111-1-1111-11-1-111
χ7111111111-1-1111111-1-111111111-1-1-1-111-1-111-1-1-1-1-11-1111-1-1111111-1-111-1-1-1-11-1-111
χ8111111111-1-1111111-1-111111111-1-1-1-111-1-111-1-1-1-1-11-11-1-1-1-111-1-1-1-1-1-1111111-111-1-1
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
χ112222222222222-12-1222-1-12-1-1-1222222-1-1-1-1-1-1-1-1-1-100000000000000000000022-1-1-1-1
χ122222222222222-12-1222-1-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1000000000000000000000-2-21111
χ13222222222-2-2222-12-1-2-2-12-1-1-1-1-1-1111122-2-2-1-111112-22-200-1-1110000-1-111000000000
χ14222222222-2-2222-12-1-2-2-12-1-1-1-1-1-1111122-2-2-1-11111-22-220011-1-1000011-1-1000000000
χ15222222222-2-222-12-12-2-2-1-12-1-1-122-2-2-2-2-1-111-1-111110000000000000000000002-2-1-111
χ16222222222-2-222-12-12-2-2-1-12-1-1-122-2-2-2-2-1-111-1-11111000000000000000000000-2211-1-1
χ172222-2-22222-2-2-222222-2222222-2-222-2-2-2-22-2-2-222-2-2000000000000000000000000000
χ182222-2-22222-2-2-22-12-12-2-12-1-1-1-111-1-111-2-22-211-1-111000000−i3i3−i3i30000−i3i3−i3i3000000000
χ192222-2-22222-2-2-22-12-12-2-12-1-1-1-111-1-111-2-22-211-1-111000000i3−i3i3−i30000i3−i3i3−i3000000000
χ202222-2-22222-2-2-2-12-122-2-1-12-1-1-1-2-222-2-211-1111-1-111000000000000000000000003−33−3
χ212222-2-22222-2-2-2-12-122-2-1-12-1-1-1-2-222-2-211-1111-1-11100000000000000000000000−33−33
χ222222-2-2222-22-2-22222-22222222-2-2-2-222-2-2-22-2-2-2-222000000000000000000000000000
χ232222-2-2222-22-2-22-12-1-22-12-1-1-1-11111-1-1-2-2-221111-1-1000000−i3i3i3−i30000−i3i3i3−i3000000000
χ242222-2-2222-22-2-22-12-1-22-12-1-1-1-11111-1-1-2-2-221111-1-1000000i3−i3−i3i30000i3−i3−i3i3000000000
χ252222-2-2222-22-2-2-12-12-22-1-12-1-1-1-2-2-2-222111-11111-1-1000000000000000000000003−3−33
χ262222-2-2222-22-2-2-12-12-22-1-12-1-1-1-2-2-2-222111-11111-1-100000000000000000000000−333−3
χ2722-222-22-2-2002-22222002-2-2-2-222-200002-2002-20000020-2000022000000-2-2000000000
χ2822-222-22-2-2002-22222002-2-2-2-222-200002-2002-200000-2020000-2-200000022000000000
χ2922-222-22-2-2002-22-12-100-1-2111-1-11−i3i3−i3i32-200-11−i3i3−i3i3020-200−i3i3-1-10000i3−i311000000000
χ3022-222-22-2-2002-22-12-100-1-2111-1-11−i3i3−i3i32-200-11−i3i3−i3i30-20200i3−i3110000−i3i3-1-1000000000
χ3122-222-22-2-2002-22-12-100-1-2111-1-11i3−i3i3−i32-200-11i3−i3i3−i3020-200i3−i3-1-10000−i3i311000000000
χ3222-222-22-2-2002-22-12-100-1-2111-1-11i3−i3i3−i32-200-11i3−i3i3−i30-20200−i3i3110000i3−i3-1-1000000000
χ3322-22-222-2-200-222222002-2-2-2-22-220000-2200-22000020-200022000000-2-200000000000
χ3422-22-222-2-200-222222002-2-2-2-22-220000-2200-220000-202000-2-20000002200000000000
χ3522-22-222-2-200-222-12-100-1-2111-11-1−i3i3i3−i3-22001-1−i3i3i3−i320-2000-1-1−i3i3000011i3−i3000000000
χ3622-22-222-2-200-222-12-100-1-2111-11-1−i3i3i3−i3-22001-1−i3i3i3−i3-20200011i3−i30000-1-1−i3i3000000000
χ3722-22-222-2-200-222-12-100-1-2111-11-1i3−i3−i3i3-22001-1i3−i3−i3i320-2000-1-1i3−i3000011−i3i3000000000
