Finite Group Databasebeta

← Group #13140565

Character table — Group #13140565

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size112222244444666666889912121212121212121212121212181818181818182424242424242424363636363636363636363636363636367272727272727272
order12234462261212336666662236666666612121212244666666666612122266668888888812122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-11111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-11111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ51111111-1-1111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ61111111-1-1111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-111
χ71111111-1-1111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-111
χ81111111-1-1111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1
χ91111-1-111-11-1-11111111-1111111-1-1111-1-1-1-11-1-111111-111-1-1-1-11-111-1-1i−ii−ii−ii−i-1-1i−ii−ii−ii−i
χ101111-1-111-11-1-11111111-1111111-1-1111-1-1-1-11-1-111111-111-1-1-1-11-111-1-1−ii−ii−ii−ii-1-1−ii−ii−ii−ii
χ111111-1-111-11-1-11111111-1-1-11111-1-1111-1-1-1-1-111-1-1-1-11-111-1-1-1-1-11-1-111i−ii−i−ii−ii11i−ii−i−ii−ii
χ121111-1-111-11-1-11111111-1-1-11111-1-1111-1-1-1-1-111-1-1-1-11-111-1-1-1-1-11-1-111−ii−iii−ii−i11−ii−iii−ii−i
χ131111-1-11-111-1-1111111-111111-1-111111-1-1-1-11-1-11111-11-1-111-1-1-11-1-111i−i−iii−i−ii-1-1i−i−iii−i−ii
χ141111-1-11-111-1-1111111-111111-1-111111-1-1-1-11-1-11111-11-1-111-1-1-11-1-111−iii−i−iii−i-1-1−iii−i−iii−i
χ151111-1-11-111-1-1111111-11-1-111-1-111111-1-1-1-1-111-1-1-1-1-11-1-111-1-11-111-1-1i−i−ii−iii−i11i−i−ii−iii−i
χ161111-1-11-111-1-1111111-11-1-111-1-111111-1-1-1-1-111-1-1-1-1-11-1-111-1-11-111-1-1−iii−ii−i−ii11−iii−ii−i−ii
χ172222222222222-1-1-12-12222-12-1-1-1-1-1-1-1-1-122222-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000-1-100000000
χ182222222222222-1-1-12-122-2-2-12-1-1-1-1-1-1-1-1-122-2-2-2111122-1-1-1-1-1-1-2-21111000000001100000000
χ19222222222222-1222-122200-1-12222-1-1-122-1-10000000-1-1-1-1-1-1-1-100000000002222000000-1-1-1-1
χ20222222222222-1222-122200-1-12222-1-1-122-1-10000000-1-1-1-1-1-1-1-10000000000-2-2-2-20000001111
χ212222222-2-22222-1-1-12-1-2-222-121111-1-1-1-1-122222-1-1-1-1-2-21111-1-1-2-2111100000000-1-100000000
χ222222222-2-22222-1-1-12-1-2-2-2-2-121111-1-1-1-1-122-2-2-21111-2-21111-1-122-1-1-1-1000000001100000000
χ232222222-2-2222-1222-12-2-200-1-1-2-2-2-2-1-1-122-1-10000000111111-1-1000000000022-2-2000000-1-111
χ242222222-2-2222-1222-12-2-200-1-1-2-2-2-2-1-1-122-1-10000000111111-1-10000000000-2-22200000011-1-1
χ252222-2-222-22-2-22-1-1-12-12-222-12-1-111-1-1-111-2-22-2-2-1-1-1-12-2-1-111112-2-1-111000000001100000000
χ262222-2-222-22-2-22-1-1-12-12-2-2-2-12-1-111-1-1-111-2-2-22211112-2-1-11111-2211-1-100000000-1-100000000
χ272222-2-222-22-2-2-1222-122-200-1-122-2-2-1-1-1-2-2110000000-11-1-1111100000000002i−2i2i−2i000000−ii−ii
χ282222-2-222-22-2-2-1222-122-200-1-122-2-2-1-1-1-2-2110000000-11-1-111110000000000−2i2i−2i2i000000i−ii−i
χ292222-2-22-222-2-22-1-1-12-1-2222-1211-1-1-1-1-111-2-22-2-2-1-1-1-1-2211-1-111-2211-1-1000000001100000000
χ302222-2-22-222-2-22-1-1-12-1-22-2-2-1211-1-1-1-1-111-2-2-2221111-2211-1-1112-2-1-11100000000-1-100000000
χ312222-2-22-222-2-2-1222-12-2200-1-1-2-222-1-1-1-2-21100000001-111-1-11100000000002i−2i−2i2i000000−iii−i
χ322222-2-22-222-2-2-1222-12-2200-1-1-2-222-1-1-1-2-21100000001-111-1-1110000000000−2i2i2i−2i000000i−i−ii
χ3322-222-2200-22-222-2-22200222-20000-2-222-22-2-22-222-2-20000002-2000000000000002-200000000
χ3422-222-2200-22-222-2-22200-2-22-20000-2-222-22-22-22-2-2220000002-200000000000000-2200000000
χ3522-222-2200-22-22-1112-10022-1-2−i3i3−i3i311-1-112-2-22-2-1-11100−i3i3−i3i3-1100−i3i3−i3i300000000-1100000000
χ3622-222-2200-22-22-1112-10022-1-2i3−i3i3−i311-1-112-2-22-2-1-11100i3−i3i3−i3-1100i3−i3i3−i300000000-1100000000
