Finite Group Databasebeta

← Group #13140567

Character table — Group #13140567

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222224444466666688121212121212121212121212122424242424242424363636363636363636363636363636363636727272727272727272
order1223446226121233666666366666666121212126666661212224444666612121212121212122668824242424
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
χ51111111-1-1111111111-1-111-1-1-1-11111111-1-1-1-1-1-1111-11-11111-1-1111111-1-1-1-1-11-111-1-1
χ61111111-1-1111111111-1-111-1-1-1-11111111-1-1-1-1-1-1111-11-1-1-111-1-1-1-1-1-111-1-1111-11-1-111
χ71111111-1-1111111111-1-111-1-1-1-11111111-1-1-1-1-1-111-11-1111-1-1111111-1-111-1-1-1-11-1-111
χ81111111-1-1111111111-1-111-1-1-1-11111111-1-1-1-1-1-111-11-11-1-1-1-111-1-1-1-1-1-1111111-111-1-1
χ92222222222222-1222-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1222200-1-1-1-10000-1-1-1-1000000000
χ102222222222222-1222-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2-2-200111100001111000000000
χ11222222222222-12-1-1-1222-122222-1-1-1-1-122-1-1-1-1-1-1-1-10000220000-1-1-1-100002-1-1000000
χ12222222222222-12-1-1-1222-122222-1-1-1-1-122-1-1-1-1-1-1-1-10000-2-2000011110000-211000000
χ132222222-2-22222-1222-1-2-2-1-11111-1-1-122-1-1-2-21111-1-12-22-200-1-1110000-1-111000000000
χ142222222-2-22222-1222-1-2-2-1-11111-1-1-122-1-1-2-21111-1-1-22-220011-1-1000011-1-1000000000
χ152222222-2-2222-12-1-1-12-2-2-12-2-2-2-2-1-1-1-1-122111111-1-10000220000-1-1-1-10000-211000000
χ162222222-2-2222-12-1-1-12-2-2-12-2-2-2-2-1-1-1-1-122111111-1-10000-2-20000111100002-1-1000000
χ172222-2-222-22-2-22222222-22222-2-2222-2-2-2-22-222-2-2-2-2000000000000000000000000000
χ182222-2-222-22-2-22-1222-12-2-1-1-1-111-1-1-1-2-2112-2-1-11111000000−i3i3−i3i30000−i3i3−i3i3000000000
χ192222-2-222-22-2-22-1222-12-2-1-1-1-111-1-1-1-2-2112-2-1-11111000000i3−i3i3−i30000i3−i3i3−i3000000000
χ202222-2-222-22-2-2-12-1-1-122-2-1222-2-2-1-1-111-2-2-11-1-111110000000000−i3−i3i3i300000−i3i3000000
χ212222-2-222-22-2-2-12-1-1-122-2-1222-2-2-1-1-111-2-2-11-1-111110000000000i3i3−i3−i300000i3−i3000000
χ222222-2-22-222-2-2222222-2222-2-222222-2-2-2-2-22-2-222-2-2000000000000000000000000000
χ232222-2-22-222-2-22-1222-1-22-1-111-1-1-1-1-1-2-211-2211-1-111000000−i3i3i3−i30000−i3i3i3−i3000000000
χ242222-2-22-222-2-22-1222-1-22-1-111-1-1-1-1-1-2-211-2211-1-111000000i3−i3−i3i30000i3−i3−i3i3000000000
χ252222-2-22-222-2-2-12-1-1-12-22-12-2-222-1-1-111-2-21-111-1-1110000000000−i3−i3i3i300000i3−i3000000
χ262222-2-22-222-2-2-12-1-1-12-22-12-2-222-1-1-111-2-21-111-1-1110000000000i3i3−i3−i300000−i3i3000000
χ2722-222-2200-22-2222-2-22002-20000-2-222-22-20000002-2020-2000022000000-2-2000000000
χ2822-222-2200-22-2222-2-22002-20000-2-222-22-20000002-20-2020000-2-200000022000000000
χ2922-222-2200-22-22-12-2-2-100-11−i3i3−i3i311-12-2-1100−i3i3−i3i3-11020-200−i3i3-1-10000i3−i311000000000
