Finite Group Databasebeta

← Group #285658

Character table — Group #285658

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822244444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ10111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ11111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-11111-1-1-1-1-1-111-1-1111-1
χ12111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111111111-1-111-1-1-11
χ13111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11-1
χ14111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111111111-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-11
χ15111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-11111-1-1-11
χ16111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1
χ172222222222222-2-222-2-22-2-2-2-2220000000000000000-222-2-2-2-22200000000000000000000000000
χ182222222222222-2-222-2-22-2-2-2-2220000000000000000-2-2-22222-2-200000000000000000000000000
χ19222222222-2-2-2-2-2-222-2-22-2-222-2-2000000000000000022222-2-2-2-200000000000000000000000000
χ20222222222-2-2-2-2-2-222-2-22-2-222-2-200000000000000002-2-2-2-2222200000000000000000000000000
χ2122222222-2222222-2-222-2-2-222-2-22222222200000000-200000000-2-20000-2-2000000000000000000
χ2222222222-2222222-2-222-2-2-222-2-2-2-2-2-2-2-2-2-200000000-20000000022000022000000000000000000
χ2322222222-22222-2-2-2-2-2-2-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i200000000000000002i2i−2i−2i00000000000000
χ2422222222-22222-2-2-2-2-2-2-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i20000000000000000−2i−2i2i2i00000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-2-2-2222222-2-2-2-200000000200000000-2-2000022000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-2-2-222-2-2-2-2222200000000200000000220000-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-20000000000000000−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-200000000000000002i2i−2i−2i00000000000000
χ2922-2-2-222-202i2i−2i−2i2-2002-20002i−2i002i2i−2i−2i22-2-2000000000000000000022−2−2000000i2i2−i2−i200002−2i2−i200
χ3022-2-2-222-202i2i−2i−2i2-2002-20002i−2i002i2i−2i−2i22-2-20000000000000000000−2−222000000−i2−i2i2i20000−22−i2i200
χ3122-2-2-222-202i2i−2i−2i2-2002-20002i−2i00−2i−2i2i2i-2-222000000000000000000022−2−2000000i2i2−i2−i20000−22−i2i200
χ3222-2-2-222-202i2i−2i−2i2-2002-20002i−2i00−2i−2i2i2i-2-2220000000000000000000−2−222000000−i2−i2i2i200002−2i2−i200
χ3322-2-2-222-20−2i−2i2i2i2-2002-2000−2i2i002i2i−2i−2i-2-222000000000000000000022−2−2000000−i2−i2i2i20000−22i2−i200
χ3422-2-2-222-20−2i−2i2i2i2-2002-2000−2i2i002i2i−2i−2i-2-2220000000000000000000−2−222000000i2i2−i2−i200002−2−i2i200
χ3522-2-2-222-20−2i−2i2i2i2-2002-2000−2i2i00−2i−2i2i2i22-2-2000000000000000000022−2−2000000−i2−i2i2i200002−2−i2i200
χ3622-2-2-222-20−2i−2i2i2i2-2002-2000−2i2i00−2i−2i2i2i22-2-20000000000000000000−2−222000000i2i2−i2−i20000−22i2−i200
χ372-222-22-2-220000-2-22-222-22-200000000000022-2-222-2-20000000000000000000002i−2i2i−2i002i−2i000000
χ382-222-22-2-220000-2-22-222-22-200000000000022-2-222-2-2000000000000000000000−2i2i−2i2i00−2i2i000000
χ392-222-22-2-220000-2-22-222-22-2000000000000-2-222-2-2220000000000000000000002i−2i2i−2i00−2i2i000000
χ402-222-22-2-220000-2-22-222-22-2000000000000-2-222-2-222000000000000000000000−2i2i−2i2i002i−2i000000
χ412-222-22-2-2-2000022-22-2-222-20000000000002i2i−2i−2i−2i−2i2i2i000000000002-22-200000000002i−2i00000000
χ422-222-22-2-2-2000022-22-2-222-20000000000002i2i−2i−2i−2i−2i2i2i00000000000-22-220000000000−2i2i00000000
χ432-222-22-2-2-2000022-22-2-222-2000000000000−2i−2i2i2i2i2i−2i−2i000000000002-22-20000000000−2i2i00000000
