Finite Group Databasebeta

← Group #252211

Character table — Group #252211

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444444444442444444444444488888888222444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-11-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-111-1-111-111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ911111111111111111-1-1-1-11-1-111-1-11111-1-1111111-1-1-1-1111-11-1-1-1-1-111-1-111-1-1
χ1011111111111111111-1-1-1-11-1-111-1-11111-1-111-1-1-1-111111-1-1-11-1-1-111-1-111-1-111
χ1111111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11111-11111-1-1-1-111
χ1211111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1111111-1-1-1-1-11111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111111111-1-11111-1-1-1-1-1111-1-1-11-1-1-1-111-1-111
χ1411111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-11-1-1-111111-1-111-1-1
χ1511111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-111111-1-11111-1-1
χ1611111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-111-1-1-1-111
χ172222222222-2-222-2-2-22222-2-2-200000000222200000000-200-200000000000000
χ182222222222-2-222-2-2-22222-2-2-200000000-2-2-2-200000000200200000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2220000000022-2-200000000200-200000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22200000000-2-22200000000-200200000000000000
χ2122222222-2-222-2-222-222-2-2-2-22222200000000000000000000-200-20000000000
χ2222222222-2-222-2-222-222-2-2-2-22-2-2-2-20000000000000000000020020000000000
χ2322222222-2-222-2-222-2-2-222-22-222-2-200000000000000000000-20020000000000
χ2422222222-2-222-2-222-2-2-222-22-2-2-22200000000000000000000200-20000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-222-2000022-2-2000000000000000002-200000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-222-20000-2-22200000000000000000-2200000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2222-22000022-2-200000000000000000-2200000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2222-220000-2-222000000000000000002-200000000000
χ29222-2-2-22-22-2002-20002i−2i2i−2i000000000002-22i−2ii2i2−i2−i222−2−2000000000000002−2i2−i2
χ30222-2-2-22-22-2002-20002i−2i2i−2i000000000002-22i−2i−i2−i2i2i2−2−22200000000000000−22−i2i2
χ31222-2-2-22-22-2002-20002i−2i2i−2i00000000000-22−2i2ii2i2−i2−i222−2−200000000000000−22−i2i2
χ32222-2-2-22-22-2002-20002i−2i2i−2i00000000000-22−2i2i−i2−i2i2i2−2−222000000000000002−2i2−i2
χ33222-2-2-22-22-2002-2000−2i2i−2i2i000000000002-2−2i2ii2i2−i2−i2−2−22200000000000000−22i2−i2
χ34222-2-2-22-22-2002-2000−2i2i−2i2i000000000002-2−2i2i−i2−i2i2i222−2−2000000000000002−2−i2i2
χ35222-2-2-22-22-2002-2000−2i2i−2i2i00000000000-222i−2ii2i2−i2−i2−2−222000000000000002−2−i2i2
χ36222-2-2-22-22-2002-2000−2i2i−2i2i00000000000-222i−2i−i2−i2i2i222−2−200000000000000−22i2−i2
χ3722-2-22-2-222-22-2-222-220000-20000002i−2i2i−2i00002i−2i2i−2i000002-2000000000000000
χ3822-2-22-2-222-22-2-222-220000-20000002i−2i2i−2i0000−2i2i−2i2i00000-22000000000000000
χ3922-2-22-2-222-22-2-222-220000-2000000−2i2i−2i2i00002i−2i2i−2i00000-22000000000000000
χ4022-2-22-2-222-22-2-222-220000-2000000−2i2i−2i2i0000−2i2i−2i2i000002-2000000000000000
χ4122-2-22-2-22-22-222-2-2220000-20000002i−2i−2i2i000000002i−2i2i−2i000000002-200000000
χ4222-2-22-2-22-22-222-2-2220000-20000002i−2i−2i2i00000000−2i2i−2i2i00000000-2200000000
χ4322-2-22-2-22-22-222-2-2220000-2000000−2i2i2i−2i000000002i−2i2i−2i00000000-2200000000
χ4422-2-22-2-22-22-222-2-2220000-2000000−2i2i2i−2i00000000−2i2i−2i2i000000002-200000000
χ45444-4-4-44-4-4400-440004i−4i−4i4i00000000000000000000000000000000000000000
χ46444-4-4-44-4-4400-44000−4i4i4i−4i00000000000000000000000000000000000000000
χ4744-44-44-4-44400-4-4000000000000000000000022−22−22220000000000000000000000
χ4844-44-44-4-44400-4-40000000000000000000000−222222−220000000000000000000000
χ4944-44-44-4-4-4-40044000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ5044-44-44-4-4-4-4004400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ5144-4-44-4-444-4-44-44-44-4000040000000000000000000000000000000000000000
χ5244-4-44-4-44-444-44-44-4-4000040000000000000000000000000000000000000000
χ534-44-4-44-44004400-4-400000000004i−4i0000000000000000000000000000000000
χ544-44-4-44-44004400-4-40000000000−4i4i0000000000000000000000000000000000
χ554-44-4-44-4400-4-40044000000004-4000000000000000000000000000000000000
χ564-44-4-44-4400-4-4004400000000-44000000000000000000000000000000000000
χ574-4-44-4-444004-400-44000000000000000000000000000000000000000022−220000
χ584-4-44-4-444004-400-440000000000000000000000000000000000000000−22220000
χ594-4-44-4-44400-44004-40000000000000000000000000000000000000022−22000000
χ604-4-44-4-44400-44004-400000000000000000000000000000000000000−2222000000
χ618-8888-8-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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