Finite Group Databasebeta

← Group #500085

Character table — Group #500085

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222222244448888888822444444888888888888161616161616161616161616161616164444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ6111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-111
χ8111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1
χ911111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1
χ1011111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111111
χ1111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-11111
χ1211111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ1311111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1511111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-20000000022-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ192222222222222222-2-2-2-20000000022-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-200000000-2-222-2-22200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2522222222-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ292222-2-2-2-222-2-222-2-200002222−2−2−2−22-200000022−2−222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ302222-2-2-2-222-2-222-2-200002222−2−2−2−22-200000022−2−222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ312222-2-2-2-222-2-222-2-20000−2−2−2−222222-2000000−2−222−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ322222-2-2-2-222-2-222-2-20000−2−2−2−222222-2000000−2−222−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ332222-2-2-2-222-2-2-2-22200002222−2−2−2−2-2200000022−2−2−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ342222-2-2-2-222-2-2-2-22200002222−2−2−2−2-2200000022−2−2−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ352222-2-2-2-222-2-2-2-2220000−2−2−2−22222-22000000−2−22222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ362222-2-2-2-222-2-2-2-2220000−2−2−2−22222-22000000−2−22222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ372222-2-2-2-2-2-22222-2-200002222−2−2−2−2-22000000−2−22222−2−2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ382222-2-2-2-2-2-22222-2-200002222−2−2−2−2-22000000−2−22222−2−2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ392222-2-2-2-2-2-22222-2-20000−2−2−2−22222-2200000022−2−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ402222-2-2-2-2-2-22222-2-20000−2−2−2−22222-2200000022−2−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ412222-2-2-2-2-2-222-2-22200002222−2−2−2−22-2000000−2−222−2−22222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ422222-2-2-2-2-2-222-2-22200002222−2−2−2−22-2000000−2−222−2−22222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ432222-2-2-2-2-2-222-2-2220000−2−2−2−222222-200000022−2−222−2−2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000000000000000
χ442222-2-2-2-2-2-222-2-2220000−2−2−2−222222-200000022−2−222−2−2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000000000000000
χ4522-2-22-22-200002-22-22-2-2222-2-222-2-200002-20000002-22-200000000000000000000002i−2i0000002i−2i0000
χ4622-2-22-22-200002-22-22-2-2222-2-222-2-200002-20000002-22-20000000000000000000000−2i2i000000−2i2i0000
χ4722-2-22-22-200002-22-22-2-22-2-222-2-22200002-2000000-22-22000000000000000000002i−2i0000002i−2i000000
χ4822-2-22-22-200002-22-22-2-22-2-222-2-22200002-2000000-22-2200000000000000000000−2i2i000000−2i2i000000
χ4922-2-22-22-20000-22-222-2-2222-2-222-2-20000-22000000-22-2200000000000000000000002i−2i000000−2i2i0000
χ5022-2-22-22-20000-22-222-2-2222-2-222-2-20000-22000000-22-220000000000000000000000−2i2i0000002i−2i0000
χ5122-2-22-22-20000-22-222-2-22-2-222-2-2220000-220000002-22-2000000000000000000002i−2i000000−2i2i000000
χ5222-2-22-22-20000-22-222-2-22-2-222-2-2220000-220000002-22-200000000000000000000−2i2i0000002i−2i000000
χ532-22-2-2-2222-22-20000-22-222-22-22-22-2002-200002-22-20000000000000000000000000000002-20000002-2
χ542-22-2-2-2222-22-20000-22-222-22-22-22-2002-200002-22-2000000000000000000000000000000-22000000-22
χ552-22-2-2-2222-22-20000-22-22-22-22-22-22002-20000-22-2200000000000000000000000000002-20000002-200
χ562-22-2-2-2222-22-20000-22-22-22-22-22-22002-20000-22-220000000000000000000000000000-22000000-2200
χ572-22-2-2-222-22-220000-22-222-22-22-22-200-220000-22-220000000000000000000000000000002-2000000-22
χ582-22-2-2-222-22-220000-22-222-22-22-22-200-220000-22-22000000000000000000000000000000-220000002-2
χ592-22-2-2-222-22-220000-22-22-22-22-22-2200-2200002-22-200000000000000000000000000002-2000000-2200
χ602-22-2-2-222-22-220000-22-22-22-22-22-2200-2200002-22-20000000000000000000000000000-220000002-200
χ6144-4-44-44-400004-44-4-444-4000000000000-440000000000000000000000000000000000000000000000
χ6244-4-44-44-40000-44-44-444-40000000000004-40000000000000000000000000000000000000000000000
χ6344-4-4-44-4400004-4-4400002222−22−22−22−22222200000000000022−22−2222000000000000000000000000000000000000
χ6444-4-4-44-4400004-4-440000−22−2222222222−22−22000000000000−222222−22000000000000000000000000000000000000
χ6544-4-4-44-440000-444-400002222−22−22−22−222222000000000000−222222−22000000000000000000000000000000000000
χ6644-4-4-44-440000-444-40000−22−2222222222−22−2200000000000022−22−2222000000000000000000000000000000000000
χ674-44-444-4-44-4-440000000022−2222−22−2222−22220000000022−22−22220000000000000000000000000000000000000000
χ684-44-444-4-44-4-4400000000−2222−222222−2222−2200000000−222222−220000000000000000000000000000000000000000
χ694-44-444-4-4-444-40000000022−2222−22−2222−222200000000−222222−220000000000000000000000000000000000000000
χ704-44-444-4-4-444-400000000−2222−222222−2222−220000000022−22−22220000000000000000000000000000000000000000
χ714-44-4-4-4444-44-400004-44-40000000000-44000000000000000000000000000000000000000000000000
χ724-44-4-4-444-44-4400004-44-400000000004-4000000000000000000000000000000000000000000000000
χ734-4-444-4-4400000000000022−22−2222−222222−220000004i−4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ744-4-444-4-4400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ754-4-444-4-44000000000000−222222−2222−22−22220000004i−4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ764-4-444-4-44000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ774-4-44-444-40000000044-4-40000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ784-4-44-444-40000000044-4-4000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ794-4-44-444-400000000-4-4444-4-444-4-440000000000000000000000000000000000000000000000000000
χ804-4-44-444-400000000-4-444-444-4-444-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.