Finite Group Databasebeta

← Group #72319609

Character table — Group #72319609

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size1122244444444888888888888888888888888888161616163232323232326464646464646464
order1222222444444222222444444444444444444444224444888844448888
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ7111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-11-11-11-1
χ101111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-11-11-11-11
χ111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111i−i−iii−i−ii
χ121111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−iii−i−iii−i
χ131111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-11-1-11-11
χ141111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-11-111-11-1
χ151111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ161111111111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ172222222222222-2-20000-2-20000222-2-2-2-20000000022-2-22-2000000000000
χ182222222222222-2-20000-2-20000222-2-2-2-200000000-2-222-22000000000000
χ192222222222-2-22-2-20000-2-20000-2-2-222220000000022-2-2-22000000000000
χ202222222222-2-22-2-20000-2-20000-2-2-2222200000000-2-2222-2000000000000
χ2122222-2-22-2-20022222-2-2-2-222-2-20000000000000002-22-2002-20000000000
χ2222222-2-22-2-20022222-2-2-2-222-2-2000000000000000-22-2200-220000000000
χ2322222-2-22-2-200222-2-222-2-2-2-2220000000000000002-22-200-220000000000
χ2422222-2-22-2-200222-2-222-2-2-2-222000000000000000-22-22002-20000000000
χ2522222-2-22-2-2002-2-2000022000000000002222-2-2-2-22-2-2200002-200000000
χ2622222-2-22-2-2002-2-2000022000000000002222-2-2-2-2-222-20000-2200000000
χ2722222-2-22-2-2002-2-200002200000000000-2-2-2-222222-2-220000-2200000000
χ2822222-2-22-2-2002-2-200002200000000000-2-2-2-22222-222-200002-200000000
χ294444444-4-4-400-400000000000000044-4-400000000000000000000000000
χ304444444-4-4-400-4000000000000000-4-44400000000000000000000000000
χ3144444-4-4-44444-40000000000004-4-4000000000000000000000000000000
χ3244444-4-4-444-4-4-4000000000000-444000000000000000000000000000000
χ33444-4-44-4000000002-22-2002-22-2000004i−4i2i2i−2i−2i2i2i−2i−2i000000000000000000
χ34444-4-44-4000000002-22-2002-22-200000−4i4i−2i−2i2i2i−2i−2i2i2i000000000000000000
χ35444-4-44-400000000-22-2200-22-22000004i−4i−2i−2i2i2i−2i−2i2i2i000000000000000000
χ36444-4-44-400000000-22-2200-22-2200000−4i4i2i2i−2i−2i2i2i−2i−2i000000000000000000
χ37444-4-4-44000000002-2-22002-2-220004i−4i002i2i−2i−2i−2i−2i2i2i000000000000000000
χ38444-4-4-44000000002-2-22002-2-22000−4i4i00−2i−2i2i2i2i2i−2i−2i000000000000000000
χ39444-4-4-4400000000-222-200-222-20004i−4i00−2i−2i2i2i2i2i−2i−2i000000000000000000
χ40444-4-4-4400000000-222-200-222-2000−4i4i002i2i−2i−2i−2i−2i2i2i000000000000000000
χ4144-44-40040000-40000004-40000000000000004i−4i4i−4i000000000000000000
χ4244-44-40040000-40000004-4000000000000000−4i4i−4i4i000000000000000000
χ4344-44-40040000-4000000-44000000000004i−4i4i−4i0000000000000000000000
χ4444-44-40040000-4000000-4400000000000−4i4i−4i4i0000000000000000000000
χ4544-44-400-4000044-4004-40000-44000000000000000000000000000000000
χ4644-44-400-4000044-400-4400004-4000000000000000000000000000000000
χ4744-44-400-400004-444-40000-4400000000000000000000000000000000000
χ4844-44-400-400004-44-4400004-400000000000000000000000000000000000
χ4944-4-440004-400000222200-2-2-2-204-400002-2-222-2-22000000000000000000
χ5044-4-440004-400000222200-2-2-2-20-440000-222-2-222-2000000000000000000
χ5144-4-440004-400000-2-2-2-200222204-40000-222-2-222-2000000000000000000
χ5244-4-440004-400000-2-2-2-20022220-4400002-2-222-2-22000000000000000000
χ5344-4-44000-444400022-2-200-2-222-40000002-2-22-222-2000000000000000000
χ5444-4-44000-4444000-2-2220022-2-2-4000000-222-22-2-22000000000000000000
χ5544-4-44000-44-4-400022-2-200-2-2224000000-222-22-2-22000000000000000000
χ5644-4-44000-44-4-4000-2-2220022-2-240000002-2-22-222-2000000000000000000
χ5716-16000000008i−8i0000000000000000000000000000000000000000000000
χ5816-1600000000−8i8i0000000000000000000000000000000000000000000000

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