Finite Group Databasebeta

← Group #120076

Character table — Group #120076

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222222224444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111
χ911111111-1-1-1-111-1-1111-1-1-11-1iiii−i−i−i−i111-1-1-11-1i−iii−i−ii−iii−i−i11-1-1
χ1011111111-1-1-1-111-1-1111-1-1-11-1iiii−i−i−i−i11-11-1-1-11−iiii−i−i−ii−i−iii-1-111
χ1111111111-1-1-1-111-1-1111-1-1-11-1iiii−i−i−i−i-1-11-1111-1−ii−i−iii−iiii−i−i-1-111
χ1211111111-1-1-1-111-1-1111-1-1-11-1iiii−i−i−i−i-1-1-1111-11i−i−i−iiii−i−i−iii11-1-1
χ1311111111-1-1-1-111-1-1111-1-1-11-1−i−i−i−iiiii111-1-1-11-1−ii−i−iii−ii−i−iii11-1-1
χ1411111111-1-1-1-111-1-1111-1-1-11-1−i−i−i−iiiii11-11-1-1-11i−i−i−iiii−iii−i−i-1-111
χ1511111111-1-1-1-111-1-1111-1-1-11-1−i−i−i−iiiii-1-11-1111-1i−iii−i−ii−i−i−iii-1-111
χ1611111111-1-1-1-111-1-1111-1-1-11-1−i−i−i−iiiii-1-1-1111-11−iiii−i−i−iiii−i−i11-1-1
χ172222222222222222-2-2-2-2-2-2-2-20000000000000000002-22-20000000000
χ182222222222222222-2-2-2-2-2-2-2-2000000000000000000-22-220000000000
χ19222222222222-2-2-2-222-22-2-2-220000000000000000220000-2-200000000
χ20222222222222-2-2-2-222-22-2-2-220000000000000000-2-200002200000000
χ21222222222222-2-2-2-2-2-22-2222-200000000002200-2-20000000000000000
χ22222222222222-2-2-2-2-2-22-2222-20000000000-2-200220000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2222-220000000000000000002i−2i−2i2i0000000000
χ2422222222-2-2-2-222-2-2-2-2-2222-22000000000000000000−2i2i2i−2i0000000000
χ2522222222-2-2-2-2-2-22222-2-222-2-200000000000000002i−2i0000−2i2i00000000
χ2622222222-2-2-2-2-2-22222-2-222-2-20000000000000000−2i2i00002i−2i00000000
χ2722222222-2-2-2-2-2-222-2-222-2-22200000000002-200-220000000000000000
χ2822222222-2-2-2-2-2-222-2-222-2-2220000000000-22002-20000000000000000
χ29222-22-2-2-222-2-22-22-22-22-22-2-220000000000000000000000002-22-20000
χ30222-22-2-2-222-2-22-22-22-22-22-2-22000000000000000000000000-22-220000
χ31222-22-2-2-222-2-22-22-2-22-22-222-200000000000000000000000000002-22-2
χ32222-22-2-2-222-2-22-22-2-22-22-222-20000000000000000000000000000-22-22
χ33222-22-2-2-222-2-2-22-222-2-2-2-2222000000002i−2i002i−2i000000000000000000
χ34222-22-2-2-222-2-2-22-222-2-2-2-222200000000−2i2i00−2i2i000000000000000000
χ35222-22-2-2-222-2-2-22-22-22222-2-2-222-2-222-2-2000000000000000000000000
χ36222-22-2-2-222-2-2-22-22-22222-2-2-2-2-222-2-222000000000000000000000000
χ37222-22-2-2-2-2-2222-2-222-222-22-2-20000000000000000000000002i−2i−2i2i0000
χ38222-22-2-2-2-2-2222-2-222-222-22-2-2000000000000000000000000−2i2i2i−2i0000
χ39222-22-2-2-2-2-2222-2-22-22-2-22-22200000000000000000000000000002-2-22
χ40222-22-2-2-2-2-2222-2-22-22-2-22-2220000000000000000000000000000-222-2
χ41222-22-2-2-2-2-222-222-22-2-222-22-2000000002i−2i00−2i2i000000000000000000
χ42222-22-2-2-2-2-222-222-22-2-222-22-200000000−2i2i002i−2i000000000000000000
χ43222-22-2-2-2-2-222-222-2-222-2-22-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ44222-22-2-2-2-2-222-222-2-222-2-22-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ4544-44-44-4-44-44-40000000000002-22-22-22-2000000000000000000000000
χ4644-44-44-4-44-44-4000000000000-22-22-22-22000000000000000000000000
χ4744-44-44-4-4-44-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4844-44-44-4-4-44-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ4944-4-4-4-4444-4-440000000000002-2-222-2-22000000000000000000000000
χ5044-4-4-4-4444-4-44000000000000-222-2-222-2000000000000000000000000
χ5144-4-4-4-444-444-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ5244-4-4-4-444-444-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ538-888-8-88-8000000000000000000000000000000000000000000000000
χ548-88-8-88-88000000000000000000000000000000000000000000000000
χ558-8-888-8-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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