Finite Group Databasebeta

← Group #103159

Character table — Group #103159

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
χ92222222222222-2-2-2-2-2-222-2-2222-2-2-2-20000000000000000000000002222-2-2-2-2000000000000
χ102222222222222-2-2-2-2-2-222-2-2222-2-2-2-2000000000000000000000000-2-2-2-22222000000000000
χ1122222222222-2-222-2-2-2-2-2-2222-2-222-2-200000000000000002222-2-2-2-200000000000000000000
χ1222222222222-2-222-2-2-2-2-2-2222-2-222-2-20000000000000000-2-2-2-2222200000000000000000000
χ1322222222222-2-2-2-22222-2-2-2-22-2-2-2-22222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1422222222222-2-2-2-22222-2-2-2-22-2-2-2-222-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1522222222-2-2-2222222222222-2-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ1622222222-2-2-2222222222222-2-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ1722222222-2-2-222-2-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000000000000000002-2
χ1822222222-2-2-222-2-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000000000000000-22
χ1922222222-2-2-2-2-222-2-2-2-2-2-222-222-2-22200000000000000000000000000000000000000002-200
χ2022222222-2-2-2-2-222-2-2-2-2-2-222-222-2-2220000000000000000000000000000000000000000-2200
χ2122222222-2-2-2-2-2-2-22222-2-2-2-2-22222-2-20000000000000000000000000000000000002i2i−2i−2i0000
χ2222222222-2-2-2-2-2-2-22222-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i−2i2i2i0000
χ23222-22-2-2-2000222222-2-2-2-2-2-200000002222−2−2−2−22222−2−2−2−20000000000000000002-22−22−20000
χ24222-22-2-2-2000222222-2-2-2-2-2-200000002222−2−2−2−22222−2−2−2−2000000000000000000-22−22−220000
χ25222-22-2-2-2000222222-2-2-2-2-2-20000000−2−2−2−22222−2−2−2−222220000000000000000002-2−22−220000
χ26222-22-2-2-2000222222-2-2-2-2-2-20000000−2−2−2−22222−2−2−2−22222000000000000000000-222−22−20000
χ27222-22-2-2-2000-2-2-2-222-2-2222200000002222−2−2−2−2−2−2−2−2222200000000000000002i−2i00i2−i2−i2i20000
χ28222-22-2-2-2000-2-2-2-222-2-2222200000002222−2−2−2−2−2−2−2−222220000000000000000−2i2i00−i2i2i2−i20000
χ29222-22-2-2-2000-2-2-2-222-2-222220000000−2−2−2−222222222−2−2−2−200000000000000002i−2i00−i2i2i2−i20000
χ30222-22-2-2-2000-2-2-2-222-2-222220000000−2−2−2−222222222−2−2−2−20000000000000000−2i2i00i2−i2−i2i20000
χ3122-22-2-22-22-2-2002-20000002-22002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000022-2-2i2i2−i2−i2i2i2−i2−i2000000000000
χ3222-22-2-22-22-2-2002-20000002-22002-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-2-222−i2−i2i2i2−i2−i2i2i2000000000000
χ3322-22-2-22-22-2-2002-20000002-22002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000022-2-2−i2−i2i2i2−i2−i2i2i2000000000000
χ3422-22-2-22-22-2-2002-20000002-22002-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-2-222i2i2−i2−i2i2i2−i2−i2000000000000
χ3522-22-2-22-22-2-200-22000000-22200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222-2-20000i2i2−i2−i2−i2−i2i2i2000000000000
χ3622-22-2-22-22-2-200-22000000-22200-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2-2-2220000−i2−i2i2i2i2i2−i2−i2000000000000
χ3722-22-2-22-22-2-200-22000000-22200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222-2-20000−i2−i2i2i2i2i2−i2−i2000000000000
χ3822-22-2-22-22-2-200-22000000-22200-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2-2-2220000i2i2−i2−i2−i2−i2i2i2000000000000
χ392-222-2-2-22-22-22-20000002-20022-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200002-22-2000000000000
χ402-222-2-2-22-22-22-20000002-20022-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000-22-22000000000000
χ412-222-2-2-22-22-22-20000002-20022-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000-22-22000000000000
χ422-222-2-2-22-22-22-20000002-20022-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200002-22-2000000000000
χ432-222-2-2-22-22-2-22000000-22002-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22-22-20000000000000000
χ442-222-2-2-22-22-2-22000000-22002-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2-22-220000000000000000
χ452-222-2-2-22-22-2-22000000-22002-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2-22-220000000000000000
χ462-222-2-2-22-22-2-22000000-22002-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22-22-20000000000000000
χ472-2-2222-2-2-2-2200002-22-20000200002-2000000002-2-222-2-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ482-2-2222-2-2-2-2200002-22-20000200002-2000000002-2-222-2-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ492-2-2222-2-2-2-2200002-22-20000200002-200000000-222-2-222-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-2222-2-2-2-2200002-22-20000200002-200000000-222-2-222-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-2222-2-2-2-220000-22-22000020000-222-2-222-2-2200000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000
χ522-2-2222-2-2-2-220000-22-22000020000-222-2-222-2-2200000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000
χ532-2-2222-2-2-2-220000-22-22000020000-22-222-2-222-200000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000
χ542-2-2222-2-2-2-220000-22-22000020000-22-222-2-222-200000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000
χ55444-44-4-4-400044-4-4-4-444-4-444000000000000000000000000000000000000000000000000000
χ56444-44-4-4-4000-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000
χ5744-44-4-44-4-444004-40000004-4-400-440000000000000000000000000000000000000000000000
χ5844-44-4-44-4-44400-44000000-44-4004-40000000000000000000000000000000000000000000000
χ5944-4-4-44-44000004-4000000-4400000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6044-4-4-44-44000004-4000000-440000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6144-4-4-44-4400000-440000004-400000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6244-4-4-44-4400000-440000004-40000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ634-444-4-4-444-444-40000004-400-4-44000000000000000000000000000000000000000000000000
χ644-444-4-4-444-44-44000000-4400-44-4000000000000000000000000000000000000000000000000
χ654-44-4-444-40004-4000000-440000000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ664-44-4-444-40004-4000000-44000000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ674-44-4-444-4000-440000004-40000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ684-44-4-444-4000-440000004-4000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ694-4-4444-4-444-400004-44-40000-40000-4400000000000000000000000000000000000000000000
χ704-4-4444-4-444-40000-44-440000-400004-400000000000000000000000000000000000000000000
χ714-4-4-44-44400000004-4-44000000000000000000022−22−2222−222222−220000000000000000000000000000
χ724-4-4-44-44400000004-4-440000000000000000000−222222−2222−22−22220000000000000000000000000000
χ734-4-4-44-4440000000-444-40000000000022−22−2222−222222−22000000000000000000000000000000000000
χ744-4-4-44-4440000000-444-400000000000−222222−2222−22−2222000000000000000000000000000000000000

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