χ442-222-22-2-2-2000022-22-2-222-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000-22-2200000000002i−2i00000000
χ452-22-22-22-222i−2i2i−2i00-2-200200002i−2ii2−i2i2−i22−22−2i2−i2i2−i2i2−i2i2−i20002-22i−2i00i2−i200002−22−22−200000000000000
χ462-22-22-22-222i−2i2i−2i00-2-200200002i−2ii2−i2i2−i22−22−2−i2i2−i2i2−i2i2−i2i2000-22−2i2i00i2−i200002−2−22−2200000000000000
χ472-22-22-22-222i−2i2i−2i00-2-200200002i−2i−i2i2−i2i2−22−22i2−i2i2−i2i2−i2i2−i2000-22−2i2i00−i2i20000−222−22−200000000000000
χ482-22-22-22-222i−2i2i−2i00-2-200200002i−2i−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−i2i20002-22i−2i00−i2i20000−22−22−2200000000000000
χ492-22-22-22-22−2i2i−2i2i00-2-20020000−2i2ii2−i2i2−i2−22−22i2−i2i2−i2i2−i2i2−i20002-2−2i2i00i2−i20000−22−22−2200000000000000
χ502-22-22-22-22−2i2i−2i2i00-2-20020000−2i2ii2−i2i2−i2−22−22−i2i2−i2i2−i2i2−i2i2000-222i−2i00i2−i20000−222−22−200000000000000
χ512-22-22-22-22−2i2i−2i2i00-2-20020000−2i2i−i2i2−i2i22−22−2i2−i2i2−i2i2−i2i2−i2000-222i−2i00−i2i200002−2−22−2200000000000000
χ522-22-22-22-22−2i2i−2i2i00-2-20020000−2i2i−i2i2−i2i22−22−2−i2i2−i2i2−i2i2−i2i20002-2−2i2i00−i2i200002−22−22−200000000000000
χ532-22-22-22-2-22i−2i2i−2i002200-20000−2i2ii2−i2i2−i22−22−22−22−2−22−2202-200002i−2i−i2i20000−22−i2i2i2−i200000000000000
χ542-22-22-22-2-22i−2i2i−2i002200-20000−2i2ii2−i2i2−i22−22−2−22−222−22−20-220000−2i2i−i2i20000−22i2−i2−i2i200000000000000
χ552-22-22-22-2-22i−2i2i−2i002200-20000−2i2i−i2i2−i2i2−22−222−22−2−22−220-220000−2i2ii2−i200002−2−i2i2i2−i200000000000000
χ562-22-22-22-2-22i−2i2i−2i002200-20000−2i2i−i2i2−i2i2−22−22−22−222−22−202-200002i−2ii2−i200002−2i2−i2−i2i200000000000000
χ572-22-22-22-2-2−2i2i−2i2i002200-200002i−2ii2−i2i2−i2−22−222−22−2−22−220-2200002i−2i−i2i200002−2i2−i2−i2i200000000000000
χ582-22-22-22-2-2−2i2i−2i2i002200-200002i−2ii2−i2i2−i2−22−22−22−222−22−202-20000−2i2i−i2i200002−2−i2i2i2−i200000000000000
χ592-22-22-22-2-2−2i2i−2i2i002200-200002i−2i−i2i2−i2i22−22−22−22−2−22−2202-20000−2i2ii2−i20000−22i2−i2−i2i200000000000000
χ602-22-22-22-2-2−2i2i−2i2i002200-200002i−2i−i2i2−i2i22−22−2−22−222−22−20-2200002i−2ii2−i20000−22−i2i2i2−i200000000000000
χ61444-4-4-4-444000000-4400-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ62444-4-4-4-444000000-4400-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ63444-4-4-4-44-40000004-40040000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ64444-4-4-4-44-40000004-400400000000000000−222222−2222−22−222200000000000000000000000000000000000
χ6544-4-4-444-404i4i−4i−4i-4400-44000−4i4i00000000000000000000000000000000000000000000000000000
χ6644-4-4-444-40−4i−4i4i4i-4400-440004i−4i00000000000000000000000000000000000000000000000000000
χ674-444-44-4-440000444-4-4-4-4-440000000000000000000000000000000000000000000000000000000
χ684-444-44-4-4-40000-4-4-44444-440000000000000000000000000000000000000000000000000000000
χ694-4-44-4-44404-4-44000000000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ704-4-44-4-44404-4-440000000000000−222222−22−222222−220000000000000000000000000000000000000000000
χ714-4-44-4-4440-444-4000000000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ724-4-44-4-4440-444-40000000000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ734-4-4-444-44000004-400-44000000000000000000000000000000000022−22−222200000000000000000000
χ744-4-4-444-44000004-400-440000000000000000000000000000000000−222222−2200000000000000000000
χ754-4-4-444-4400000-44004-40000000000000000000000000000000000000000000022−22−22220000000000
χ764-4-4-444-4400000-44004-400000000000000000000000000000000000000000000−222222−220000000000
χ7788-888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000

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