Finite Group Databasebeta

← Group #511889

Character table — Group #511889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222222244444488888888888824444444448888888888222244448888888816161616161616164444
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
χ511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111-1-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111-1-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ1111111-1-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ1211111-1-1111-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-111-1-11111-1-1
χ1311111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ1611111-1-1111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1922222-2-2222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222222-2-20000000000000000000000000000
χ2022222-2-2222-2-222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2220000000000000000000000000000
χ212222-222-22-222-22222222220000-2-200000000000000-2-2-2-200000000000000002−22−22−22−20000
χ222222-222-22-222-22222222220000-2-200000000000000-2-2-2-20000000000000000−22−22−22−220000
χ232222-222-22-222-22-2-2-2-2-2-2-2-20000-2-200000000000000222200000000000000002−22−2−22−220000
χ242222-222-22-222-22-2-2-2-2-2-2-2-20000-2-20000000000000022220000000000000000−22−222−22−20000
χ252222-222-2-22-2-22-2000000002222-2200000000-2-222-2-200002222-2-2-2-200000000000000000000
χ262222-222-2-22-2-22-2000000002222-2200000000-2-222-2-20000-2-2-2-2222200000000000000000000
χ272222-222-2-22-2-22-200000000-2-2-2-2-220000000022-2-2220000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ282222-222-2-22-2-22-200000000-2-2-2-2-220000000022-2-222000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ292222-2-2-2-22-2-2-2-222222-2-2-2-200002200000000000000-2-22200000000000000002−2−222−2−220000
χ302222-2-2-2-22-2-2-2-222222-2-2-2-200002200000000000000-2-2220000000000000000−222−2−222−20000
χ312222-2-2-2-22-2-2-2-22-2-2-2-222220000220000000000000022-2-200000000000000002−2−22−222−20000
χ322222-2-2-2-22-2-2-2-22-2-2-2-222220000220000000000000022-2-20000000000000000−222−22−2−220000
χ332222-2-2-2-2-22222-20000000022222-200000000-2-2-2-222000022-2-2-2-22200000000000000000000
χ342222-2-2-2-2-22222-20000000022222-200000000-2-2-2-2220000-2-22222-2-200000000000000000000
χ352222-2-2-2-2-22222-200000000-2-2-2-22-2000000002222-2-20000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ362222-2-2-2-2-22222-200000000-2-2-2-22-2000000002222-2-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ372-2-22200-22-2002-200002i2i−2i−2i22-2-20000002i2i−2i−2i2-20000002i−2i002-2002-22i−2i2i−2i0000000000000000
χ382-2-22200-22-2002-200002i2i−2i−2i22-2-20000002i2i−2i−2i2-20000002i−2i00-2200-22−2i2i−2i2i0000000000000000
χ392-2-22200-22-2002-200002i2i−2i−2i-2-222000000−2i−2i2i2i-220000002i−2i2-2002-20000002i−2i2i−2i000000000000
χ402-2-22200-22-2002-200002i2i−2i−2i-2-222000000−2i−2i2i2i-220000002i−2i-2200-22000000−2i2i−2i2i000000000000
χ412-2-22200-22-2002-20000−2i−2i2i2i22-2-2000000−2i−2i2i2i2-2000000−2i2i002-2002-2−2i2i−2i2i0000000000000000
χ422-2-22200-22-2002-20000−2i−2i2i2i22-2-2000000−2i−2i2i2i2-2000000−2i2i00-2200-222i−2i2i−2i0000000000000000
χ432-2-22200-22-2002-20000−2i−2i2i2i-2-2220000002i2i−2i−2i-22000000−2i2i2-2002-2000000−2i2i−2i2i000000000000
