Finite Group Databasebeta

← Group #103137

Character table — Group #103137

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444444444488888888888888888888888888888888224488884444
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
χ1522222222-2-2-2-222-2-222222-2-2222-2-2-2-20000000000000000000000002222-2-2-2-2000000000000
χ1622222222-2-2-2-222-2-222222-2-2222-2-2-2-2000000000000000000000000-2-2-2-22222000000000000
χ1722222222-2-2-2-222-2-2-2-2-222-2-2-2-2-222220000000000000000000000000000000000000000002-2
χ1822222222-2-2-2-222-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000000000000000-22
χ1922222222-2-2-2-2-2-222222-2-2222-2-222-2-200000000000000002222-2-2-2-200000000000000000000
χ2022222222-2-2-2-2-2-222222-2-2222-2-222-2-20000000000000000-2-2-2-2222200000000000000000000
χ2122222222-2-2-2-2-2-222-2-2-2-2-222-222-2-22200000000000000000000000000000000000000002-200
χ2222222222-2-2-2-2-2-222-2-2-2-2-222-222-2-2220000000000000000000000000000000000000000-2200
χ232222-2-2-2-222-2-22222000-2-2-2-200000002222−2−2−2−22222−2−2−2−200000000000000002-2002−22−20000
χ242222-2-2-2-222-2-22222000-2-2-2-200000002222−2−2−2−22222−2−2−2−20000000000000000-2200−22−220000
χ252222-2-2-2-222-2-22222000-2-2-2-20000000−2−2−2−22222−2−2−2−2222200000000000000002-200−22−220000
χ262222-2-2-2-222-2-22222000-2-2-2-20000000−2−2−2−22222−2−2−2−222220000000000000000-22002−22−20000
χ272222-2-2-2-222-2-2-2-2-2-2000222200000002222−2−2−2−2−2−2−2−222220000000000000000002i−2ii2−i2−i2i20000
χ282222-2-2-2-222-2-2-2-2-2-2000222200000002222−2−2−2−2−2−2−2−22222000000000000000000−2i2i−i2i2i2−i20000
χ292222-2-2-2-222-2-2-2-2-2-200022220000000−2−2−2−222222222−2−2−2−20000000000000000002i−2i−i2i2i2−i20000
χ302222-2-2-2-222-2-2-2-2-2-200022220000000−2−2−2−222222222−2−2−2−2000000000000000000−2i2ii2−i2−i2i20000
χ3122-2-22-22-200002-2002-2-22-20022-2000022−2−222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i200002i2i−2i−2i000000000000
χ3222-2-22-22-200002-2002-2-22-20022-2000022−2−222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i20000−2i−2i2i2i000000000000
χ3322-2-22-22-200002-2002-2-22-20022-20000−2−222−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i20000−2i−2i2i2i000000000000
χ3422-2-22-22-200002-2002-2-22-20022-20000−2−222−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i200002i2i−2i−2i000000000000
χ3522-2-22-22-20000-22002-2-2-22002-22000022−2−222−2−2−2−222−2−222i2i2−i2−i2−i2−i2i2i22i2i−2i−2i0000000000000000
χ3622-2-22-22-20000-22002-2-2-22002-22000022−2−222−2−2−2−222−2−222−i2−i2i2i2i2i2−i2−i2−2i−2i2i2i0000000000000000
χ3722-2-22-22-20000-22002-2-2-22002-220000−2−222−2−22222−2−222−2−2i2i2−i2−i2−i2−i2i2i2−2i−2i2i2i0000000000000000
χ3822-2-22-22-20000-22002-2-2-22002-220000−2−222−2−22222−2−222−2−2−i2−i2i2i2i2i2−i2−i22i2i−2i−2i0000000000000000