χ3722-222-2200-22-22-1112-100-2-2-1-2−i3i3−i3i311-1-112-22-2211-1-100−i3i3−i3i3-1100i3−i3i3−i3000000001-100000000
χ3822-222-2200-22-22-1112-100-2-2-1-2i3−i3i3−i311-1-112-22-2211-1-100i3−i3i3−i3-1100−i3i3−i3i3000000001-100000000
χ3922-22-22200-2-2222-2-22200222-20000-2-22-22-22-2-2222-2-2000000-2200000000000000-2200000000
χ4022-22-22200-2-2222-2-22200-2-22-20000-2-22-22-2222-2-2-222000000-22000000000000002-200000000
χ4122-22-22200-2-222-1112-10022-1-2−i3i3i3−i311-11-1-22-2-22-1-11100−i3i3i3−i31-100−i3i3i3−i3000000001-100000000
χ4222-22-22200-2-222-1112-10022-1-2i3−i3−i3i311-11-1-22-2-22-1-11100i3−i3−i3i31-100i3−i3−i3i3000000001-100000000
χ4322-22-22200-2-222-1112-100-2-2-1-2−i3i3i3−i311-11-1-2222-211-1-100−i3i3i3−i31-100i3−i3−i3i300000000-1100000000
χ4422-22-22200-2-222-1112-100-2-2-1-2i3−i3−i3i311-11-1-2222-211-1-100i3−i3−i3i31-100−i3i3i3−i300000000-1100000000
χ45444444444444-2-2-2-2-2-244001-2-2-2-2-2111-2-2-2-20000000-2-2111111000000000000000000000000
χ464444444-4-4444-2-2-2-2-2-2-4-4001-22222111-2-2-2-2000000022-1-1-1-111000000000000000000000000
χ474444-4-444-44-4-4-2-2-2-2-2-24-4001-2-2-22211122220000000-2211-1-1-1-1000000000000000000000000
χ484444-4-44-444-4-4-2-2-2-2-2-2-44001-222-2-2111222200000002-2-1-111-1-1000000000000000000000000
χ4944-444-4400-44-4-24-4-4-240000-22000022-24-4-220000000000000-22000000000000000000000000
χ5044-444-4400-44-4-2-222-2-2000012−2i32i3−2i32i3-1-11-22-22000000000i3−i3i3−i31-1000000000000000000000000
χ5144-444-4400-44-4-2-222-2-20000122i3−2i32i3−2i3-1-11-22-22000000000−i3i3−i3i31-1000000000000000000000000
χ5244-44-44400-4-44-24-4-4-240000-22000022-2-442-200000000000002-2000000000000000000000000
χ5344-44-44400-4-44-2-222-2-2000012−2i32i32i3−2i3-1-112-22-2000000000i3−i3−i3i3-11000000000000000000000000
χ5444-44-44400-4-44-2-222-2-20000122i3−2i3−2i32i3-1-112-22-2000000000−i3i3i3−i3-11000000000000000000000000
χ554-40400-4000004400-4-4004-440000000-400000004-40000000000000000000000000000000000
χ564-40400-4000004400-4-400-4440000000-40000000-440000000000000000000000000000000000
χ574-40400-4000004-2−2i32i3-42004-4-200000−2i32i320000000-22−2i32i300000000000000000000000000000000
χ584-40400-4000004-2−2i32i3-4200-44-200000−2i32i3200000002-22i3−2i300000000000000000000000000000000
χ594-40400-4000004-22i3−2i3-42004-4-2000002i3−2i320000000-222i3−2i300000000000000000000000000000000
χ604-40400-4000004-22i3−2i3-4200-44-2000002i3−2i3200000002-2−2i32i300000000000000000000000000000000
χ61666-366-366-3-3-3000000-3-30000000000000000000000000000000000002222000000-1-1-1-10000
χ62666-366-366-3-3-3000000-3-3000000000000000000000000000000000000-2-2-2-200000011110000
χ63666-366-3-6-6-3-3-30000003300000000000000000000000000000000000022-2-2000000-1-1110000
χ64666-366-3-6-6-3-3-300000033000000000000000000000000000000000000-2-22200000011-1-10000
χ65666-3-6-6-36-6-333000000-330000000000000000000000000000000000002i−2i2i−2i000000−ii−ii0000
χ66666-3-6-6-36-6-333000000-33000000000000000000000000000000000000−2i2i−2i2i000000i−ii−i0000
χ67666-3-6-6-3-66-3330000003-30000000000000000000000000000000000002i−2i−2i2i000000−iii−i0000
χ68666-3-6-6-3-66-3330000003-3000000000000000000000000000000000000−2i2i2i−2i000000i−i−ii0000
χ698-80800-800000-48004-80000-4000000040000000000000000000000000000000000000000000
χ708-80800-800000-4-4−4i34i34400002000002i3−2i3-20000000000000000000000000000000000000000000
χ718-80800-800000-4-44i3−4i3440000200000−2i32i3-20000000000000000000000000000000000000000000
χ721212-12-612-12-6006-6600000000000000000000000000000000000000000000000000000000000000
χ731212-12-6-1212-60066-600000000000000000000000000000000000000000000000000000000000000
χ7424-240-1200120000000000000000000000000000000000000000000000000000000000000000000

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