Finite Group Databasebeta

← Group #256259

Character table — Group #256259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442224444444444488888888222444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-11-11-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-1-1-11111
χ511111111111111111111111-1-11-1-11111-1-1-1-1111111111-1-1-11-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1-1-1
χ711111111111111111111111-1-11-1-1-1-1-1-1111111111111-111-1-1-11111-1-1-1-1-1-1-1-1
χ811111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111
χ911111111111111111-1-1-1-11-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111-111-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11-111-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111-1-1-111-1-111-1-111
χ1111111111111111111-1-1-1-11-111-1-1-1-1-11111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-111
χ1211111111111111111-1-1-1-11-111-1-1-1-1-1111111-1-1-1-111111-1-11-1-111-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ1411111111111111111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111
χ1511111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-111-1-111
χ1611111111111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-111-1-1
χ172222222222-2-222-2-2-22222-2-200-2002222000000000000-2000-20000000000000
χ182222222222-2-222-2-2-22222-2-200-200-2-2-2-2000000000000200020000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-220020022-2-20000000000002000-20000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2200200-2-222000000000000-200020000000000000
χ2122222222-2-222-2-222-222-2-2-2-2222-2-20000000000000000000-202000000000000
χ2222222222-2-222-2-222-222-2-2-2-2-2-2222000000000000000000020-2000000000000
χ2322222222-2-222-2-222-2-2-222-2222-2220000000000000000000-20-2000000000000
χ2422222222-2-222-2-222-2-2-222-22-2-2-2-2-20000000000000000000202000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-22200-200000022-2-20000000002-2000000000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-22200-2000000-2-222000000000-22000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-200200000022-2-2000000000-22000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-2002000000-2-2220000000002-2000000000000000
χ2922-22-22-2-22-2002-20002i−2i2i−2i00000002-22i−2i0000i2i2−i2−i222−2−200000000000000i2−i22−2
χ3022-22-22-2-22-2002-20002i−2i2i−2i00000002-22i−2i0000−i2−i2i2i2−2−22200000000000000−i2i2−22
χ3122-22-22-2-22-2002-20002i−2i2i−2i0000000-22−2i2i0000i2i2−i2−i222−2−200000000000000−i2i2−22
χ3222-22-22-2-22-2002-20002i−2i2i−2i0000000-22−2i2i0000−i2−i2i2i2−2−22200000000000000i2−i22−2
χ3322-22-22-2-22-2002-2000−2i2i−2i2i00000002-2−2i2i0000i2i2−i2−i2−2−22200000000000000i2−i2−22
χ3422-22-22-2-22-2002-2000−2i2i−2i2i00000002-2−2i2i0000−i2−i2i2i222−2−200000000000000−i2i22−2
χ3522-22-22-2-22-2002-2000−2i2i−2i2i0000000-222i−2i0000i2i2−i2−i2−2−22200000000000000−i2i22−2
χ3622-22-22-2-22-2002-2000−2i2i−2i2i0000000-222i−2i0000−i2−i2i2i222−2−200000000000000i2−i2−22
χ372-222-2-2-222-22-2-222-220000-200000000002-22-200002i−2i2i−2i0000002i−2i0000000000
χ382-222-2-2-222-22-2-222-220000-200000000002-22-20000−2i2i−2i2i000000−2i2i0000000000
χ392-222-2-2-222-22-2-222-220000-20000000000-22-2200002i−2i2i−2i000000−2i2i0000000000
χ402-222-2-2-222-22-2-222-220000-20000000000-22-220000−2i2i−2i2i0000002i−2i0000000000
χ412-222-2-2-22-22-222-2-2220000-200000000002-2-222i−2i2i−2i0000000000002i−2i00000000
χ422-222-2-2-22-22-222-2-2220000-200000000002-2-22−2i2i−2i2i000000000000−2i2i00000000
χ432-222-2-2-22-22-222-2-2220000-20000000000-222-22i−2i2i−2i000000000000−2i2i00000000
χ442-222-2-2-22-22-222-2-2220000-20000000000-222-2−2i2i−2i2i0000000000002i−2i00000000
χ4544-44-44-4-4-4400-440004i−4i−4i4i00000000000000000000000000000000000000000
χ4644-44-44-4-4-4400-44000−4i4i4i−4i00000000000000000000000000000000000000000
χ4744-4-4-4-444004400-4-4000000000000000000000000000000000000002i2−2i2000000
χ4844-4-4-4-444004400-4-400000000000000000000000000000000000000−2i22i2000000
χ4944-4-4-4-44400-4-40044000000000000000000000000000000000000000022−220000
χ5044-4-4-4-44400-4-400440000000000000000000000000000000000000000−22220000
χ514-444-4-4-444-4-44-44-44-4000040000000000000000000000000000000000000000
χ524-444-4-4-44-444-44-44-4-4000040000000000000000000000000000000000000000
χ534-4-444-44-44400-4-4000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ544-4-444-44-44400-4-400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ554-4-444-44-4-4-40044000000000000000000000022−22−22220000000000000000000000
χ564-4-444-44-4-4-400440000000000000000000000−222222−220000000000000000000000
χ574-4-4-444-44004-400-4400000000004-40000000000000000000000000000000000
χ584-4-4-444-44004-400-440000000000-440000000000000000000000000000000000
χ594-4-4-444-4400-44004-400000004-40000000000000000000000000000000000000
χ604-4-4-444-4400-44004-40000000-440000000000000000000000000000000000000
χ61888-88-8-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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