Finite Group Databasebeta

← Group #316779

Character table — Group #316779

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888822444444888888884444444488888888
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
χ911111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1722222222222222-2-2-2-2220000000022-2-2-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-2-2220000000022-2-2-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-2-22222-2-222222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ20222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-222-2-2-2-22200000000-2-22222-2-200000000000022-2-2-2-222000000000000000000000000
χ2422222222-2-2-2-222-2-2-2-22200000000-2-22222-2-2000000000000-2-22222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-22222-2-22222222222-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ292222-2-2-2-222-2-2220000-2-22222−2−2−2−22-200000022−2−222−2−222−2−22-22-200002−22−22−22−20000000000000000
χ302222-2-2-2-222-2-2220000-2-22222−2−2−2−22-200000022−2−222−2−222−2−2-22-220000−22−22−22−220000000000000000
χ312222-2-2-2-222-2-2220000-2-2−2−2−2−222222-2000000−2−222−2−222−2−2222-22-20000−22−22−22−220000000000000000
χ322222-2-2-2-222-2-2220000-2-2−2−2−2−222222-2000000−2−222−2−222−2−222-22-2200002−22−22−22−20000000000000000
χ332222-2-2-2-222-2-2-2-20000222222−2−2−2−2-2200000022−2−2−2−222−2−22200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ342222-2-2-2-222-2-2-2-20000222222−2−2−2−2-2200000022−2−2−2−222−2−2220000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ352222-2-2-2-222-2-2-2-2000022−2−2−2−22222-22000000−2−22222−2−222−2−200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ362222-2-2-2-222-2-2-2-2000022−2−2−2−22222-22000000−2−22222−2−222−2−20000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ372222-2-2-2-2-2-222220000-2-22222−2−2−2−2-22000000−2−222−2−22222−2−22-2-2200002−22−2−22−220000000000000000
χ382222-2-2-2-2-2-222220000-2-22222−2−2−2−2-22000000−2−222−2−22222−2−2-222-20000−22−222−22−20000000000000000
χ392222-2-2-2-2-2-222220000-2-2−2−2−2−22222-2200000022−2−222−2−2−2−2222-2-220000−22−222−22−20000000000000000
χ402222-2-2-2-2-2-222220000-2-2−2−2−2−22222-2200000022−2−222−2−2−2−222-222-200002−22−2−22−220000000000000000
χ412222-2-2-2-2-2-222-2-20000222222−2−2−2−22-2000000−2−22222−2−2−2−22200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ422222-2-2-2-2-2-222-2-20000222222−2−2−2−22-2000000−2−22222−2−2−2−2220000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ432222-2-2-2-2-2-222-2-2000022−2−2−2−222222-200000022−2−2−2−22222−2−200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ442222-2-2-2-2-2-222-2-2000022−2−2−2−222222-200000022−2−2−2−22222−2−20000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ4522-2-22-22-22i−2i2i−2i002-22-20022-2-222-2-2002i−2i00002i−2i2i−2i000000000000000000000000000000002−2i2−i22−2i2−i2
χ4622-2-22-22-22i−2i2i−2i002-22-20022-2-222-2-2002i−2i00002i−2i2i−2i00000000000000000000000000000000−22−i2i2−22−i2i2
χ4722-2-22-22-22i−2i2i−2i002-22-200-2-222-2-222002i−2i0000−2i2i−2i2i000000000000000000000000000000002−2i2−i2−22−i2i2
χ4822-2-22-22-22i−2i2i−2i002-22-200-2-222-2-222002i−2i0000−2i2i−2i2i00000000000000000000000000000000−22−i2i22−2i2−i2
χ4922-2-22-22-2−2i2i−2i2i002-22-20022-2-222-2-200−2i2i0000−2i2i−2i2i000000000000000000000000000000002−2−i2i22−2−i2i2
