Finite Group Databasebeta

← Group #314700

Character table — Group #314700

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888844444444888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ911111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ1011111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111
χ1111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1211111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ1311111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1411111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ17222222222-2-22222222-2-222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ18222222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ19222222222-2-2-2-2-2-2222-2-2222222222222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ20222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ2122222222-2222222-2-2-22200000000-2-222-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-2222222-2-2-22200000000-2-222-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-222-2-2-2-2-2-2-2220000000022-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ2422222222-222-2-2-2-2-2-2-2220000000022-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ2522222222-2-2-22222-2-2-2-2-20000000022-2-222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-22222-2-2-2-2-20000000022-2-222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-2-22-200002-222-22222-2-2-2-200002-200000022-2-200000000000000000000002i−2i2i−2i0000000000
χ302222-2-2-2-2-22-200002-222-22222-2-2-2-200002-200000022-2-20000000000000000000000−2i2i−2i2i0000000000
χ312222-2-2-2-2-22-200002-222-2-2-2-2-2222200002-2000000-2-22200000000000000000000002i−2i−2i2i0000000000
χ322222-2-2-2-2-22-200002-222-2-2-2-2-2222200002-2000000-2-2220000000000000000000000−2i2i2i−2i0000000000
χ332222-2-2-2-2-2-2200002-22-222222-2-2-2-20000-22000000-2-222000000000000000000002i−2i00002i−2i00000000
χ342222-2-2-2-2-2-2200002-22-222222-2-2-2-20000-22000000-2-22200000000000000000000−2i2i0000−2i2i00000000
χ352222-2-2-2-2-2-2200002-22-22-2-2-2-222220000-2200000022-2-2000000000000000000002i−2i0000−2i2i00000000
χ362222-2-2-2-2-2-2200002-22-22-2-2-2-222220000-2200000022-2-200000000000000000000−2i2i00002i−2i00000000
χ3722-2-2-2-2222002i2i−2i−2i-2-22002i2i−2i−2i2i2i−2i−2i0000002i−2i0000000022-2-20000000000000000000000002−2i2−i2i2−i22−2
χ3822-2-2-2-2222002i2i−2i−2i-2-22002i2i−2i−2i2i2i−2i−2i0000002i−2i0000000022-2-2000000000000000000000000−22−i2i2−i2i2−22
χ3922-2-2-2-2222002i2i−2i−2i-2-2200−2i−2i2i2i−2i−2i2i2i0000002i−2i00000000-2-2220000000000000000000000002−2i2−i2−i2i2−22
χ4022-2-2-2-2222002i2i−2i−2i-2-2200−2i−2i2i2i−2i−2i2i2i0000002i−2i00000000-2-222000000000000000000000000−22−i2i2i2−i22−2
χ4122-2-2-2-222200−2i−2i2i2i-2-22002i2i−2i−2i2i2i−2i−2i000000−2i2i00000000-2-2220000000000000000000000002−2−i2i2i2−i2−22
χ4222-2-2-2-222200−2i−2i2i2i-2-22002i2i−2i−2i2i2i−2i−2i000000−2i2i00000000-2-222000000000000000000000000−22i2−i2−i2i22−2
χ4322-2-2-2-222200−2i−2i2i2i-2-2200−2i−2i2i2i−2i−2i2i2i000000−2i2i0000000022-2-20000000000000000000000002−2−i2i2−i2i22−2
χ4422-2-2-2-222200−2i−2i2i2i-2-2200−2i−2i2i2i−2i−2i2i2i000000−2i2i0000000022-2-2000000000000000000000000−22i2−i2i2−i2−22
χ452-22-22-22-202-22i−2i2i−2i000-222−22−22−22−2002i−2i0000i2i2−i2−i22−22−2i2−i2i2−i2002i−2i002-22−22−2i2−i2i2−i20000000000000000
χ462-22-22-22-202-22i−2i2i−2i000-222−22−22−22−2002i−2i0000i2i2−i2−i22−22−2i2−i2i2−i200−2i2i00-22−22−22−i2i2−i2i20000000000000000
χ472-22-22-22-202-22i−2i2i−2i000-22−22−22−22−22002i−2i0000−i2−i2i2i2−22−22−i2i2−i2i2002i−2i002-2−22−22−i2i2−i2i20000000000000000
