Finite Group Databasebeta

← Group #13151302

Character table — Group #13151302

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order1222344666221212336666666636666666121212124444444444121212126666661212222244412121212121212121212121212126666
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-11-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-11-1-1-1-1-1-11111-1-1-1-1-1-111
χ51111111111-1-11111111111-1-11-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11111-1-1-1-1-1-11111-1-111
χ61111111111-1-11111111111-1-11-1-1-1-111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-11111111111-1-1
χ71111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ81111111111-1-11111111111-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ911111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111111111111-111-1-1-1-11-11-1-1-1-111-1-1-1-111-1-111-1-11-11-1
χ1011111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-111-1-111-1-1-1-111111-111-1-1-1-1-11-11-111-1-111-1-1-1-11111-1-1-11-11
χ1111111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111-1-1-1-11-1-111-1111-1-111-1-111-1-1111-1-11
χ1211111-1-11111-1-1-1111111111-1111-1-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-1-111-111-1-1-1111111-1-1-1-111-111-1
χ1311111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-111-1-1-111-11-1111-1-111-1-11111-1-1-111-1
χ1411111-1-1111-11-1-111111111-111-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-11-1-111-1-11-1-1111-1-1-1111111-1-111-1-11-1-11
χ1511111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-1111111111111-11-1-111-1-1-11-11-1-1-111-1-1-1-111-1-1-1-111-11-11
χ1611111-1-1111-11-1-111111111-111-1-111111-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-11-11-1-111-1-111-1-1-1-111-1-1111-11-1
χ17222222222222222-12-12-1-1222-12222-1-1-122-1-100000000220000-1-1-1-1-1-1-1-10022002000000-1-1-1-1000000-1-1
χ18222222222222222-12-12-1-1222-12222-1-1-122-1-100000000-2-20000-1-1-1-1-1-1-1-100-2-200-2000000111100000011
χ1922222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-1222222220000-1-1-1-122-1-1-1-1-1-100002000000-1-10000-1-1-1-10000
χ2022222222222222-12-12-122-122-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-20000111122-1-1-1-1-1-10000-200000011000011110000
χ212222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-100000000220000111111-1-100-2-2002000000-1-1-1-100000011
χ222222222222-2-2222-12-12-1-12-2-2-1-2-2-2-2-1-1-122-1-100000000-2-20000111111-1-1002200-20000001111000000-1-1
χ232222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-1222222-2-200001111-2-21111-1-10000-2000000110000-1-1-1-10000
χ242222222222-2-222-12-12-122-1-2-2-11111-1-1-1-1-122-2-2-2-2220000-1-1-1-1-2-21111-1-100002000000-1-1000011110000
χ2522222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-21100000000220000-11-1-11111002-200-2000000-1-111000000-11
χ2622222-2-22222-2-2-22-12-12-1-122-2-122-2-2-1-1-1-2-21100000000-2-20000-11-1-1111100-2200200000011-1-10000001-1
χ2722222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-222-2-2220000-1-1-1-12-2-1-111110000-2000000110000-1-1110000
χ2822222-2-22222-2-2-2-12-12-122-12-2-1-1-111-1-1-111-2-2-2-222-2-2000011112-2-1-1111100002000000-1-1000011-1-10000
χ2922222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-211000000002200001-111-1-11100-2200-2000000-1-1110000001-1
χ3022222-2-2222-22-2-22-12-12-1-12-22-1-2-222-1-1-1-2-21100000000-2-200001-111-1-111002-200200000011-1-1000000-11
χ3122222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-222-2-2-2-200001111-2211-1-11100002000000-1-10000-1-1110000
χ3222222-2-2222-22-2-2-12-12-122-1-22-111-1-1-1-1-111-2-2-2-222220000-1-1-1-1-2211-1-1110000-200000011000011-1-10000
χ3322-2-222-22-2-2002-22222-2-2-2-20020000-2-222-22-22i−2i2i−2i00000000000000002-2000000000000000002i−2i2i−2i0000
χ3422-2-222-22-2-2002-22222-2-2-2-20020000-2-222-22-2−2i2i−2i2i00000000000000002-200000000000000000−2i2i−2i2i0000
χ3522-2-222-22-2-2002-2-12-121-2-2100-1−i3i3−i3i311-1-112-22i−2i2i−2i00000033−3−300−i3i3−i3i3-11000000000003−30000−ii−ii0000
χ3622-2-222-22-2-2002-2-12-121-2-2100-1−i3i3−i3i311-1-112-2−2i2i−2i2i000000−3−33300−i3i3−i3i3-1100000000000−330000i−ii−i0000
χ3722-2-222-22-2-2002-2-12-121-2-2100-1i3−i3i3−i311-1-112-22i−2i2i−2i000000−3−33300i3−i3i3−i3-1100000000000−330000−ii−ii0000
χ3822-2-222-22-2-2002-2-12-121-2-2100-1i3−i3i3−i311-1-112-2−2i2i−2i2i00000033−3−300i3−i3i3−i3-11000000000003−30000i−ii−i0000