χ5022-2-22-22-2−2i2i−2i2i002-22-20022-2-222-2-200−2i2i0000−2i2i−2i2i00000000000000000000000000000000−22i2−i2−22i2−i2
χ5122-2-22-22-2−2i2i−2i2i002-22-200-2-222-2-22200−2i2i00002i−2i2i−2i000000000000000000000000000000002−2−i2i2−22i2−i2
χ5222-2-22-22-2−2i2i−2i2i002-22-200-2-222-2-22200−2i2i00002i−2i2i−2i00000000000000000000000000000000−22i2−i22−2−i2i2
χ532-2-22-2-22200002-222-2-22-22i−2i2i−2i2i−2i2i−2i0000002-2000000002i−2i2i−2i0000000000000000002i−2i2-20000000000
χ542-2-22-2-22200002-222-2-22-22i−2i2i−2i2i−2i2i−2i0000002-2000000002i−2i2i−2i000000000000000000−2i2i-220000000000
χ552-2-22-2-22200002-222-2-22-2−2i2i−2i2i−2i2i−2i2i0000002-200000000−2i2i−2i2i0000000000000000002i−2i-220000000000
χ562-2-22-2-22200002-222-2-22-2−2i2i−2i2i−2i2i−2i2i0000002-200000000−2i2i−2i2i000000000000000000−2i2i2-20000000000
χ572-2-22-2-2220000-2222-2-2-222i−2i2i−2i2i−2i2i−2i000000-2200000000−2i2i−2i2i00000000000000002i−2i00002-200000000
χ582-2-22-2-2220000-2222-2-2-222i−2i2i−2i2i−2i2i−2i000000-2200000000−2i2i−2i2i0000000000000000−2i2i0000-2200000000
χ592-2-22-2-2220000-2222-2-2-22−2i2i−2i2i−2i2i−2i2i000000-22000000002i−2i2i−2i00000000000000002i−2i0000-2200000000
χ602-2-22-2-2220000-2222-2-2-22−2i2i−2i2i−2i2i−2i2i000000-22000000002i−2i2i−2i0000000000000000−2i2i00002-200000000
χ6144-4-44-44-44i−4i4i−4i00-44-44000000000000−4i4i000000000000000000000000000000000000000000000000
χ6244-4-44-44-4−4i4i−4i4i00-44-440000000000004i−4i000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i−4i−4i4i000000002222−22−22−22−222222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6444-4-4-44-444i−4i−4i4i00000000−22−2222222222−22−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6544-4-4-44-44−4i4i4i−4i000000002222−22−22−22−22222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6644-4-4-44-44−4i4i4i−4i00000000−22−2222222222−22−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ674-44-44-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i200004-40000002i2−2i22i2−2i2000000000000000000000000000000000000
χ684-44-44-4-440000000000002i2−2i2−2i22i2−2i22i22i2−2i20000-44000000−2i22i2−2i22i2000000000000000000000000000000000000
χ694-44-44-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i200004-4000000−2i22i2−2i22i2000000000000000000000000000000000000
χ704-44-44-4-44000000000000−2i22i22i2−2i22i2−2i2−2i22i20000-440000002i2−2i22i2−2i2000000000000000000000000000000000000
χ714-44-4-444-40000004-4-44004i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ724-44-4-444-40000004-4-4400−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ734-44-4-444-4000000-444-400000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ744-44-4-444-4000000-444-40000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ754-4-4444-4-400004-40000-442i2−2i22i2−2i2−2i22i2−2i22i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ764-4-4444-4-400004-40000-44−2i22i2−2i22i22i2−2i22i2−2i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ774-4-4444-4-40000-4400004-42i2−2i22i2−2i2−2i22i2−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ784-4-4444-4-40000-4400004-4−2i22i2−2i22i22i2−2i22i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ794-4-44-4-44400004-4-4-4444-400000000000000-4400000000000000000000000000000000000000000000
χ804-4-44-4-4440000-44-4-444-44000000000000004-400000000000000000000000000000000000000000000

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