χ442-2-22200-22-2002-20000−2i−2i2i2i-2-2220000002i2i−2i−2i-22000000−2i2i-2200-220000002i−2i2i−2i000000000000
χ452-2-22-2002-2-2002222-2-2000022-2-20022-2-20000-2200002-200002-200-2200002-2-22000000000000
χ462-2-22-2002-2-2002222-2-2000022-2-20022-2-20000-2200002-20000-22002-20000-222-2000000000000
χ472-2-22-2002-2-2002222-2-20000-2-22200-2-22200002-200002-2002-200-22002-2-220000000000000000
χ482-2-22-2002-2-2002222-2-20000-2-22200-2-22200002-200002-200-22002-200-222-20000000000000000
χ492-2-22-2002-2-20022-2-222000022-2-200-2-2220000-220000-2200002-200-220000-222-2000000000000
χ502-2-22-2002-2-20022-2-222000022-2-200-2-2220000-220000-220000-22002-200002-2-22000000000000
χ512-2-22-2002-2-20022-2-2220000-2-2220022-2-200002-20000-22002-200-2200-222-20000000000000000
χ522-2-22-2002-2-20022-2-2220000-2-2220022-2-200002-20000-2200-22002-2002-2-220000000000000000
χ5344444444-4-4-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ5444444-4-44-4-444-4-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-404-4000000022−2222−2222−2222−2222−2222−22002-22-22-22-20022−220000000000000000000000000000000000
χ5644-4-404-4000000022−2222−2222−2222−22−2222−222200-22-22-22-2200−22220000000000000000000000000000000000
χ5744-4-404-40000000−2222−2222−2222−222222−2222−2200-22-22-22-220022−220000000000000000000000000000000000
χ5844-4-404-40000000−2222−2222−2222−2222−2222−2222002-22-22-22-200−22220000000000000000000000000000000000
χ5944-4-40-44000000022−2222−22−2222−222222−2222−22002-22-2-22-2200−22220000000000000000000000000000000000
χ6044-4-40-44000000022−2222−22−2222−2222−2222−222200-22-222-22-20022−220000000000000000000000000000000000
χ6144-4-40-440000000−2222−222222−2222−2222−2222−2200-22-222-22-200−22220000000000000000000000000000000000
χ6244-4-40-440000000−2222−222222−2222−22−2222−2222002-22-2-22-220022−220000000000000000000000000000000000
χ634-44-40000004i−4i0022−22−22222i2−2i2−2i22i222−22−2222002-2-222i−2i−2i2i00002i2−2i200000000000000000000000000000000
χ644-44-40000004i−4i0022−22−22222i2−2i2−2i22i2−222222−2200-222-2−2i2i2i−2i0000−2i22i200000000000000000000000000000000
χ654-44-40000004i−4i00−222222−22−2i22i22i2−2i222−22−222200-222-2−2i2i2i−2i00002i2−2i200000000000000000000000000000000
χ664-44-40000004i−4i00−222222−22−2i22i22i2−2i2−222222−22002-2-222i−2i−2i2i0000−2i22i200000000000000000000000000000000
χ674-44-4000000−4i4i0022−22−2222−2i22i22i2−2i222−22−2222002-2-22−2i2i2i−2i0000−2i22i200000000000000000000000000000000
χ684-44-4000000−4i4i0022−22−2222−2i22i22i2−2i2−222222−2200-222-22i−2i−2i2i00002i2−2i200000000000000000000000000000000
χ694-44-4000000−4i4i00−222222−222i2−2i2−2i22i222−22−222200-222-22i−2i−2i2i0000−2i22i200000000000000000000000000000000
χ704-44-4000000−4i4i00−222222−222i2−2i2−2i22i2−222222−22002-2-22−2i2i2i−2i00002i2−2i200000000000000000000000000000000
χ714-4-44400-4-4400-4444-4-4000000000000000000000000-44000000000000000000000000000000
χ724-4-44400-4-4400-44-4-4440000000000000000000000004-4000000000000000000000000000000
χ734-4-44-40044400-4-400004i4i−4i−4i0000000000000000000000−4i4i0000000000000000000000000000
χ744-4-44-40044400-4-40000−4i−4i4i4i00000000000000000000004i−4i0000000000000000000000000000

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