Finite Group Databasebeta

← Group #456708

Character table — Group #456708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12222222222244444444224444444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-111
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1111-1-1-11-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-11-1-1-111-1-1-1-111-1-1
χ51111111111111111111111-1-111-1-1-1-1-1-1111111111111-11-1-1-1-1-11-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1111-1-1-111-1-111-1-111
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1111111-1-1
χ911111111111111111111-1-111-1-111-1-1-1-11111111111111-1-1-11-1-1-1-1-11111-1-1-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-111111-1-111-1-1
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1111111
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-111-111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1111-1-1-1-1-111-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-11111111-1-111
χ1722222222-2-2-2-222-22-2-2-22002200-2-200000000000022-2-22000-20000000000000
χ1822222222-2-2-2-222-22-2-2-22002200-2-2000000000000-2-222-200020000000000000
χ1922222222-2-2-2-222-22-2-2-2200-2-2002200000000000022-2-2-200020000000000000
χ2022222222-2-2-2-222-22-2-2-2200-2-20022000000000000-2-2222000-20000000000000
χ2122222222-2-2-2-2-2-22-2222-22200-2-2000000000022-2-200000200000-20000000000
χ2222222222-2-2-2-2-2-22-2222-22200-2-20000000000-2-22200000-20000020000000000
χ2322222222-2-2-2-2-2-22-2222-2-2-20022000000000022-2-200000-20000020000000000
χ2422222222-2-2-2-2-2-22-2222-2-2-200220000000000-2-22200000200000-20000000000
χ25222-2-22-2-22-2-222-2-2-222-22000000002i2i−2i−2i22-2-200000000000002i−2i00000000000
χ26222-2-22-2-22-2-222-2-2-222-22000000002i2i−2i−2i-2-2220000000000000−2i2i00000000000
χ27222-2-22-2-22-2-222-2-2-222-2200000000−2i−2i2i2i22-2-20000000000000−2i2i00000000000
χ28222-2-22-2-22-2-222-2-2-222-2200000000−2i−2i2i2i-2-22200000000000002i−2i00000000000
χ292-2-22-222-222-2-222-2-22-22-22-22i−2i2-22i−2i2i−2i2i−2i000000000000000000000000000000
χ302-2-22-222-222-2-222-2-22-22-22-2−2i2i2-2−2i2i−2i2i−2i2i000000000000000000000000000000
χ312-2-22-222-222-2-222-2-22-22-2-222i−2i-222i−2i−2i2i−2i2i000000000000000000000000000000
χ322-2-22-222-222-2-222-2-22-22-2-22−2i2i-22−2i2i2i−2i2i−2i000000000000000000000000000000
χ332-2-22-222-2-2-222222-2-22-2-2002i−2i00−2i2i0000000000000000000000002-200002i−2i00
χ342-2-22-222-2-2-222222-2-22-2-2002i−2i00−2i2i000000000000000000000000-220000−2i2i00
χ352-2-22-222-2-2-222222-2-22-2-200−2i2i002i−2i0000000000000000000000002-20000−2i2i00
χ362-2-22-222-2-2-222222-2-22-2-200−2i2i002i−2i000000000000000000000000-2200002i−2i00
χ372-2-22-222-2-2-222-2-2-222-2222-200-22000000000000000000002-2000000002-20000
χ382-2-22-222-2-2-222-2-2-222-2222-200-2200000000000000000000-2200000000-220000
χ392-2-22-222-2-2-222-2-2-222-222-22002-2000000000000000000002-200000000-220000
χ402-2-22-222-2-2-222-2-2-222-222-22002-200000000000000000000-22000000002-20000
χ412-2-2-222-222-22-22-2222-2-2-2000000002-2-2200000000000000000000002i−2i00002i−2i
χ422-2-2-222-222-22-22-2222-2-2-2000000002-2-220000000000000000000000−2i2i0000−2i2i
χ432-2-2-222-222-22-22-2222-2-2-200000000-222-200000000000000000000002i−2i0000−2i2i
χ442-2-2-222-222-22-22-2222-2-2-200000000-222-20000000000000000000000−2i2i00002i−2i
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000
χ46444-4-44-4-44-4-44-4444-4-44-4000000000000000000000000000000000000000000
χ47444-4-44-4-4-444-44-44-4-4-444000000000000000000000000000000000000000000
χ48444-4-44-4-4-444-4-44-4444-4-4000000000000000000000000000000000000000000
χ4944-44-4-4-440000000000000000000000002i−2i2i−2i0022−222i2−2i200000000000000000000
χ5044-44-4-4-440000000000000000000000002i−2i2i−2i00−2222−2i22i200000000000000000000
χ5144-44-4-4-44000000000000000000000000−2i2i−2i2i0022−22−2i22i200000000000000000000
χ5244-44-4-4-44000000000000000000000000−2i2i−2i2i00−22222i2−2i200000000000000000000
χ5344-4-44-44-40000000000000000000000002i−2i−2i2i22−2200002i2−2i2000000000000000000
χ5444-4-44-44-40000000000000000000000002i−2i−2i2i−22220000−2i22i2000000000000000000
χ5544-4-44-44-4000000000000000000000000−2i2i2i−2i22−220000−2i22i2000000000000000000
χ5644-4-44-44-4000000000000000000000000−2i2i2i−2i−222200002i2−2i2000000000000000000
χ574-4-44-444-444-4-4-4-444-44-44000000000000000000000000000000000000000000
χ584-4-4-444-444-44-4-44-4-4-4444000000000000000000000000000000000000000000
χ594-4-4-444-44-44-444-4-44-444-4000000000000000000000000000000000000000000
χ604-4-4-444-44-44-44-444-44-4-44000000000000000000000000000000000000000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-8-888000000000000000000000000000000000000000000000000000000

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