Finite Group Databasebeta

← Group #507607

Character table — Group #507607

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888844444444888888888888161616161616161616161616161616164444444444444444
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
χ5111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-200000000-2-2-2-222-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ192222222222222222-2-2-2-200000000-2-2-2-222-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000000022-2-2-2-22200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000000022-2-2-2-222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
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
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000
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
χ29222-22-2-2-2000022-2-222-2-22222-2-2-2-22-2000000000022-2-20000000000000000000000000000002-2002-2
χ30222-22-2-2-2000022-2-222-2-22222-2-2-2-22-2000000000022-2-2000000000000000000000000000000-2200-22
χ31222-22-2-2-2000022-2-222-2-2-2-2-2-222222-20000000000-2-22200000000000000000000000000002i−2i002i−2i00
χ32222-22-2-2-2000022-2-222-2-2-2-2-2-222222-20000000000-2-2220000000000000000000000000000−2i2i00−2i2i00
χ33222-22-2-2-20000-2-22222-2-22222-2-2-2-2-220000000000-2-2220000000000000000000000000000002-200-22
χ34222-22-2-2-20000-2-22222-2-22222-2-2-2-2-220000000000-2-222000000000000000000000000000000-22002-2
χ35222-22-2-2-20000-2-22222-2-2-2-2-2-22222-22000000000022-2-200000000000000000000000000002i−2i00−2i2i00
χ36222-22-2-2-20000-2-22222-2-2-2-2-2-22222-22000000000022-2-20000000000000000000000000000−2i2i002i−2i00
χ3722-22-22-2-222-2-200002-22-222-2-222-2-2002-2000022-2-200000000000000000000000000002-22-200000000
χ3822-22-22-2-222-2-200002-22-222-2-222-2-2002-2000022-2-20000000000000000000000000000-22-2200000000
χ3922-22-22-2-222-2-200002-22-2-2-222-2-222002-20000-2-2220000000000000000000000002i−2i2i−2i000000000000
χ4022-22-22-2-222-2-200002-22-2-2-222-2-222002-20000-2-222000000000000000000000000−2i2i−2i2i000000000000
χ4122-22-22-2-2-2-22200002-22-222-2-222-2-200-220000-2-22200000000000000000000000000002-2-2200000000
χ4222-22-22-2-2-2-22200002-22-222-2-222-2-200-220000-2-2220000000000000000000000000000-222-200000000
χ4322-22-22-2-2-2-22200002-22-2-2-222-2-22200-22000022-2-20000000000000000000000002i−2i−2i2i000000000000
χ4422-22-22-2-2-2-22200002-22-2-2-222-2-22200-22000022-2-2000000000000000000000000−2i2i2i−2i000000000000
χ452-2-222-22-22-22-22-22-200002−22−22−22−200002-2002−22−22−22−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ462-2-222-22-22-22-22-22-200002−22−22−22−200002-2002−22−22−22−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ472-2-222-22-22-22-22-22-20000−22−22−22−2200002-200−22−22−22−22−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ482-2-222-22-22-22-22-22-20000−22−22−22−2200002-200−22−22−22−22−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ492-2-222-22-22-22-2-22-2200002−22−22−22−20000-22002−22−2−22−22−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ502-2-222-22-22-22-2-22-2200002−22−22−22−20000-22002−22−2−22−22−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ512-2-222-22-22-22-2-22-220000−22−22−22−220000-2200−22−222−22−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ522-2-222-22-22-22-2-22-220000−22−22−22−220000-2200−22−222−22−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ532-2-222-22-2-22-222-22-200002−22−22−22−20000-2200−22−222−22−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ542-2-222-22-2-22-222-22-200002−22−22−22−20000-2200−22−222−22−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ552-2-222-22-2-22-222-22-20000−22−22−22−220000-22002−22−2−22−2222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ562-2-222-22-2-22-222-22-20000−22−22−22−220000-22002−22−2−22−2222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ572-2-222-22-2-22-22-22-2200002−22−22−22−200002-200−22−22−22−2222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ582-2-222-22-2-22-22-22-2200002−22−22−22−200002-200−22−22−22−2222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ592-2-222-22-2-22-22-22-220000−22−22−22−2200002-2002−22−22−22−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ602-2-222-22-2-22-22-22-220000−22−22−22−2200002-2002−22−22−22−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ61444-44-4-4-4000044-4-4-4-44400000000-4400000000000000000000000000000000000000000000000000
χ62444-44-4-4-40000-4-444-4-444000000004-400000000000000000000000000000000000000000000000000
χ6344-44-44-4-444-4-40000-44-440000000000-44000000000000000000000000000000000000000000000000
χ6444-44-44-4-4-4-4440000-44-4400000000004-4000000000000000000000000000000000000000000000000
χ6544-4-4-4-444000000004-4-4444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ6644-4-4-4-444000000004-4-44-4-44444-4-40000000000000000000000000000000000000000000000000000
χ6744-4-4-4-44400000000-444-40000000000000000000000004i−4i4i−4i00000000000000000000000000000000
χ6844-4-4-4-44400000000-444-4000000000000000000000000−4i4i−4i4i00000000000000000000000000000000
χ694-444-4-4-444-4-440000000022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ704-444-4-4-444-4-4400000000−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ714-444-4-4-44-444-40000000022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ724-444-4-4-44-444-400000000−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ734-44-4-444-400000000000022−22−2222−222222−220000004i−4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ744-44-4-444-400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ754-44-4-444-4000000000000−222222−2222−22−22220000004i−4i00000000−2i22i22i2−2i200000000000000000000000000000000
χ764-44-4-444-4000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i2−2i22i200000000000000000000000000000000
χ774-4-4-444-4400004-4-44000022−2222−22−2222−222200000000000022−22−2222000000000000000000000000000000000000
χ784-4-4-444-4400004-4-440000−2222−222222−2222−22000000000000−222222−22000000000000000000000000000000000000
χ794-4-4-444-440000-444-4000022−2222−22−2222−2222000000000000−222222−22000000000000000000000000000000000000
χ804-4-4-444-440000-444-40000−2222−222222−2222−2200000000000022−22−2222000000000000000000000000000000000000

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