Finite Group Databasebeta

← Group #286713

Character table — Group #286713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888884444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
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
χ911111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-11
χ172222222222222-222-2-22-2-2-222-2-20000000000000000-222-2-222-2-200000000000000000000000000
χ182222222222222-222-2-22-2-2-222-2-20000000000000000-2-2-222-2-22200000000000000000000000000
χ19222222222222-22-2-222-22-2-2-2-2220000000022222222-200000000-2-200000000-2-200000000000000
χ20222222222222-22-2-222-22-2-2-2-22200000000-2-2-2-2-2-2-2-2-20000000022000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000002000000000000002i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-2−2i−2i−2i−2i2i2i2i2i00000000200000000000000−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22-222-2-22-2-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ2422222222-2-2-2-22-222-2-22-2-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ2522222222-2-2-2-2-22-2-222-22-2-222-2-2000000002222-2-2-2-22000000002200000000-2-200000000000000
χ2622222222-2-2-2-2-22-2-222-22-2-222-2-200000000-2-2-2-22222200000000-2-2000000002200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i00000000-200000000000000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i00000000-2000000000000002i2i−2i−2i0000000000000000
χ2922-2-2-22-2200002-22-22-2-222-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000002i2i−2i−2i002-2000000
χ3022-2-2-22-2200002-22-22-2-222-200002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000−2i−2i2i2i00-22000000
χ3122-2-2-22-2200002-22-22-2-222-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000002i2i−2i−2i00-22000000
χ3222-2-2-22-2200002-22-22-2-222-20000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000−2i−2i2i2i002-2000000
χ3322-2-2-22-220000-22-22-222-22-2000022-2-2-2-22200000000000000000002i2i−2i−2i00000000002i−2i00000000
χ3422-2-2-22-220000-22-22-222-22-2000022-2-2-2-2220000000000000000000−2i−2i2i2i0000000000−2i2i00000000
χ3522-2-2-22-220000-22-22-222-22-20000-2-22222-2-200000000000000000002i2i−2i−2i0000000000−2i2i00000000
χ3622-2-2-22-220000-22-22-222-22-20000-2-22222-2-20000000000000000000−2i−2i2i2i00000000002i−2i00000000
χ372-222-2-2-222i2i−2i−2i0-200220-200002i−2i0000000022-2-22i2i−2i−2i00000000000i2−i2i2−i20000002−22−20000i2−i22−200
χ382-222-2-2-222i2i−2i−2i0-200220-200002i−2i0000000022-2-22i2i−2i−2i00000000000−i2i2−i2i2000000−22−220000−i2i2−2200
χ392-222-2-2-222i2i−2i−2i0-200220-200002i−2i00000000-2-222−2i−2i2i2i00000000000i2−i2i2−i20000002−22−20000−i2i2−2200
χ402-222-2-2-222i2i−2i−2i0-200220-200002i−2i00000000-2-222−2i−2i2i2i00000000000−i2i2−i2i2000000−22−220000i2−i22−200
χ412-222-2-2-22−2i−2i2i2i0-200220-20000−2i2i0000000022-2-2−2i−2i2i2i00000000000i2−i2i2−i2000000−22−220000i2−i2−2200
χ422-222-2-2-22−2i−2i2i2i0-200220-20000−2i2i0000000022-2-2−2i−2i2i2i00000000000−i2i2−i2i20000002−22−20000−i2i22−200
χ432-222-2-2-22−2i−2i2i2i0-200220-20000−2i2i00000000-2-2222i2i−2i−2i00000000000i2−i2i2−i2000000−22−220000−i2i22−200
χ442-222-2-2-22−2i−2i2i2i0-200220-20000−2i2i00000000-2-2222i2i−2i−2i00000000000−i2i2−i2i20000002−22−20000i2−i2−2200
χ452-22-2-222-22i−2i2i−2i20-2-20020002i−2i00i2−i2i2−i2i2−i2i2−i22−22−2i2−i2i2−i20002i−2i002-2i2−i200002−22−22−200000000000000