χ482-22-22-22-202-22i−2i2i−2i000-22−22−22−22−22002i−2i0000−i2−i2i2i2−22−22−i2i2−i2i200−2i2i00-222−22−2i2−i2i2−i20000000000000000
χ492-22-22-22-202-2−2i2i−2i2i000-222−22−22−22−200−2i2i0000−i2−i2i2i22−22−2−i2i2−i2i2002i−2i00-22−22−22i2−i2i2−i20000000000000000
χ502-22-22-22-202-2−2i2i−2i2i000-222−22−22−22−200−2i2i0000−i2−i2i2i22−22−2−i2i2−i2i200−2i2i002-22−22−2−i2i2−i2i20000000000000000
χ512-22-22-22-202-2−2i2i−2i2i000-22−22−22−22−2200−2i2i0000i2i2−i2−i2−22−22i2−i2i2−i2002i−2i00-222−22−2−i2i2−i2i20000000000000000
χ522-22-22-22-202-2−2i2i−2i2i000-22−22−22−22−2200−2i2i0000i2i2−i2−i2−22−22i2−i2i2−i200−2i2i002-2−22−22i2−i2i2−i20000000000000000
χ532-22-22-22-20-222i−2i2i−2i0002-22−22−22−22−200−2i2i0000−i2−i2i2i2−22−22i2−i2i2−i22-2002i−2i00i2−i2−i2i2−222−20000000000000000
χ542-22-22-22-20-222i−2i2i−2i0002-22−22−22−22−200−2i2i0000−i2−i2i2i2−22−22i2−i2i2−i2-2200−2i2i00−i2i2i2−i22−2−220000000000000000
χ552-22-22-22-20-222i−2i2i−2i0002-2−22−22−22−2200−2i2i0000i2i2−i2−i22−22−2−i2i2−i2i22-2002i−2i00−i2i2i2−i22−2−220000000000000000
χ562-22-22-22-20-222i−2i2i−2i0002-2−22−22−22−2200−2i2i0000i2i2−i2−i22−22−2−i2i2−i2i2-2200−2i2i00i2−i2−i2i2−222−20000000000000000
χ572-22-22-22-20-22−2i2i−2i2i0002-22−22−22−22−2002i−2i0000i2i2−i2−i2−22−22−i2i2−i2i22-200−2i2i00−i2i2i2−i2−222−20000000000000000
χ582-22-22-22-20-22−2i2i−2i2i0002-22−22−22−22−2002i−2i0000i2i2−i2−i2−22−22−i2i2−i2i2-22002i−2i00i2−i2−i2i22−2−220000000000000000
χ592-22-22-22-20-22−2i2i−2i2i0002-2−22−22−22−22002i−2i0000−i2−i2i2i22−22−2i2−i2i2−i22-200−2i2i00i2−i2−i2i22−2−220000000000000000
χ602-22-22-22-20-22−2i2i−2i2i0002-2−22−22−22−22002i−2i0000−i2−i2i2i22−22−2i2−i2i2−i2-22002i−2i00−i2i2i2−i2−222−20000000000000000
χ614444-4-4-4-444-40000-44-44-4000000000000-440000000000000000000000000000000000000000000000
χ624444-4-4-4-44-440000-44-4-440000000000004-40000000000000000000000000000000000000000000000
χ6344-4-444-4-440000004-4-40000000000000000004-44-40000000000000000000000000000000000000000
χ6444-4-444-4-440000004-4-4000000000000000000-44-440000000000000000000000000000000000000000
χ6544-4-444-4-4-4000000-444004i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ6644-4-444-4-4-4000000-44400−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-4004i4i−4i−4i44-40000000000000000−4i4i00000000000000000000000000000000000000000000
χ6844-4-4-4-444-400−4i−4i4i4i44-400000000000000004i−4i00000000000000000000000000000000000000000000
χ694-44-4-44-440440000000-4-422−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ704-44-4-44-440440000000-4-4−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ714-44-4-44-440-4-400000004422−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ724-44-4-44-440-4-4000000044−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000
χ734-4-444-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i24-40000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ744-4-444-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i2-44000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ754-4-444-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i24-4000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ764-4-444-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i2-440000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ774-4-44-444-40004-4-44000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ784-4-44-444-40004-4-4400000−2i22i22i2−2i2−2i22i22i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ794-4-44-444-4000-444-4000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ804-4-44-444-4000-444-400000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000−2i22i22i2−2i200000000000000000000000000000000

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