χ392-22-2-222-22-22-20000-22-20000200002-2000000002-22-22-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ402-22-2-222-22-22-20000-22-20000200002-2000000002-22-22-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ412-22-2-222-22-22-20000-22-20000200002-200000000-22-22-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ422-22-2-222-22-22-20000-22-20000200002-200000000-22-22-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ432-22-2-222-2-22-220000-22-2000020000-222-22-22-22-200000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ442-22-2-222-2-22-220000-22-2000020000-222-22-22-22-200000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ452-22-2-222-2-22-220000-22-2000020000-22-22-22-22-2200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ462-22-2-222-2-22-220000-22-2000020000-22-22-22-22-2200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ472-2-22-2-2220000002-2-2-22002-22002-2002−2−222−2−222−2−222−2−2200002-2-222−2−222−2−22000000000000
χ482-2-22-2-2220000002-2-2-22002-22002-2002−2−222−2−222−2−222−2−220000-222-2−222−2−222−2000000000000
χ492-2-22-2-2220000002-2-2-22002-22002-200−222−2−222−2−222−2−222−200002-2-22−222−2−222−2000000000000
χ502-2-22-2-2220000002-2-2-22002-22002-200−222−2−222−2−222−2−222−20000-222-22−2−222−2−22000000000000
χ512-2-22-2-222000000-22-2-2200-22200-22002−2−222−2−22−222−2−222−22-2-2200002−2−22−222−2000000000000
χ522-2-22-2-222000000-22-2-2200-22200-22002−2−222−2−22−222−2−222−2-222-20000−222−22−2−22000000000000
χ532-2-22-2-222000000-22-2-2200-22200-2200−222−2−222−22−2−222−2−222-2-220000−222−22−2−22000000000000
χ542-2-22-2-222000000-22-2-2200-22200-2200−222−2−222−22−2−222−2−22-222-200002−2−22−222−2000000000000
χ554444-4-4-4-4-4-44444-4-4000-4-444000000000000000000000000000000000000000000000000000
χ564444-4-4-4-4-4-444-4-44400044-4-4000000000000000000000000000000000000000000000000000
χ5744-4-44-44-400004-400-4444-400-4-44000000000000000000000000000000000000000000000000
χ5844-4-44-44-40000-4400-444-4400-44-4000000000000000000000000000000000000000000000000
χ5944-4-4-44-4400004-400000-4400000000022-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ6044-4-4-44-4400004-400000-44000000000-2-22222-2-2-2-22222-2-20000000000000000000000000000
χ6144-4-4-44-440000-44000004-400000000022-2-2-2-222-2-22222-2-20000000000000000000000000000
χ6244-4-4-44-440000-44000004-4000000000-2-22222-2-222-2-2-2-2220000000000000000000000000000
χ634-44-44-4-444-4-440000000000000000000000000022−2222−22−2222−22220000000000000000000000000000
χ644-44-44-4-444-4-4400000000000000000000000000−2222−222222−2222−220000000000000000000000000000
χ654-44-44-4-44-444-400000000000000000022−2222−22−2222−2222000000000000000000000000000000000000
χ664-44-44-4-44-444-4000000000000000000−2222−222222−2222−22000000000000000000000000000000000000
χ674-44-4-444-44-44-400004-440000-40000-4400000000000000000000000000000000000000000000
χ684-44-4-444-4-44-4400004-440000-400004-400000000000000000000000000000000000000000000
χ694-4-4444-4-40000004-400000-4400000002-2-22-222-22-2-22-222-20000000000000000000000000000
χ704-4-4444-4-40000004-400000-440000000-222-22-2-22-222-22-2-220000000000000000000000000000
χ714-4-4444-4-4000000-44000004-400000002-2-22-222-2-222-22-2-220000000000000000000000000000
χ724-4-4444-4-4000000-44000004-40000000-222-22-2-222-2-22-222-20000000000000000000000000000
χ734-4-44-4-4440000004-444-4004-4-400-440000000000000000000000000000000000000000000000
χ744-4-44-4-444000000-4444-400-44-4004-40000000000000000000000000000000000000000000000

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