Finite Group Databasebeta

← Group #13149554

Character table — Group #13149554

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size1111222222444466666666881212121212121212121212121818181818181818181818181818242424242424242436363636363636363636363636363636363636363672727272
order12223446664412123366666612123666121212121212121222444444446666121212121212121224444446612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-11111-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111-1-11111111111-1-1111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-111111111-1-1-1-111-1-1-1-1
χ61111111111-1-11111111111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1111-1-1-1-1-1-111-1-1-1-1-1-11111
χ71111111111-1-11111111111-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11-111-1-11111-1-11111-1-1-1-111
χ81111111111-1-11111111111-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-111111111-1-1
χ911111-1-11111-1-1-1111111111-11111-1-111-1-1-1-1111111-1-11111111-1-1-111-1-1-11-1-1-11-1-1-1-1-111-1-111-1-1111-11-1
χ1011111-1-11111-1-1-1111111111-11111-1-111-1-1-1-111-1-111-1-1-1-111111-1-1-111-1-11-111-1-111111-1-1-1-111-1-1-1-1-11-11
χ1111111-1-11111-1-1-1111111111-11111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-1-111-1-111-1-11-1111-1-11111-1-111-1-11-1-11
χ1211111-1-11111-1-1-1111111111-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-1-1-1-11111-1-1-111-1-111-1-11111-111-1
χ1311111-1-1111-11-1-111111111-111111-1-1-1-111-1-11111-1-111111111-11-1-1-1-111-1-11-1-1-11-1-1-1-111-1-1-1-11111-11-11
χ1411111-1-1111-11-1-111111111-111111-1-1-1-111-1-111-1-1-1-111-1-11111-11-1-1-1-11111-11-11-11111-1-1-1-1-1-111-1-11-11-1
χ1511111-1-1111-11-1-111111111-111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1111-11-111-111-1-1111111-1-1-1-1-111-1
χ1611111-1-1111-11-1-111111111-111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-11-1-1-1-111-11-111-11-1-111-1-11111-1-1111-1-11
χ17222222222222222-12-12-1-1222-1-1-1-1-1-1-1-1-1-1222200222200-1-1-1-122-1-1-1-1-1-10000200000000-1-1-1-1-1-1000000
χ18222222222222222-12-12-1-1222-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-200111122-1-1-1-1-1-10000-200000000111111000000
χ1922222222222222-12-12-122-122-1-1-1-1222222-1-100000000220000-1-1-1-1-1-1-1-12000022-1-10000000000-1-100-1-1
χ2022222222222222-12-12-122-122-1-1-1-1222222-1-100000000-2-20000-1-1-1-1-1-1-1-1-20000-2-2110000000000110011
χ212222222222-2-2222-12-12-1-12-2-2-1-1-1-1-1-11111222200-2-2-2-200-1-1-1-1-2-2-1-111110000200000000-1-11111000000
χ222222222222-2-2222-12-12-1-12-2-2-1-1-1-1-1-1111122-2-2002222001111-2-2-1-111110000-20000000011-1-1-1-1000000
χ232222222222-2-222-12-12-122-1-2-2-1-1-1-122-2-2-2-2-1-10000000022000011-1-1111120000-2-2-1-10000000000-1-10011
χ242222222222-2-222-12-12-122-1-2-2-1-1-1-122-2-2-2-2-1-100000000-2-2000011-1-11111-20000221100000000001100-1-1
χ2522222-2-22222-2-2-22-12-12-1-122-2-1-1-1-111-1-111-2-2220022-2-200-1-1-1-12-211-1-1110000-20000000011-1-111000000
χ2622222-2-22222-2-2-22-12-12-1-122-2-1-1-1-111-1-111-2-2-2-200-2-2220011112-211-1-1110000200000000-1-111-1-1000000