χ3922-2-22-222-2-200-222222-2-2-2-20020000-2-22-22-222i−2i−2i2i0000000000000000-22000000000000000002i−2i−2i2i0000
χ4022-2-22-222-2-200-222222-2-2-2-20020000-2-22-22-22−2i2i2i−2i0000000000000000-2200000000000000000−2i2i2i−2i0000
χ4122-2-22-222-2-200-22-12-121-2-2100-1−i3i3i3−i311-11-1-222i−2i−2i2i00000033−3−300−i3i3i3−i31-100000000000−330000−iii−i0000
χ4222-2-22-222-2-200-22-12-121-2-2100-1−i3i3i3−i311-11-1-22−2i2i2i−2i000000−3−33300−i3i3i3−i31-1000000000003−30000i−i−ii0000
χ4322-2-22-222-2-200-22-12-121-2-2100-1i3−i3−i3i311-11-1-222i−2i−2i2i000000−3−33300i3−i3−i3i31-1000000000003−30000−iii−i0000
χ4422-2-22-222-2-200-22-12-121-2-2100-1i3−i3−i3i311-11-1-22−2i2i2i−2i00000033−3−300i3−i3−i3i31-100000000000−330000i−i−ii0000
χ452-2-22200-22-2000022-2-2-22-2200200002-2-2000000002-22-22-22-22-20000000000000002-200002-20000000000
χ462-2-22200-22-2000022-2-2-22-2200200002-2-2000000002-2-22-222-22-2000000000000000-220000-220000000000
χ472-2-22200-22-2000022-2-2-22-2200200002-2-200000000-222-2-22-22-220000000000000002-20000-220000000000
χ482-2-22200-22-2000022-2-2-22-2200200002-2-200000000-22-222-2-22-22000000000000000-2200002-20000000000
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
χ5344-4-444-44-4-4004-44-24-2-422-400-2000022-24-4-2200000000000000000000-220000000000000000000000000
χ5444-4-444-44-4-4004-4-2-2-2-22222001−2i32i3−2i32i3-1-11-22-220000000000000000i3−i3i3−i31-10000000000000000000000000
χ5544-4-444-44-4-4004-4-2-2-2-222220012i3−2i32i3−2i3-1-11-22-220000000000000000−i3i3−i3i31-10000000000000000000000000
χ5644-4-44-444-4-400-444-24-2-422-400-2000022-2-442-2000000000000000000002-20000000000000000000000000
χ5744-4-44-444-4-400-44-2-2-2-22222001−2i32i32i3−2i3-1-112-22-20000000000000000i3−i3−i3i3-110000000000000000000000000
χ5844-4-44-444-4-400-44-2-2-2-222220012i3−2i3−2i32i3-1-112-22-20000000000000000−i3i3i3−i3-110000000000000000000000000
χ594-44-4400-4-44000044-4-44-44-40040000-44-4000000000000000000000000000000000000000000000000000
χ604-44-4400-4-4400004-2-4242-2-400-200002-2200000000000000000000000000000000000000000−2i32i300000000
χ614-44-4400-4-4400004-2-4242-2-400-200002-22000000000000000000000000000000000000000002i3−2i300000000
χ624-44-4400-4-440000-242-4-2-44200-200002-220000000000000023−23−2323000000000000000000000000000000000
χ634-44-4400-4-440000-242-4-2-44200-200002-2200000000000000−232323−23000000000000000000000000000000000
χ644-4-44400-44-400004-2-42-4-22400-20000-2220000000000004-40000000000000000000000000-220000000000
χ654-4-44400-44-400004-2-42-4-22400-20000-222000000000000-4400000000000000000000000002-20000000000
χ664-4-44400-44-40000-242-424-4-200-20000-222000000004-40000-22-22000000000000000000000000000000000
χ674-4-44400-44-40000-242-424-4-200-20000-22200000000-4400002-22-2000000000000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-300000000000000000022000000000000002200020-1-1-1-10000000000-1-100
χ696666-366-3-3-366-3-300000000-3-3000000000000000000-2-200000000000000-2-2000-20111100000000001100
χ706666-366-3-3-3-6-6-3-300000000330000000000000000002200000000000000-2-200020-1-1-1-100000000001100
χ716666-366-3-3-3-6-6-3-30000000033000000000000000000-2-20000000000000022000-2011110000000000-1-100
χ726666-3-6-6-3-3-36-63300000000-3300000000000000000022000000000000002-2000-20-1-1110000000000-1100
χ736666-3-6-6-3-3-36-63300000000-33000000000000000000-2-200000000000000-220002011-1-100000000001-100
χ746666-3-6-6-3-3-3-6633000000003-30000000000000000002200000000000000-22000-20-1-11100000000001-100
χ756666-3-6-6-3-3-3-6633000000003-3000000000000000000-2-2000000000000002-20002011-1-10000000000-1100
χ768-88-8800-8-880000-4-444-44-440020000-22-2000000000000000000000000000000000000000000000000000
χ778-8-88800-88-80000-4-4444-44-400200002-2-2000000000000000000000000000000000000000000000000000
χ781212-12-12-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000
χ791212-12-12-6-1212-666006-6000000000000000000000000000000000000000000000000000000000000000000000
χ8012-1212-12-60066-6000000000000000000000000000000000000000000000000000000000−2i32i300000000000000
χ8112-1212-12-60066-60000000000000000000000000000000000000000000000000000000002i3−2i300000000000000
χ8212-12-1212-6006-66000000000000000000000000000000004-4000000000000000000000-220000000000000000
χ8312-12-1212-6006-6600000000000000000000000000000000-440000000000000000000002-20000000000000000

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