χ462-22-2-222-22i−2i2i−2i20-2-20020002i−2i00i2−i2i2−i2i2−i2i2−i2−22−22−i2i2−i2i2000−2i2i00-22−i2i200002−22−2−2200000000000000
χ472-22-2-222-22i−2i2i−2i20-2-20020002i−2i00−i2i2−i2i2−i2i2−i2i22−22−2i2−i2i2−i2000−2i2i00-22i2−i20000−22−222−200000000000000
χ482-22-2-222-22i−2i2i−2i20-2-20020002i−2i00−i2i2−i2i2−i2i2−i2i2−22−22−i2i2−i2i20002i−2i002-2−i2i20000−22−22−2200000000000000
χ492-22-2-222-22i−2i2i−2i-202200-2000−2i2i002−22−2−22−222−22−2i2−i2i2−i202-2002i−2i00−i2i20000−i2i2i2−i2−2200000000000000
χ502-22-2-222-22i−2i2i−2i-202200-2000−2i2i002−22−2−22−22−22−22−i2i2−i2i20-2200−2i2i00i2−i20000−i2i2i2−i22−200000000000000
χ512-22-2-222-22i−2i2i−2i-202200-2000−2i2i00−22−222−22−22−22−2i2−i2i2−i20-2200−2i2i00−i2i20000i2−i2−i2i2−2200000000000000
χ522-22-2-222-22i−2i2i−2i-202200-2000−2i2i00−22−222−22−2−22−22−i2i2−i2i202-2002i−2i00i2−i20000i2−i2−i2i22−200000000000000
χ532-22-2-222-2−2i2i−2i2i20-2-2002000−2i2i00i2−i2i2−i2i2−i2i2−i22−22−2−i2i2−i2i20002i−2i00-22−i2i20000−22−222−200000000000000
χ542-22-2-222-2−2i2i−2i2i20-2-2002000−2i2i00i2−i2i2−i2i2−i2i2−i2−22−22i2−i2i2−i2000−2i2i002-2i2−i20000−22−22−2200000000000000
χ552-22-2-222-2−2i2i−2i2i20-2-2002000−2i2i00−i2i2−i2i2−i2i2−i2i22−22−2−i2i2−i2i2000−2i2i002-2−i2i200002−22−22−200000000000000
χ562-22-2-222-2−2i2i−2i2i20-2-2002000−2i2i00−i2i2−i2i2−i2i2−i2i2−22−22i2−i2i2−i20002i−2i00-22i2−i200002−22−2−2200000000000000
χ572-22-2-222-2−2i2i−2i2i-202200-20002i−2i002−22−2−22−222−22−2−i2i2−i2i202-200−2i2i00i2−i20000i2−i2−i2i2−2200000000000000
χ582-22-2-222-2−2i2i−2i2i-202200-20002i−2i002−22−2−22−22−22−22i2−i2i2−i20-22002i−2i00−i2i20000i2−i2−i2i22−200000000000000
χ592-22-2-222-2−2i2i−2i2i-202200-20002i−2i00−22−222−22−22−22−2−i2i2−i2i20-22002i−2i00i2−i20000−i2i2i2−i2−2200000000000000
χ602-22-2-222-2−2i2i−2i2i-202200-20002i−2i00−22−222−22−2−22−22i2−i2i2−i202-200−2i2i00−i2i20000−i2i2i2−i22−200000000000000
χ61444-44-4-4-44-4-44000000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ62444-44-4-4-44-4-440000000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ63444-44-4-4-4-444-4000000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ64444-44-4-4-4-444-40000000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ6544-4-4-44-440000444-4-44-4-4-440000000000000000000000000000000000000000000000000000000
χ6644-4-4-44-440000-4-4-444-444-440000000000000000000000000000000000000000000000000000000
χ674-444-4-4-444i4i−4i−4i0400-4-4040000−4i4i000000000000000000000000000000000000000000000000000
χ684-444-4-4-44−4i−4i4i4i0400-4-40400004i−4i000000000000000000000000000000000000000000000000000
χ694-4-4444-4-4000040-4400-4000000022−22−222222−22−22220000000000000000000000000000000000000000000
χ704-4-4444-4-4000040-4400-40000000−222222−22−222222−220000000000000000000000000000000000000000000
χ714-4-4444-4-40000-404-400400000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ724-4-4444-4-40000-404-40040000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ734-4-4-44-444000004004-40-400000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ744-4-4-44-444000004004-40-40000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ754-4-4-44-44400000-400-440400000000000000000000000000000000022−22−222200000000000000000000
χ764-4-4-44-44400000-400-4404000000000000000000000000000000000−222222−2200000000000000000000
χ7788-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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