Finite Group Databasebeta

← Group #314705

Character table — Group #314705

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
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1
χ10111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ11111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-111-1-111
χ12111111111-1-1-1-1111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-111-1-1
χ13111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ14111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ15111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ16111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-111
χ17222222222222222-2-2-2-222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2222222222-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
χ2122222222-22222-2-22222-200000000-2-2-2-222-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-22222-2-22222-200000000-2-2-2-222-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-22222-2-2-2-2-2-2-200000000-2-222-2-222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-22222-2-2-2-2-2-2-200000000-2-222-2-22200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000000022-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000000022-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-2-200002-222-2-222222-2-2-2-2002-20000000022-2-200000000000000000000002i−2i002i−2i00000000
χ302222-2-2-2-2-200002-222-2-222222-2-2-2-2002-20000000022-2-20000000000000000000000−2i2i00−2i2i00000000
χ312222-2-2-2-2-200002-222-2-22-2-2-2-22222002-200000000-2-22200000000000000000000002i−2i00−2i2i00000000
χ322222-2-2-2-2-200002-222-2-22-2-2-2-22222002-200000000-2-2220000000000000000000000−2i2i002i−2i00000000
χ332222-2-2-2-2-200002-2-2-22222222-2-2-2-200-2200000000-2-222000000000000000000002i−2i002i−2i0000000000
χ342222-2-2-2-2-200002-2-2-22222222-2-2-2-200-2200000000-2-22200000000000000000000−2i2i00−2i2i0000000000
χ352222-2-2-2-2-200002-2-2-2222-2-2-2-2222200-220000000022-2-2000000000000000000002i−2i00−2i2i0000000000
χ362222-2-2-2-2-200002-2-2-2222-2-2-2-2222200-220000000022-2-200000000000000000000−2i2i002i−2i0000000000
χ3722-2-222-2-2-222-2-2-22000022i2i−2i−2i2i2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ3822-2-222-2-2-222-2-2-22000022i2i−2i−2i2i2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ3922-2-222-2-2-222-2-2-2200002−2i−2i2i2i−2i−2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ4022-2-222-2-2-222-2-2-2200002−2i−2i2i2i−2i−2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ4122-2-222-2-2-2-2-222-22000022i2i−2i−2i2i2i−2i−2i-22000000−2i−2i2i2i00000000000000000000000000000000i2−i2−i2i22−2−22
χ4222-2-222-2-2-2-2-222-22000022i2i−2i−2i2i2i−2i−2i-22000000−2i−2i2i2i00000000000000000000000000000000−i2i2i2−i2−222−2
χ4322-2-222-2-2-2-2-222-2200002−2i−2i2i2i−2i−2i2i2i-220000002i2i−2i−2i00000000000000000000000000000000i2−i2−i2i2−222−2
χ4422-2-222-2-2-2-2-222-2200002−2i−2i2i2i−2i−2i2i2i-220000002i2i−2i−2i00000000000000000000000000000000−i2i2i2−i22−2−22
χ452-22-22-22-202i−2i2i−2i002-22-20i2−i2i2−i2i2−i2i2−i200002i−2i002−22−2i2−i2i2−i222−2−2002i−2i002-2i2−i2i2−i22−22−20000000000000000
χ462-22-22-22-202i−2i2i−2i002-22-20i2−i2i2−i2i2−i2i2−i200002i−2i002−22−2i2−i2i2−i222−2−200−2i2i00-22−i2i2−i2i2−22−220000000000000000
χ472-22-22-22-202i−2i2i−2i002-22-20−i2i2−i2i2−i2i2−i2i200002i−2i00−22−22−i2i2−i2i2−2−222002i−2i002-2−i2i2−i2i2−22−220000000000000000
χ482-22-22-22-202i−2i2i−2i002-22-20−i2i2−i2i2−i2i2−i2i200002i−2i00−22−22−i2i2−i2i2−2−22200−2i2i00-22i2−i2i2−i22−22−20000000000000000
