Finite Group Databasebeta

← Group #13151327

Character table — Group #13151327

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order122234466622121233666666663666666612121212444444444412121212666666121222444441212121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1
χ3111111111111111111111111111111111111-1-1111111-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-11-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1-1-1-11111-1-11111-1-111
χ61111111111-1-11111111111-1-11-1-1-1-1111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11111-1-1-1-1-1-1111111-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-11111-1-1111111111-111-1-1-1-11-11-1-1-1-111-1-111-1-1-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-111-1-1-1-11-1-1111-1-1-11111-1-111-1-1111-1-11
χ1111111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-111-1-111111-111-1-1-1-1-11-11-111-1-111-1-111-1-111-1-1-11-11
χ1211111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-1-1-111-1-111-1-1-1-11-111-1-1-1-1-111-11-1111-1-1-1-11111-1-111-111-1
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-111-111-1-1-11111-1-11111-1-1-111-1
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-11111111111-11-1-111-1-1-11-11-1-1-111-1-111-1-1-1-1-1-111-11-11
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-11-1-111-1-11-1-111-1111-1-1-1-1111111-1-11-1-11
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-1-1-11111-1-11111-11-1-111-1-11-11-1-111-1-111-1-111-1-1-1-1111-11-1
χ17222222222222222-12-12-1-1222-12222-1-1-122-1-122000000000000-1-1-1-1-1-1-1-122000020000-1-1-1-1000000-1-100
χ18222222222222222-12-12-1-1222-12222-1-1-122-1-1-2-2000000000000-1-1-1-1-1-1-1-1-2-20000-2000011110000001100
χ1922222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-1220022222200-1-1-1-122-1-1-1-1-1-1000020000000000-1-1-1-1-1-10000
χ2022222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-12200-2-2-2-2-2-200111122-1-1-1-1-1-10000-200000000001111110000
χ212222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-122000000000000111111-1-1-2-2000020000-1-1-1-10000001100
χ222222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-1-2-2000000000000111111-1-1220000-200001111000000-1-100
χ232222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-122002222-2-2001111-2-21111-1-10000-2000000000011-1-1-1-10000
χ242222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-12200-2-2-2-22200-1-1-1-1-2-21111-1-1000020000000000-1-111110000
χ2522222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-21122000000000000-11-1-111112-20000-20000-1-111000000-1100
χ2622222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-211-2-2000000000000-11-1-11111-2200002000011-1-10000001-100
χ2722222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-20022-2-22200-1-1-1-12-2-1-111110000-2000000000011-1-1110000
χ2822222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-200-2-222-2-20011112-2-1-11111000020000000000-1-111-1-10000
χ2922222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-211220000000000001-111-1-111-220000-20000-1-1110000001-100
χ3022222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-211-2-20000000000001-111-1-1112-200002000011-1-1000000-1100
χ3122222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-20022-2-2-2-2001111-2211-1-111000020000000000-1-1-1-1110000
χ3222222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-200-2-2222200-1-1-1-1-2211-1-1110000-200000000001111-1-10000
χ3322-2-222-2-2-22002-22222-2-2-2-20020000-2-222-22-2002i−2i2i−2i000000000000002-2000000000000000002i−2i2i−2i0000
χ3422-2-222-2-2-22002-22222-2-2-2-20020000-2-222-22-200−2i2i−2i2i000000000000002-200000000000000000−2i2i−2i2i0000
χ3522-2-222-2-2-22002-2-12-121-2-2100-1−i3i3−i3i311-1-112-2002i−2i2i−2i000033−3−300−i3i3−i3i3-110000000000000003−3−ii−ii0000
χ3622-2-222-2-2-22002-2-12-121-2-2100-1−i3i3−i3i311-1-112-200−2i2i−2i2i0000−3−33300−i3i3−i3i3-11000000000000000−33i−ii−i0000
χ3722-2-222-2-2-22002-2-12-121-2-2100-1i3−i3i3−i311-1-112-2002i−2i2i−2i0000−3−33300i3−i3i3−i3-11000000000000000−33−ii−ii0000
χ3822-2-222-2-2-22002-2-12-121-2-2100-1i3−i3i3−i311-1-112-200−2i2i−2i2i000033−3−300i3−i3i3−i3-110000000000000003−3i−ii−i0000
χ3922-2-22-22-2-2200-222222-2-2-2-20020000-2-22-22-22002i−2i−2i2i00000000000000-22000000000000000002i−2i−2i2i0000
χ4022-2-22-22-2-2200-222222-2-2-2-20020000-2-22-22-2200−2i2i2i−2i00000000000000-2200000000000000000−2i2i2i−2i0000
