Finite Group Databasebeta

← Group #13140992

Character table — Group #13140992

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112222244444444466666612121212121212121224242424242424242424363636363636363636363636363636363636727272727272727272
order1223446446121212121212336666366661212121212121212121212121212224444666612121212121212122668824242424
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111-1-1111-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-11-11111-1-111-1-11111-1-1-11-111-1-1
χ61111111-1-1111-1-1-1-1111111111111111-1-1-1-111-1-1-1-11-11-1-1-111-1-111-1-1-1-1-1-1111-11-1-111
χ71111111-1-1111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-11-1111-1-111-1-1111111-1-1-1-11-1-111
χ81111111-1-1111-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-11-11-1-1-1-111-1-111-1-1-1-11111-111-1-1
χ922222222222222222-12-1-1-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-100002200000000-1-1-1-12-1-1000000
χ1022222222222222222-12-1-1-1-12-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2000000001111-211000000
χ112222222222222222-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-1-100000000000000000000022-1-1-1-1
χ122222222222222222-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-1-1000000000000000000000-2-21111
χ132222222-2-2222-2-2-2-22-12-1-1-1-12-1-1-1-1-122-2-211-1-1111100002200000000-1-1-1-1-211000000
χ142222222-2-2222-2-2-2-22-12-1-1-1-12-1-1-1-1-122-2-211-1-111110000-2-20000000011112-1-1000000
χ152222222-2-2222-2-2-2-2-12-1222-1-1-1-1-122-1-111-2-2-1-111110000000000000000000002-2-1-111
χ162222222-2-2222-2-2-2-2-12-1222-1-1-1-1-122-1-111-2-2-1-11111000000000000000000000-2211-1-1
χ172222-2-222-22-2-222-2-222222222222-2-2-2-22-22-2-2-222-2-2000000000000000000000000000
χ182222-2-222-22-2-222-2-22-12-1-1-1-12-1-1-111-2-22-2-1111-1-11100000000000000−i3−i3i3i30−i3i3000000
χ192222-2-222-22-2-222-2-22-12-1-1-1-12-1-1-111-2-22-2-1111-1-11100000000000000i3i3−i3−i30i3−i3000000
χ202222-2-222-22-2-222-2-2-12-1222-1-1-1-1-1-2-211-112-211-1-111000000000000000000000003−33−3
χ212222-2-222-22-2-222-2-2-12-1222-1-1-1-1-1-2-211-112-211-1-11100000000000000000000000−33−33
χ222222-2-22-222-2-2-2-22222222222222-2-2-2-2-22-22-2-2-2-222000000000000000000000000000
χ232222-2-22-222-2-2-2-2222-12-1-1-1-12-1-1-111-2-2-221-11111-1-100000000000000−i3−i3i3i30i3−i3000000
χ242222-2-22-222-2-2-2-2222-12-1-1-1-12-1-1-111-2-2-221-11111-1-100000000000000i3i3−i3−i30−i3i3000000
χ252222-2-22-222-2-2-2-222-12-1222-1-1-1-1-1-2-2111-1-221111-1-1000000000000000000000003−3−33
χ262222-2-22-222-2-2-2-222-12-1222-1-1-1-1-1-2-2111-1-221111-1-100000000000000000000000−333−3
χ2722-222-2200-22-200002222-2-22-2-2-222-22-200002-20000020-200002200-2-20000000000000
χ2822-222-2200-22-200002222-2-22-2-2-222-22-200002-200000-2020000-2-200220000000000000
χ2922-22-22200-2-2200002222-2-22-2-2-22-22-220000-22000020-20002200-2-2000000000000000
χ3022-22-22200-2-2200002222-2-22-2-2-22-22-220000-220000-202000-2-20022000000000000000
χ314444444444444444-2-2-2-2-2-21-2111-2-2-2-2-2-2-2-2111111000000000000000000000000000
χ324444444-4-4444-4-4-4-4-2-2-2-2-2-21-2111-2-2-2-2222211-1-1-1-1000000000000000000000000000
χ334444-4-444-44-4-444-4-4-2-2-2-2-2-21-21112222-22-22-1-111-1-1000000000000000000000000000