χ3822-22-222-2-200-222-12-100-1-2111-11-1i3−i3−i3i3-22001-1i3−i3−i3i3-20200011−i3i30000-1-1i3−i3000000000
χ394444444444444-2-2-2-2441-2-2111-2-2-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ40444444444-4-444-2-2-2-2-4-41-2-2111-2-22222-2-22211-1-1-1-1000000000000000000000000000
χ414444-4-44444-4-4-4-2-2-2-24-41-2-211122-2-22222-22-1-111-1-1000000000000000000000000000
χ424444-4-4444-44-4-4-2-2-2-2-441-2-21112222-2-2222-2-1-1-1-111000000000000000000000000000
χ4344-444-44-4-4004-4-24-2400-22-422-24-40000-2200-220000000000000000000000000000000
χ4444-444-44-4-4004-4-2-2-2-200122-1-11-22−2i32i3−2i32i3-22001-1i3−i3i3−i3000000000000000000000000000
χ4544-444-44-4-4004-4-2-2-2-200122-1-11-222i3−2i32i3−2i3-22001-1−i3i3−i3i3000000000000000000000000000
χ4644-44-444-4-400-44-24-2400-22-422-2-4400002-2002-20000000000000000000000000000000
χ4744-44-444-4-400-44-2-2-2-200122-1-112-2−2i32i32i3−2i32-200-11i3−i3−i3i3000000000000000000000000000
χ4844-44-444-4-400-44-2-2-2-200122-1-112-22i3−2i3−2i32i32-200-11−i3i3i3−i3000000000000000000000000000
χ494-40400-400000044-4-40040000-4000000000000000000002i−2i00002i2i−2i−2i0000000000000
χ504-40400-400000044-4-40040000-400000000000000000000−2i2i0000−2i−2i2i2i0000000000000
χ51666-366-3-3-366-3-30000-3-300000000000000000000000000220000-1-1-1-100002-1-1000000
χ52666-366-3-3-366-3-30000-3-300000000000000000000000000-2-2000011110000-211000000
χ53666-366-3-3-3-6-6-3-300003300000000000000000000000000220000-1-1-1-10000-211000000
χ54666-366-3-3-3-6-6-3-300003300000000000000000000000000-2-20000111100002-1-1000000
χ55666-3-6-6-3-3-36-6330000-3300000000000000000000000000000000−i3i3−i3i300000−i3i3000000
χ56666-3-6-6-3-3-36-6330000-3300000000000000000000000000000000i3−i3i3−i300000i3−i3000000
χ57666-3-6-6-3-3-3-663300003-300000000000000000000000000000000−i3i3−i3i300000i3−i3000000
χ58666-3-6-6-3-3-3-663300003-300000000000000000000000000000000i3−i3i3−i300000−i3i3000000
χ598-80800-80000008-4-8400-4000040000000000000000000000000000000000000000000
χ608-80800-8000000-484-800-4000040000000000000000000000000000000000000000000
χ618-80800-8000000-4-444002006-6-20000000000000000000000000000000000000000000
χ628-80800-8000000-4-44400200-66-20000000000000000000000000000000000000000000
χ631212-12-612-12-66600-660000000000000000000000000000000000000000000000000000000
χ641212-12-6-1212-666006-60000000000000000000000000000000000000000000000000000000
χ6512-120-6006−6i36i30000000000000000000000000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ110000000000000
χ6612-120-6006−6i36i3000000000000000000000000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ110000000000000
χ6712-120-60066i3−6i30000000000000000000000000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ70000000000000
χ6812-120-60066i3−6i3000000000000000000000000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ70000000000000

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