χ3022-222-2200-22-22-12-2-2-100-11−i3i3−i3i311-12-2-1100−i3i3−i3i3-110-20200i3−i3110000−i3i3-1-1000000000
χ3122-222-2200-22-22-12-2-2-100-11i3−i3i3−i311-12-2-1100i3−i3i3−i3-11020-200i3−i3-1-10000−i3i311000000000
χ3222-222-2200-22-22-12-2-2-100-11i3−i3i3−i311-12-2-1100i3−i3i3−i3-110-20200−i3i3110000i3−i3-1-1000000000
χ3322-22-22200-2-22222-2-22002-20000-2-22-22-22000000-2220-200022000000-2-200000000000
χ3422-22-22200-2-22222-2-22002-20000-2-22-22-22000000-22-202000-2-20000002200000000000
χ3522-22-22200-2-222-12-2-2-100-11−i3i3i3−i311-1-221-100−i3i3i3−i31-120-2000-1-1−i3i3000011i3−i3000000000
χ3622-22-22200-2-222-12-2-2-100-11−i3i3i3−i311-1-221-100−i3i3i3−i31-1-20200011i3−i30000-1-1−i3i3000000000
χ3722-22-22200-2-222-12-2-2-100-11i3−i3−i3i311-1-221-100i3−i3−i3i31-120-2000-1-1i3−i3000011−i3i3000000000
χ3822-22-22200-2-222-12-2-2-100-11i3−i3−i3i311-1-221-100i3−i3−i3i31-1-20200011−i3i30000-1-1i3−i3000000000
χ39444444444444-2-2-2-2-2-2441-2-2-2-2-2111-2-2-2-2-2-2111111000000000000000000000000000
χ404444444-4-4444-2-2-2-2-2-2-4-41-22222111-2-2-2-222-1-1-1-111000000000000000000000000000
χ414444-4-444-44-4-4-2-2-2-2-2-24-41-2-2-2221112222-2211-1-1-1-1000000000000000000000000000
χ424444-4-44-444-4-4-2-2-2-2-2-2-441-222-2-211122222-2-1-111-1-1000000000000000000000000000
χ4344-444-4400-44-4-24-222400-2-4000022-2-224-4000000-22000000000000000000000000000
χ4444-444-4400-44-4-2-2-222-20012−2i32i3−2i32i3-1-11-22-2200i3−i3i3−i31-1000000000000000000000000000
χ4544-444-4400-44-4-2-2-222-200122i3−2i32i3−2i3-1-11-22-2200−i3i3−i3i31-1000000000000000000000000000
χ4644-44-44400-4-44-24-222400-2-4000022-22-2-440000002-2000000000000000000000000000
χ4744-44-44400-4-44-2-2-222-20012−2i32i32i3−2i3-1-112-22-200i3−i3−i3i3-11000000000000000000000000000
χ4844-44-44400-4-44-2-2-222-200122i3−2i3−2i32i3-1-112-22-200−i3i3i3−i3-11000000000000000000000000000
χ494-40400-40000044-400-40040000000-400000000000000002-200002-22-20000000000000
χ504-40400-40000044-400-40040000000-40000000000000000-220000-22-220000000000000
χ514-40400-400000-242−2i32i3-400-200000−2i32i3200000000000000002-20000−1−i31+i3−1+i31−i30000000000000
χ524-40400-400000-242−2i32i3-400-200000−2i32i320000000000000000-2200001+i3−1−i31−i3−1+i30000000000000
χ534-40400-400000-2422i3−2i3-400-2000002i3−2i3200000000000000002-20000−1+i31−i3−1−i31+i30000000000000
χ544-40400-400000-2422i3−2i3-400-2000002i3−2i320000000000000000-2200001−i3−1+i31+i3−1−i30000000000000
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
χ638-80800-8000008-4-800400-400000004000000000000000000000000000000000000000
χ648-80800-800000-4-44−4i34i34002000002i3−2i3-2000000000000000000000000000000000000000
χ658-80800-800000-4-444i3−4i3400200000−2i32i3-2000000000000000000000000000000000000000
χ661212-12-612-12-6006-6600000000000000000000000000000000000000000000000000000000
χ671212-12-6-1212-60066-600000000000000000000000000000000000000000000000000000000
χ6824-240-1200120000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).