Finite Group Databasebeta

← Group #100593

Character table — Group #100593

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111111112222444444444488888888888888888888816161616161616161616161616163232
order12222222444444444444444444488888888888888884488888888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ911111111-1-1-1-111-11-1-1-1-11-1111-1-1ii−i−iii−i−iiiii−i−i−i−i1-1i−ii−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-11-1-1-1-11-1111-1-1ii−i−iii−i−i−i−i−i−iiiii1-1i−ii−i−i−iii-1-111-11
χ1111111111-1-1-1-111-11-1-1-1-11-1111-1-1−i−iii−i−iiiiiii−i−i−i−i1-1−ii−iiii−i−i-1-111-11
χ1211111111-1-1-1-111-11-1-1-1-11-1111-1-1−i−iii−i−iii−i−i−i−iiiii1-1−ii−ii−i−iii11-1-11-1
χ1311111111-1-1-1-111-11-1-1-1-11-11-1-111ii−i−i−i−iiiiiii−i−i−i−i-11i−i−ii−i−iii11-1-1-11
χ1411111111-1-1-1-111-11-1-1-1-11-11-1-111ii−i−i−i−iii−i−i−i−iiiii-11i−i−iiii−i−i-1-1111-1
χ1511111111-1-1-1-111-11-1-1-1-11-11-1-111−i−iiiii−i−iiiii−i−i−i−i-11−iii−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-11-1-1-1-11-11-1-111−i−iiiii−i−i−i−i−i−iiiii-11−iii−iii−i−i11-1-1-11
χ17222222222222222-2-2-2-22-2-2-20000222200000000000000-2-2000000000000
χ18222222222222222-2-2-2-22-2-2-20000-2-2-2-20000000000000022000000000000
χ19222222222222-2-2-2222-2-22-2-222220000000000000000-2-200000000000000
χ20222222222222-2-2-2222-2-22-2-2-2-2-2-200000000000000002200000000000000
χ21222222222222-2-2-2-2-2-22-2-222000000002222000000000000-2-20000000000
χ22222222222222-2-2-2-2-2-22-2-22200000000-2-2-2-2000000000000220000000000
χ2322222222-2-2-2-222-2-2222-2-22-200002i2i−2i−2i00000000000000−2i2i000000000000
χ2422222222-2-2-2-222-2-2222-2-22-20000−2i−2i2i2i000000000000002i−2i000000000000
χ2522222222-2-2-2-2-2-222-2-22222-222-2-20000000000000000-2200000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-22200000000000000002-200000000000000
χ2722222222-2-2-2-2-2-22-222-22-2-22000000002i2i−2i−2i000000000000−2i2i0000000000
χ2822222222-2-2-2-2-2-22-222-22-2-2200000000−2i−2i2i2i0000000000002i−2i0000000000
χ292222-2-2-2-22-22-22-220000-200000002-22-2000022−2−222−2−200000000002−22−200
χ302222-2-2-2-22-22-22-220000-200000002-22-20000−2−222−2−2220000000000−22−2200
χ312222-2-2-2-22-22-22-220000-20000000-22-22000022−2−222−2−20000000000−22−2200
χ322222-2-2-2-22-22-22-220000-20000000-22-220000−2−222−2−22200000000002−22−200
χ332222-2-2-2-2-22-222-2-20000200000002i−2i−2i2i0000i2i2−i2−i2−i2−i2i2i200000000002−2−2200
χ342222-2-2-2-2-22-222-2-20000200000002i−2i−2i2i0000−i2−i2i2i2i2i2−i2−i20000000000−222−200
χ352222-2-2-2-2-22-222-2-2000020000000−2i2i2i−2i0000i2i2−i2−i2−i2−i2i2i20000000000−222−200
χ362222-2-2-2-2-22-222-2-2000020000000−2i2i2i−2i0000−i2−i2i2i2i2i2−i2−i200000000002−2−2200
χ3722-2-222-2-222-2-200022-200-2002-22-2000000002−22−22−22−20000002−22−2000000
χ3822-2-222-2-222-2-200022-200-2002-22-200000000−22−22−22−22000000−22−22000000
χ3922-2-222-2-222-2-200022-200-200-22-22000000002−22−22−22−2000000−22−22000000
χ4022-2-222-2-222-2-200022-200-200-22-2200000000−22−22−22−220000002−22−2000000
χ4122-2-222-2-2-2-2220002-2200-2002-2-2200000000i2−i2i2−i2−i2i2−i2i2000000i2−i2−i2i2000000
χ4222-2-222-2-2-2-2220002-2200-2002-2-2200000000−i2i2−i2i2i2−i2i2−i2000000−i2i2i2−i2000000
χ4322-2-222-2-2-2-2220002-2200-200-222-200000000i2−i2i2−i2−i2i2−i2i2000000−i2i2i2−i2000000
χ4422-2-222-2-2-2-2220002-2200-200-222-200000000−i2i2−i2i2i2−i2i2−i2000000i2−i2−i2i2000000
χ454444-4-4-4-44-44-4-44-400004000000000000000000000000000000000000000
χ464444-4-4-4-4-44-44-4440000-4000000000000000000000000000000000000000
χ4744-4-444-4-444-4-4000-4-4400400000000000000000000000000000000000000
χ4844-4-444-4-4-4-444000-44-400400000000000000000000000000000000000000
χ4944-4-4-4-4444-4-44000000000000000000000002-2-222-2-220000000000000000
χ5044-4-4-4-4444-4-4400000000000000000000000-222-2-222-20000000000000000
χ5144-4-4-4-444-444-4000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5244-4-4-4-444-444-400000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-44-44-4-440000000000400-40000000002i2−2i22i2−2i2000000000000000000000000
χ544-44-44-4-440000000000400-4000000000−2i22i2−2i22i2000000000000000000000000
χ554-44-44-4-440000000000-400400000000022−22−2222000000000000000000000000
χ564-44-44-4-440000000000-4004000000000−222222−22000000000000000000000000
χ578-88-8-888-8000000000000000000000000000000000000000000000000000
χ588-8-888-88-8000000000000000000000000000000000000000000000000000
χ598-8-88-88-88000000000000000000000000000000000000000000000000000

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