Finite Group Databasebeta

← Group #103104

Character table — Group #103104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ92222222222222222-2-2-22222-2-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ102222222222222222-2-2-22222-2-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ11222222222222-2-2-2-2222-2-2-2-22-2-2-2-22222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ12222222222222-2-2-2-2222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000002i2i−2i−2i0000
χ14222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i−2i2i2i0000
χ1522222222-2-2-2-222-2-222222-2-22-2-222-2-20000000000000000000000002222-2-2-2-2000000000000
χ1622222222-2-2-2-222-2-222222-2-22-2-222-2-2000000000000000000000000-2-2-2-22222000000000000
χ1722222222-2-2-2-222-2-2-2-2-222-2-2-222-2-2220000000000000000000000000000000000000000002-2
χ1822222222-2-2-2-222-2-2-2-2-222-2-2-222-2-222000000000000000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-222222-2-222222-2-2-2-200000000000000002222-2-2-2-200000000000000000000
χ2022222222-2-2-2-2-2-222222-2-222222-2-2-2-20000000000000000-2-2-2-2222200000000000000000000
χ2122222222-2-2-2-2-2-222-2-2-2-2-222-2-2-2222200000000000000000000000000000000000000002-200
χ2222222222-2-2-2-2-2-222-2-2-2-2-222-2-2-222220000000000000000000000000000000000000000-2200
χ23222-2-2-22-222-2-200002-2-20000200002-2000000002i2i2i2i−2i−2i−2i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ24222-2-2-22-222-2-200002-2-20000200002-2000000002i2i2i2i−2i−2i−2i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ25222-2-2-22-222-2-200002-2-20000200002-200000000−2i−2i−2i−2i2i2i2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ26222-2-2-22-222-2-200002-2-20000200002-200000000−2i−2i−2i−2i2i2i2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ27222-2-2-22-2-2-22200002-2-2000020000-222i2i2i2i−2i−2i−2i−2i0000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2000000000000
χ28222-2-2-22-2-2-22200002-2-2000020000-222i2i2i2i−2i−2i−2i−2i00000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2000000000000
χ29222-2-2-22-2-2-22200002-2-2000020000-22−2i−2i−2i−2i2i2i2i2i0000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2000000000000
χ30222-2-2-22-2-2-22200002-2-2000020000-22−2i−2i−2i−2i2i2i2i2i00000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2000000000000
χ3122-2-22-2-222-22-222-2-2000-2-2220000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000002-2i2−i2i2−i20000
χ3222-2-22-2-222-22-222-2-2000-2-2220000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000-22−i2i2−i2i20000
χ3322-2-22-2-222-22-222-2-2000-2-2220000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000002-2−i2i2−i2i20000
χ3422-2-22-2-222-22-222-2-2000-2-2220000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000-22i2−i2i2−i20000
χ3522-2-22-2-222-22-2-2-22200022-2-20000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000002i−2i002−2−220000
χ3622-2-22-2-222-22-2-2-22200022-2-20000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000−2i2i00−222−20000
χ3722-2-22-2-222-22-2-2-22200022-2-20000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000002i−2i00−222−20000
χ3822-2-22-2-222-22-2-2-22200022-2-20000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000−2i2i002−2−220000
χ392-2-22-2-2220000002-222-2002-2-22-200002−22−22−22−22−22−22−22−200002i−2i2i−2ii2−i2i2−i2i2−i2i2−i2000000000000
χ402-2-22-2-2220000002-222-2002-2-22-200002−22−22−22−22−22−22−22−20000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2000000000000
χ412-2-22-2-2220000002-222-2002-2-22-20000−22−22−22−22−22−22−22−2200002i−2i2i−2i−i2i2−i2i2−i2i2−i2i2000000000000
χ422-2-22-2-2220000002-222-2002-2-22-20000−22−22−22−22−22−22−22−220000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2000000000000
χ432-2-22-2-222000000-2222-200-22-2-2200002−22−22−22−2−22−22−22−222i−2i2i−2i0000i2−i2i2−i2−i2i2−i2i2000000000000
χ442-2-22-2-222000000-2222-200-22-2-2200002−22−22−22−2−22−22−22−22−2i2i−2i2i0000−i2i2−i2i2i2−i2i2−i2000000000000
χ452-2-22-2-222000000-2222-200-22-2-220000−22−22−22−222−22−22−22−22i−2i2i−2i0000−i2i2−i2i2i2−i2i2−i2000000000000
χ462-2-22-2-222000000-2222-200-22-2-220000−22−22−22−222−22−22−22−2−2i2i−2i2i0000i2−i2i2−i2−i2i2−i2i2000000000000
χ472-2-2-2222-200002-2002-222-200-2002-200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i20000-222-2000000000000
χ482-2-2-2222-200002-2002-222-200-2002-200i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i200002-2-22000000000000
χ492-2-2-2222-200002-2002-222-200-2002-200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i200002-2-22000000000000
χ502-2-2-2222-200002-2002-222-200-2002-200−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i20000-222-2000000000000
χ512-2-2-2222-20000-22002-22-2200-200-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2-222-20000000000000000
χ522-2-2-2222-20000-22002-22-2200-200-2200i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i2i2−i2−i2i22-2-220000000000000000
χ532-2-2-2222-20000-22002-22-2200-200-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i2−i2i2i2−i22-2-220000000000000000
χ542-2-2-2222-20000-22002-22-2200-200-2200−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2-222-20000000000000000
χ55444-4-4-44-444-4-40000-4440000-40000-4400000000000000000000000000000000000000000000
χ56444-4-4-44-4-4-4440000-4440000-400004-400000000000000000000000000000000000000000000
χ5744-44-44-4-44-4-44000000000000000000000000002222−22−22−22−2222220000000000000000000000000000
χ5844-44-44-4-44-4-4400000000000000000000000000−22−2222222222−22−220000000000000000000000000000
χ5944-44-44-4-4-444-40000000000000000002222−22−22−22−222222000000000000000000000000000000000000
χ6044-44-44-4-4-444-4000000000000000000−22−2222222222−22−22000000000000000000000000000000000000
χ6144-4-44-4-44-44-444444000-4-4-4-4000000000000000000000000000000000000000000000000000
χ6244-4-44-4-44-44-44-4-4-4-40004444000000000000000000000000000000000000000000000000000
χ634-4444-4-4-400004-400000-440000000002-2-22-222-22-2-22-222-20000000000000000000000000000
χ644-4444-4-4-400004-400000-44000000000-222-22-2-22-222-22-2-220000000000000000000000000000
χ654-4444-4-4-40000-44000004-40000000002-2-22-222-2-222-22-2-220000000000000000000000000000
χ664-4444-4-4-40000-44000004-4000000000-222-22-2-222-2-22-222-20000000000000000000000000000
χ674-44-4-44-440000004-400000-4400000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ684-44-4-44-440000004-400000-440000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ694-44-4-44-44000000-44000004-400000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ704-44-4-44-44000000-44000004-40000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ714-4-44-4-4440000004-4-4-44004-44-44000000000000000000000000000000000000000000000000
χ724-4-44-4-444000000-44-4-4400-4444-4000000000000000000000000000000000000000000000000
χ734-4-4-4444-400004-400-44-44-400400-440000000000000000000000000000000000000000000000
χ744-4-4-4444-40000-4400-44-4-44004004-40000000000000000000000000000000000000000000000

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