Finite Group Databasebeta

← Group #252224

Character table — Group #252224

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1111-1-1111111111-11-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-11111-1-11-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ711111111111111111111111-1-1-1-1-1-1111-1-11111111111-11-11-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1
χ911111111111111111-1-1-1-11-1111111-1-1-1-1-1111111-1-1-1-1-111-1-1-111-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11-1111111-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-111-1-111-1-111
χ1111111111111111111-1-1-1-11-111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1211111111111111111-1-1-1-11-111-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-11-1-1-1111111-111-1-11111-1-1-1-11-1-11-1-111-1-1-1-111-1-111
χ1411111111111111111-1-1-1-11-1-1-1111111-111-1-1-1-1-1-111111-1-11-1-1-1-11111-1-111-1-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111-1-11111-1-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-111-1-1-1-111
χ172222222222-2-222-2-2-22222-2-222000000-2220000000000-20-2000000000000000
χ182222222222-2-222-2-2-22222-2-2-2-2000000-2-2-20000000000202000000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-22220000002-2-2000000000020-2000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22-2-20000002220000000000-202000000000000000
χ2122222222-2-222-2-222-222-2-2-2-200000022200-2-200000000020-200000000000000
χ2222222222-2-222-2-222-222-2-2-2-2000000-2-220022000000000-20200000000000000
χ2322222222-2-222-2-222-2-2-222-2200000022-20022000000000-20-200000000000000
χ2422222222-2-222-2-222-2-2-222-22000000-2-2-200-2-200000000020200000000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2220022-2-200-200000000000000002-2000000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-22200-2-22200-20000000000000000-22000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-20022-2-20020000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-200-2-22200200000000000000002-2000000000000
χ2922-22-2-22-22-2002-20002i−2i2i−2i002-200000002i−2i00i2i2−i2−i222−2−20000000000i2−i22−20000
χ3022-22-2-22-22-2002-20002i−2i2i−2i002-200000002i−2i00−i2−i2i2i2−2−2220000000000−i2i2−220000
χ3122-22-2-22-22-2002-20002i−2i2i−2i00-220000000−2i2i00i2i2−i2−i222−2−20000000000−i2i2−220000
χ3222-22-2-22-22-2002-20002i−2i2i−2i00-220000000−2i2i00−i2−i2i2i2−2−2220000000000i2−i22−20000
χ3322-22-2-22-22-2002-2000−2i2i−2i2i002-20000000−2i2i00i2i2−i2−i2−2−2220000000000i2−i2−220000
χ3422-22-2-22-22-2002-2000−2i2i−2i2i002-20000000−2i2i00−i2−i2i2i222−2−20000000000−i2i22−20000
χ3522-22-2-22-22-2002-2000−2i2i−2i2i00-2200000002i−2i00i2i2−i2−i2−2−2220000000000−i2i22−20000
χ3622-22-2-22-22-2002-2000−2i2i−2i2i00-2200000002i−2i00−i2−i2i2i222−2−20000000000i2−i2−220000
χ372-22-2-2-2222-22-2-222-220000-20002i−2i2i−2i000000000002i−2i2i−2i000000002-200000000
χ382-22-2-2-2222-22-2-222-220000-20002i−2i2i−2i00000000000−2i2i−2i2i00000000-2200000000
χ392-22-2-2-2222-22-2-222-220000-2000−2i2i−2i2i000000000002i−2i2i−2i00000000-2200000000
χ402-22-2-2-2222-22-2-222-220000-2000−2i2i−2i2i00000000000−2i2i−2i2i000000002-200000000
χ412-22-2-2-222-22-222-2-2220000-20002i−2i−2i2i00000002i−2i2i−2i00000000002-20000000000
χ422-22-2-2-222-22-222-2-2220000-20002i−2i−2i2i0000000−2i2i−2i2i0000000000-220000000000
χ432-22-2-2-222-22-222-2-2220000-2000−2i2i2i−2i00000002i−2i2i−2i0000000000-220000000000
χ442-22-2-2-222-22-222-2-2220000-2000−2i2i2i−2i0000000−2i2i−2i2i00000000002-20000000000
χ4544-44-4-44-4-4400-440004i−4i−4i4i00000000000000000000000000000000000000000
χ4644-44-4-44-4-4400-44000−4i4i4i−4i00000000000000000000000000000000000000000
χ4744-4-44-4-44004-400-4400000000000004i−4i0000000000000000000000000000000
χ4844-4-44-4-44004-400-440000000000000−4i4i0000000000000000000000000000000
χ4944-4-44-4-4400-44004-40000000000000000004i−4i00000000000000000000000000
χ5044-4-44-4-4400-44004-4000000000000000000−4i4i00000000000000000000000000
χ514-44-4-4-4444-4-44-44-44-4000040000000000000000000000000000000000000000
χ524-44-4-4-444-444-44-44-4-4000040000000000000000000000000000000000000000
χ534-4-44-44-44004400-4-40000000000000000000000000000000000000000002i2−2i200
χ544-4-44-44-44004400-4-4000000000000000000000000000000000000000000−2i22i200
χ554-4-44-44-4400-4-400440000000000000000000000000000000000000000000022−22
χ564-4-44-44-4400-4-4004400000000000000000000000000000000000000000000−2222
χ574-4-4-4444-44400-4-4000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ584-4-4-4444-44400-4-400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ594-4-4-4444-4-4-40044000000000000000000000022−22−22220000000000000000000000
χ604-4-4-4444-4-4-400440000000000000000000000−222222−220000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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