Finite Group Databasebeta

← Group #323608

Character table — Group #323608

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444444444444444488888888888888888888888844888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111-11-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-11-11
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-11-11
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-11-11-1
χ911111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ1011111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ1111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ1211111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ172222222222-2-2-2-2-2-222-2-22222000000002222-2-2-2-200000000-2-2000022-2-20000000000000000
χ182222222222-2-2-2-2-2-222-2-2222200000000-2-2-2-2222200000000-2-20000-2-2220000000000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2-2-2000000002222-2-2-2-200000000220000-2-2220000000000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2-2-200000000-2-2-2-222220000000022000022-2-20000000000000000
χ2122222222-2-222-2-2-2-2-2-22222-2-200000000000000002222-2-2-2-22-20000000022-2-2000000000000
χ2222222222-2-222-2-2-2-2-2-22222-2-20000000000000000-2-2-2-222222-200000000-2-222000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-22200000000000000002222-2-2-2-2-2200000000-2-222000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-2220000000000000000-2-2-2-22222-220000000022-2-2000000000000
χ2522222222-2-2-2-22222-2-2-2-222-2-22222-2-2-2-20000000000000000-2222-2-200000000000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-222220000000000000000-22-2-22200000000000000000000
χ2722222222-2-2-2-22222-2-2-2-2-2-2222222-2-2-2-200000000000000002-2-2-22200000000000000000000
χ2822222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2222200000000000000002-222-2-200000000000000000000
χ29222-22-2-2-2222222-2-2-2-2-2-2000022-2-222-2-20000000000000000000000000000002-22-200000000
χ30222-22-2-2-2222222-2-2-2-2-2-2000022-2-222-2-2000000000000000000000000000000-22-2200000000
χ31222-22-2-2-2222222-2-2-2-2-2-20000-2-222-2-2220000000000000000000000000000002-2-2200000000
χ32222-22-2-2-2222222-2-2-2-2-2-20000-2-222-2-222000000000000000000000000000000-222-200000000
χ33222-22-2-2-2-2-2-2-222-2-22222000022-2-2-2-22200000000000000000000000000000000002i−2i2i−2i0000
χ34222-22-2-2-2-2-2-2-222-2-22222000022-2-2-2-2220000000000000000000000000000000000−2i2i−2i2i0000
χ35222-22-2-2-2-2-2-2-222-2-222220000-2-22222-2-200000000000000000000000000000000002i−2i−2i2i0000
χ36222-22-2-2-2-2-2-2-222-2-222220000-2-22222-2-20000000000000000000000000000000000−2i2i2i−2i0000
χ3722-2-2-222-22-20000002-2002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2002−22−2002i−2i2−22−2000000000000
χ3822-2-2-222-22-20000002-2002i−2i2i−2ii2−i2i2−i2i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i2002−22−200−2i2i−22−22000000000000
χ3922-2-2-222-22-20000002-2002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i200−22−22002i−2i−22−22000000000000
χ4022-2-2-222-22-20000002-2002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i200−22−2200−2i2i2−22−2000000000000
χ4122-2-2-222-22-20000002-200−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i200−22−2200−2i2i−22−22000000000000
χ4222-2-2-222-22-20000002-200−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000-2-222−i2−i2i2i2−i2−i2i2i200−22−22002i−2i2−22−2000000000000
χ4322-2-2-222-22-20000002-200−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000022-2-2−i2−i2i2i2−i2−i2i2i2002−22−200−2i2i2−22−2000000000000
χ4422-2-2-222-22-20000002-200−2i2i−2i2i−i2i2−i2i2−i2i2−i2i20000-2-222i2i2−i2−i2i2i2−i2−i2002−22−2002i−2i−22−22000000000000
χ4522-2-2-222-2-22000000-22002i−2i−2i2ii2−i2i2−i2−i2i2−i2i222-2-20000i2i2−i2−i2−i2−i2i2i2002−2−222i−2i002−2−22000000000000
χ4622-2-2-222-2-22000000-22002i−2i−2i2ii2−i2i2−i2−i2i2−i2i2-2-2220000−i2−i2i2i2i2i2−i2−i2002−2−22−2i2i00−222−2000000000000
χ4722-2-2-222-2-22000000-22002i−2i−2i2i−i2i2−i2i2i2−i2i2−i222-2-20000−i2−i2i2i2i2i2−i2−i200−222−22i−2i00−222−2000000000000
χ4822-2-2-222-2-22000000-22002i−2i−2i2i−i2i2−i2i2i2−i2i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i200−222−2−2i2i002−2−22000000000000
χ4922-2-2-222-2-22000000-2200−2i2i2i−2ii2−i2i2−i2−i2i2−i2i222-2-20000i2i2−i2−i2−i2−i2i2i200−222−2−2i2i00−222−2000000000000
χ5022-2-2-222-2-22000000-2200−2i2i2i−2ii2−i2i2−i2−i2i2−i2i2-2-2220000−i2−i2i2i2i2i2−i2−i200−222−22i−2i002−2−22000000000000
χ5122-2-2-222-2-22000000-2200−2i2i2i−2i−i2i2−i2i2i2−i2i2−i222-2-20000−i2−i2i2i2i2i2−i2−i2002−2−22−2i2i002−2−22000000000000
χ5222-2-2-222-2-22000000-2200−2i2i2i−2i−i2i2−i2i2i2−i2i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i2002−2−222i−2i00−222−2000000000000
χ53444-44-4-4-444-4-4-4-444-4-444000000000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000000
χ5544-44-4-4-444-4000000-440000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ5644-44-4-4-444-4000000-44000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ5744-44-4-4-44-440000004-40000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000
χ5844-44-4-4-44-440000004-4000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000
χ594-444-44-4-4004-40000004-400000000000022−2222−2222−2222−220000000000000000000000000000000000
χ604-444-44-4-4004-40000004-4000000000000−2222−2222−2222−22220000000000000000000000000000000000
χ614-444-44-4-400-44000000-4400000000000022−2222−22−2222−22220000000000000000000000000000000000
χ624-444-44-4-400-44000000-44000000000000−2222−222222−2222−220000000000000000000000000000000000
χ634-44-4-4-444004-4000000-440000000000000000000000004-44-400000000000000000000000000
χ644-44-4-4-444004-4000000-44000000000000000000000000-44-4400000000000000000000000000
χ654-44-4-4-44400-440000004-4000000000000000000004-44-4000000000000000000000000000000
χ664-44-4-4-44400-440000004-400000000000000000000-44-44000000000000000000000000000000
χ674-4-444-44-400004-44-40000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ684-4-444-44-400004-44-4000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ694-4-444-44-40000-44-440000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000
χ704-4-444-44-40000-44-44000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000
χ714-4-4-444-4400004-4-44000000000000000022−22−2222−222222−220000000000000000000000000000000000
χ724-4-4-444-4400004-4-440000000000000000−222222−2222−22−22220000000000000000000000000000000000
χ734-4-4-444-440000-444-4000000000000000022−22−222222−22−22220000000000000000000000000000000000
χ744-4-4-444-440000-444-40000000000000000−222222−22−222222−220000000000000000000000000000000000

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