χ492-22-22-22-202i−2i2i−2i00-22-220i2−i2i2−i2i2−i2i2−i20000−2i2i002−22−2−i2i2−i2i2−2−2222-2002i−2i002−2−22−i2i2i2−i20000000000000000
χ502-22-22-22-202i−2i2i−2i00-22-220i2−i2i2−i2i2−i2i2−i20000−2i2i002−22−2−i2i2−i2i2−2−222-2200−2i2i00−222−2i2−i2−i2i20000000000000000
χ512-22-22-22-202i−2i2i−2i00-22-220−i2i2−i2i2−i2i2−i2i20000−2i2i00−22−22i2−i2i2−i222−2−22-2002i−2i00−222−2i2−i2−i2i20000000000000000
χ522-22-22-22-202i−2i2i−2i00-22-220−i2i2−i2i2−i2i2−i2i20000−2i2i00−22−22i2−i2i2−i222−2−2-2200−2i2i002−2−22−i2i2i2−i20000000000000000
χ532-22-22-22-20−2i2i−2i2i002-22-20i2−i2i2−i2i2−i2i2−i20000−2i2i00−22−22i2−i2i2−i2−2−222002i−2i00-22−i2i2−i2i22−22−20000000000000000
χ542-22-22-22-20−2i2i−2i2i002-22-20i2−i2i2−i2i2−i2i2−i20000−2i2i00−22−22i2−i2i2−i2−2−22200−2i2i002-2i2−i2i2−i2−22−220000000000000000
χ552-22-22-22-20−2i2i−2i2i002-22-20−i2i2−i2i2−i2i2−i2i20000−2i2i002−22−2−i2i2−i2i222−2−2002i−2i00-22i2−i2i2−i2−22−220000000000000000
χ562-22-22-22-20−2i2i−2i2i002-22-20−i2i2−i2i2−i2i2−i2i20000−2i2i002−22−2−i2i2−i2i222−2−200−2i2i002-2−i2i2−i2i22−22−20000000000000000
χ572-22-22-22-20−2i2i−2i2i00-22-220i2−i2i2−i2i2−i2i2−i200002i−2i00−22−22−i2i2−i2i222−2−22-200−2i2i00−222−2−i2i2i2−i20000000000000000
χ582-22-22-22-20−2i2i−2i2i00-22-220i2−i2i2−i2i2−i2i2−i200002i−2i00−22−22−i2i2−i2i222−2−2-22002i−2i002−2−22i2−i2−i2i20000000000000000
χ592-22-22-22-20−2i2i−2i2i00-22-220−i2i2−i2i2−i2i2−i2i200002i−2i002−22−2i2−i2i2−i2−2−2222-200−2i2i002−2−22i2−i2−i2i20000000000000000
χ602-22-22-22-20−2i2i−2i2i00-22-220−i2i2−i2i2−i2i2−i2i200002i−2i002−22−2i2−i2i2−i2−2−222-22002i−2i00−222−2−i2i2i2−i20000000000000000
χ614444-4-4-4-440000-4444-4-4-40000000000-44000000000000000000000000000000000000000000000000
χ624444-4-4-4-440000-44-4-444-400000000004-4000000000000000000000000000000000000000000000000
χ6344-4-444-4-4444-4-44-40000-400000000-4400000000000000000000000000000000000000000000000000
χ6444-4-444-4-44-4-4444-40000-4000000004-400000000000000000000000000000000000000000000000000
χ6544-4-4-4-44440000-4-4000044i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ6644-4-4-4-44440000-4-400004−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ6744-4-4-4-444-40000440000-40000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6844-4-4-4-444-40000440000-4000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ694-44-4-44-4400000004-4-4402i2−2i22i2−2i2−2i22i2−2i22i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ704-44-4-44-4400000004-4-440−2i22i2−2i22i22i2−2i22i2−2i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ714-44-4-44-440000000-444-402i2−2i22i2−2i2−2i22i2−2i22i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ724-44-4-44-440000000-444-40−2i22i2−2i22i22i2−2i22i2−2i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-4-444-4-4404i−4i−4i4i000000022−22−222222−22−222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ744-4-444-4-4404i−4i−4i4i0000000−222222−22−222222−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ754-4-444-4-440−4i4i4i−4i000000022−22−222222−22−2222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ764-4-444-4-440−4i4i4i−4i0000000−222222−22−222222−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ774-4-44-444-400000000000022−22−2222−222222−220000004i−4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ784-4-44-444-400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ794-4-44-444-4000000000000−222222−2222−22−22220000004i−4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ804-4-44-444-4000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i2−2i22i200000000000000000000000000000000

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