χ2722222-2-22222-2-2-2-12-12-122-12-2-1-1-1-1-2-222-2-21100000000220000-1111-1-111-200002-2110000000000-1-100-11
χ2822222-2-22222-2-2-2-12-12-122-12-2-1-1-1-1-2-222-2-21100000000-2-20000-1111-1-11120000-22-1-1000000000011001-1
χ2922222-2-2222-22-2-22-12-12-1-12-22-1-1-1-11111-1-1-2-22200-2-22200-1-1-1-1-221111-1-10000-2000000001111-1-1000000
χ3022222-2-2222-22-2-22-12-12-1-12-22-1-1-1-11111-1-1-2-2-2-20022-2-2001111-221111-1-10000200000000-1-1-1-111000000
χ3122222-2-2222-22-2-2-12-12-122-1-22-1-1-1-1-2-2-2-22211000000002200001-11111-1-1-20000-22110000000000-1-1001-1
χ3222222-2-2222-22-2-2-12-12-122-1-22-1-1-1-1-2-2-2-2221100000000-2-200001-11111-1-1200002-2-1-100000000001100-11
χ332-22-2200-22-2000022-2-22-22-2002-2-22000000002-22i−2i00002i−2i22-2-200000000000000000002i−2i0000002i−2i0000
χ342-22-2200-22-2000022-2-22-22-2002-2-22000000002-2−2i2i0000−2i2i22-2-20000000000000000000−2i2i000000−2i2i0000
χ352-22-2200-22-2000022-2-22-22-2002-2-2200000000-222i−2i0000−2i2i-2-22200000000000000000002i−2i000000−2i2i0000
χ362-22-2200-22-2000022-2-22-22-2002-2-2200000000-22−2i2i00002i−2i-2-2220000000000000000000−2i2i0000002i−2i0000
χ372-2-2222-22-2-2002-222-2-2-22-22002-22-22-200002-200002i−2i2i−2i000000002-200000000000000000002i−2i2i−2i000000
χ382-2-2222-22-2-2002-222-2-2-22-22002-22-22-200002-20000−2i2i−2i2i000000002-20000000000000000000−2i2i−2i2i000000
χ392-2-2222-22-2-2002-22-1-21-2-11200-11-11-113−33−32-200002i−2i2i−2i00−i3i3−i3i300-113−33−30000000000000−i3i3−ii−ii000000
χ402-2-2222-22-2-2002-22-1-21-2-11200-11-11-113−33−32-20000−2i2i−2i2i00i3−i3i3−i300-113−33−30000000000000i3−i3i−ii−i000000
χ412-2-2222-22-2-2002-22-1-21-2-11200-11-11-11−33−332-200002i−2i2i−2i00i3−i3i3−i300-11−33−330000000000000i3−i3−ii−ii000000
χ422-2-2222-22-2-2002-22-1-21-2-11200-11-11-11−33−332-20000−2i2i−2i2i00−i3i3−i3i300-11−33−330000000000000−i3i3i−ii−i000000
χ432-2-222-222-2-200-2222-2-2-22-22002-22-2-220000-2200002i−2i−2i2i00000000-2200000000000000000002i−2i−2i2i000000
χ442-2-222-222-2-200-2222-2-2-22-22002-22-2-220000-220000−2i2i2i−2i00000000-220000000000000000000−2i2i2i−2i000000
χ452-2-222-222-2-200-222-1-21-2-11200-11-111-13−3−33-2200002i−2i−2i2i00−i3i3−i3i3001-13−3−330000000000000i3−i3−iii−i000000
χ462-2-222-222-2-200-222-1-21-2-11200-11-111-13−3−33-220000−2i2i2i−2i00i3−i3i3−i3001-13−3−330000000000000−i3i3i−i−ii000000
χ472-2-222-222-2-200-222-1-21-2-11200-11-111-1−333−3-2200002i−2i−2i2i00i3−i3i3−i3001-1−333−30000000000000−i3i3−iii−i000000
χ482-2-222-222-2-200-222-1-21-2-11200-11-111-1−333−3-220000−2i2i2i−2i00−i3i3−i3i3001-1−333−30000000000000i3−i3i−i−ii000000
χ4944444444444444-2-2-2-2-2-2-2-2441111-2-2-2-2-2-2-2-200000000000000-2-21111110000000000000000000000000
χ504444444444-4-444-2-2-2-2-2-2-2-2-4-41111-2-22222-2-2000000000000002211-1-1-1-10000000000000000000000000
χ5144444-4-44444-4-4-4-2-2-2-2-2-2-2-24-4111122-2-2222200000000000000-22-1-111-1-10000000000000000000000000
χ5244444-4-4444-44-4-4-2-2-2-2-2-2-2-2-4411112222-2-222000000000000002-2-1-1-1-1110000000000000000000000000
χ5344-4-4400-4-4400004444-4-4-4-40044-4-40000000000000000000000000000000000000000000000000000000