χ4122-2-22-22-2-2200-22-12-121-2-2100-1−i3i3i3−i311-11-1-22002i−2i−2i2i000033−3−300−i3i3i3−i31-1000000000000000−33−iii−i0000
χ4222-2-22-22-2-2200-22-12-121-2-2100-1−i3i3i3−i311-11-1-2200−2i2i2i−2i0000−3−33300−i3i3i3−i31-10000000000000003−3i−i−ii0000
χ4322-2-22-22-2-2200-22-12-121-2-2100-1i3−i3−i3i311-11-1-22002i−2i−2i2i0000−3−33300i3−i3−i3i31-10000000000000003−3−iii−i0000
χ4422-2-22-22-2-2200-22-12-121-2-2100-1i3−i3−i3i311-11-1-2200−2i2i2i−2i000033−3−300i3−i3−i3i31-1000000000000000−33i−i−ii0000
χ452-22-22002-2-2000022-2-222-2-200200002-2-200002-200002i−2i2i−2i2i−2i2i−2i0000000000000002i−2i002-2000000000000
χ462-22-22002-2-2000022-2-222-2-200200002-2-200002-20000−2i2i−2i2i−2i2i−2i2i000000000000000−2i2i002-2000000000000
χ472-22-22002-2-2000022-2-222-2-200200002-2-20000-2200002i−2i−2i2i2i−2i2i−2i000000000000000−2i2i00-22000000000000
χ482-22-22002-2-2000022-2-222-2-200200002-2-20000-220000−2i2i2i−2i−2i2i−2i2i0000000000000002i−2i00-22000000000000
χ4944444444444444-2-2-2-2-2-2-2-2441-2-2-2-2111-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-412222111-2-2-2-20000000000000022-1-1-1-1110000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-41-2-222111222200000000000000-2211-1-1-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-44122-2-21112222000000000000002-2-1-111-1-10000000000000000000000000
χ5344-4-444-4-4-44004-44-24-2-422-400-2000022-24-4-2200000000000000000000-220000000000000000000000000
χ5444-4-444-4-4-44004-4-2-2-2-22222001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-10000000000000000000000000
χ5544-4-444-4-4-44004-4-2-2-2-222220012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-10000000000000000000000000
χ5644-4-44-44-4-4400-444-24-2-422-400-2000022-2-442-2000000000000000000002-20000000000000000000000000
χ5744-4-44-44-4-4400-44-2-2-2-22222001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-110000000000000000000000000
χ5844-4-44-44-4-4400-44-2-2-2-222220012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-110000000000000000000000000
χ594-44-44004-4-400004-2-424-22-400-20000-22200004-40000000000000000000000000000000-22000000000000
χ604-44-44004-4-400004-2-424-22-400-20000-2220000-4400000000000000000000000000000002-2000000000000
χ614-44-44004-4-40000-242-4-24-4200-20000-22200000000004i−4i00−2i2i−2i2i000000000000000000000000000000000
χ624-44-44004-4-40000-242-4-24-4200-20000-2220000000000−4i4i002i−2i2i−2i000000000000000000000000000000000
χ634-4-44400-44-4000044-4-4-4-4440040000-44-4000000000000000000000000000000000000000000000000000
χ644-4-44400-44-400004-2-42-42-2400-200002-22000000000000000000000000000000000000000−2i32i30000000000
χ654-4-44400-44-400004-2-42-42-2400-200002-220000000000000000000000000000000000000002i3−2i30000000000
χ664-4-44400-44-40000-242-42-44-200-200002-2200000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ674-4-44400-44-40000-242-42-44-200-200002-22000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000000000220000000000000022020-1-1-1-1000000000000-1-1
χ696666-366-3-3-366-3-300000000-3-300000000000000000000-2-200000000000000-2-20-20111100000000000011
χ706666-366-3-3-3-6-6-3-30000000033000000000000000000002200000000000000-2-2020-1-1-1-100000000000011
χ716666-366-3-3-3-6-6-3-3000000003300000000000000000000-2-200000000000000220-201111000000000000-1-1
χ726666-3-6-6-3-3-36-63300000000-330000000000000000000022000000000000002-20-20-1-111000000000000-11
χ736666-3-6-6-3-3-36-63300000000-3300000000000000000000-2-200000000000000-2202011-1-10000000000001-1
χ746666-3-6-6-3-3-3-6633000000003-3000000000000000000002200000000000000-220-20-1-1110000000000001-1
χ756666-3-6-6-3-3-3-6633000000003-300000000000000000000-2-2000000000000002-202011-1-1000000000000-11
χ768-88-88008-8-80000-4-444-4-44400200002-2-2000000000000000000000000000000000000000000000000000
χ778-8-88800-88-80000-4-44444-4-40020000-22-2000000000000000000000000000000000000000000000000000
χ781212-12-12-612-1266-600-66000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-6-121266-6006-6000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-12-600-66600000000000000000000000000000000004i−4i0000000000000000000−2i2i0000000000000000
χ8112-1212-12-600-6660000000000000000000000000000000000−4i4i00000000000000000002i−2i0000000000000000
χ8212-12-1212-6006-6600000000000000000000000000000000000000000000000000000000023−2300000000000000
χ8312-12-1212-6006-66000000000000000000000000000000000000000000000000000000000−232300000000000000

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