χ344444-4-44-444-4-4-4-444-2-2-2-2-2-21-211122222-22-2-1-1-1-111000000000000000000000000000
χ3544-444-4400-44-400004-24-222-2-422-2-224-40000-220000000000000000000000000000000
χ3644-444-4400-44-40000-24-24-4-4-2222-24-4-220000-220000000000000000000000000000000
χ3744-444-4400-44-40000-2-2-2-22212-1-11-22-2200001-13-33-3000000000000000000000000000
χ3844-444-4400-44-40000-2-2-2-22212-1-11-22-2200001-1-33-33000000000000000000000000000
χ3944-44-44400-4-4400004-24-222-2-422-22-2-4400002-20000000000000000000000000000000
χ4044-44-44400-4-440000-24-24-4-4-2222-2-442-200002-20000000000000000000000000000000
χ4144-44-44400-4-440000-2-2-2-22212-1-112-22-20000-113-3-33000000000000000000000000000
χ4244-44-44400-4-440000-2-2-2-22212-1-112-22-20000-11-333-3000000000000000000000000000
χ434-40400-400000000044-4-4004000-40000000000000000002i−2i000000002i−2i2i−2i000000000
χ444-40400-400000000044-4-4004000-4000000000000000000−2i2i00000000−2i2i−2i2i000000000
χ454-40400-40000000004-2-42−2i32i3-20−2i32i320000000000000000002i−2i000000002ζ7−2ζ72ζ11−2ζ11000000000
χ464-40400-40000000004-2-42−2i32i3-20−2i32i32000000000000000000−2i2i00000000−2ζ72ζ7−2ζ112ζ11000000000
χ474-40400-40000000004-2-422i3−2i3-202i3−2i320000000000000000002i−2i000000002ζ11−2ζ112ζ7−2ζ7000000000
χ484-40400-40000000004-2-422i3−2i3-202i3−2i32000000000000000000−2i2i00000000−2ζ112ζ11−2ζ72ζ7000000000
χ49666-366-366-3-3-3-3-3-3-30000000000000000000000000222200-1-1-1-1-1-1-1-10000000000000
χ50666-366-366-3-3-3-3-3-3-30000000000000000000000000-2-2-2-200111111110000000000000
χ51666-366-3-6-6-3-3-3333300000000000000000000000002-22-200-1-111-1-1110000000000000
χ52666-366-3-6-6-3-3-333330000000000000000000000000-22-220011-1-111-1-10000000000000
χ53666-3-6-6-36-6-333-3-3330000000000000000000000000000000−i3i3−i3i3−i3i3−i3i30000000000000
χ54666-3-6-6-36-6-333-3-3330000000000000000000000000000000i3−i3i3−i3i3−i3i3−i30000000000000
χ55666-3-6-6-3-66-33333-3-30000000000000000000000000000000−i3i3i3−i3−i3i3i3−i30000000000000
χ56666-3-6-6-3-66-33333-3-30000000000000000000000000000000i3−i3−i3i3i3−i3−i3i30000000000000
χ5766-6-36-6-3003-33−3i33i3−3i33i30000000000000000000000000020-200−i3i3-1-1i3−i3110000000000000
χ5866-6-36-6-3003-33−3i33i3−3i33i300000000000000000000000000-20200i3−i311−i3i3-1-10000000000000
χ5966-6-36-6-3003-333i3−3i33i3−3i30000000000000000000000000020-200i3−i3-1-1−i3i3110000000000000
χ6066-6-36-6-3003-333i3−3i33i3−3i300000000000000000000000000-20200−i3i311i3−i3-1-10000000000000
χ6166-6-3-66-30033-3−3i33i33i3−3i3000000000000000000000000020-2000-1-1−i3i311i3−i30000000000000
χ6266-6-3-66-30033-3−3i33i33i3−3i30000000000000000000000000-20200011i3−i3-1-1−i3i30000000000000
χ6366-6-3-66-30033-33i3−3i3−3i33i3000000000000000000000000020-2000-1-1i3−i311−i3i30000000000000
χ6466-6-3-66-30033-33i3−3i3−3i33i30000000000000000000000000-20200011−i3i3-1-1i3−i30000000000000
χ658-80800-8000000000-484-800-4000400000000000000000000000000000000000000000
χ668-80800-8000000000-4-444−4i34i3202i3−2i3-200000000000000000000000000000000000000000
χ678-80800-8000000000-4-4444i3−4i320−2i32i3-200000000000000000000000000000000000000000
χ6824-240-1200120000000000000000000000000000000000000000000000000000000000000

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