χ5444-4-4400-4-4400004-24-2-422-400-2-222000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ5544-4-4400-4-4400004-24-2-422-400-2-2220000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ5644-4-4400-4-440000-24-242-4-4200-2-2220000000000000000000000000000000000000−2i32i30000000000000000
χ5744-4-4400-4-440000-24-242-4-4200-2-22200000000000000000000000000000000000002i3−2i30000000000000000
χ584-44-4400-44-400004-2-4242-2-400-222-2000000004-400000000-2-222000000000000000000000000000000000
χ594-44-4400-44-400004-2-4242-2-400-222-200000000-440000000022-2-2000000000000000000000000000000000
χ604-44-4400-44-40000-242-4-2-44200-222-200000000000000004i−4i0000000000000000000000000000000−2i2i0000
χ614-44-4400-44-40000-242-4-2-44200-222-20000000000000000−4i4i00000000000000000000000000000002i−2i0000
χ624-4-4444-44-4-4004-4-242-424-4-200-22-224-40000-220000000000000000-2200000000000000000000000000000
χ634-4-4444-44-4-4004-4-2-2222-22-2001-11-1-2223−2323−23-2200000000000000001-1−33−330000000000000000000000000
χ644-4-4444-44-4-4004-4-2-2222-22-2001-11-1-22−2323−2323-2200000000000000001-13−33−30000000000000000000000000
χ654-4-444-444-4-400-44-242-424-4-200-22-22-4400002-200000000000000002-200000000000000000000000000000
χ664-4-444-444-4-400-44-2-2222-22-2001-11-12-223−23−23232-20000000000000000-11−333−30000000000000000000000000
χ674-4-444-444-4-400-44-2-2222-22-2001-11-12-2−232323−232-20000000000000000-113−3−330000000000000000000000000
χ686666-366-3-3-366-3-300000000-3-30000000000000022000000000000000000022200000-1-1-1-100000000-1-100
χ696666-366-3-3-366-3-300000000-3-300000000000000-2-20000000000000000000-2-2-2000001111000000001100
χ706666-366-3-3-3-6-6-3-3000000003300000000000000220000000000000000000-2-2200000-1-1-1-1000000001100
χ716666-366-3-3-3-6-6-3-3000000003300000000000000-2-2000000000000000000022-200000111100000000-1-100
χ726666-3-6-6-3-3-36-63300000000-33000000000000002200000000000000000002-2-20000011-1-100000000-1100
χ736666-3-6-6-3-3-36-63300000000-3300000000000000-2-20000000000000000000-22200000-1-111000000001-100
χ746666-3-6-6-3-3-3-6633000000003-300000000000000220000000000000000000-22-20000011-1-1000000001-100
χ756666-3-6-6-3-3-3-6633000000003-300000000000000-2-200000000000000000002-2200000-1-11100000000-1100
χ7688-8-8800-8-880000-4-4-4-444440022-2-20000000000000000000000000000000000000000000000000000000
χ778-88-8800-88-80000-4-444-44-44002-2-220000000000000000000000000000000000000000000000000000000
χ781212-12-12-60066-600000000000000000000000000000000000000000000000000000000023−2300000000000000
χ791212-12-12-60066-6000000000000000000000000000000000000000000000000000000000−232300000000000000
χ8012-1212-12-6006-6600000000000000000000000000004i−4i00000000000000000000000000000−2i2i000000000000
χ8112-1212-12-6006-660000000000000000000000000000−4i4i000000000000000000000000000002i−2i000000000000
χ8212-12-1212-612-12-66600-66000000000000000000000000000000000000000000000000000000000000000000000
χ8312-12-1212-6-1212-666006-6000000000000000000000000000000000000000000000000000000000000000000000

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