Finite Group Databasebeta

← Group #500086

Character table — Group #500086

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888822224444888888888888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1211111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-1111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1511111111-1-1-1-1111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-1111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-22222-200000000-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−20000000000000000
χ20222222222222-2-2-22222-200000000-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−2220000000000000000
χ21222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-200000000-2-22222-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-2-22222-200000000-2-22222-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ29222-2-22-2-200002-2-222-2-222222-2-2-2-22-2000000000022-2-200000000000000000000000000002i−2i00002i−2i
χ30222-2-22-2-200002-2-222-2-222222-2-2-2-22-2000000000022-2-20000000000000000000000000000−2i2i0000−2i2i
χ31222-2-22-2-200002-2-222-2-22-2-2-2-222222-20000000000-2-222000000000000000000000000002i−2i00002i−2i00
χ32222-2-22-2-200002-2-222-2-22-2-2-2-222222-20000000000-2-22200000000000000000000000000−2i2i0000−2i2i00
χ33222-2-22-2-200002-2-2-2-22222222-2-2-2-2-220000000000-2-22200000000000000000000000000002i−2i0000−2i2i
χ34222-2-22-2-200002-2-2-2-22222222-2-2-2-2-220000000000-2-2220000000000000000000000000000−2i2i00002i−2i
χ35222-2-22-2-200002-2-2-2-2222-2-2-2-22222-22000000000022-2-2000000000000000000000000002i−2i0000−2i2i00
χ36222-2-22-2-200002-2-2-2-2222-2-2-2-22222-22000000000022-2-200000000000000000000000000−2i2i00002i−2i00
χ3722-2-22-22-222-2-20002i−2i2i−2i022−2−222−2−20000002i−2i22−2−2i2−i2i2−i2i2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ3822-2-22-22-222-2-20002i−2i2i−2i022−2−222−2−20000002i−2i22−2−2i2−i2i2−i2i2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ3922-2-22-22-222-2-20002i−2i2i−2i0−2−222−2−2220000002i−2i−2−222−i2i2−i2i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4022-2-22-22-222-2-20002i−2i2i−2i0−2−222−2−2220000002i−2i−2−222−i2i2−i2i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4122-2-22-22-222-2-2000−2i2i−2i2i022−2−222−2−2000000−2i2i22−2−2−i2i2−i2i2−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4222-2-22-22-222-2-2000−2i2i−2i2i022−2−222−2−2000000−2i2i22−2−2−i2i2−i2i2−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4322-2-22-22-222-2-2000−2i2i−2i2i0−2−222−2−222000000−2i2i−2−222i2−i2i2−i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4422-2-22-22-222-2-2000−2i2i−2i2i0−2−222−2−222000000−2i2i−2−222i2−i2i2−i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4522-2-22-22-2-2-2220002i−2i2i−2i022−2−222−2−2000000−2i2i−2−222i2−i2i2−i2−i2−i2i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ4622-2-22-22-2-2-2220002i−2i2i−2i022−2−222−2−2000000−2i2i−2−222i2−i2i2−i2−i2−i2i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4722-2-22-22-2-2-2220002i−2i2i−2i0−2−222−2−222000000−2i2i22−2−2−i2i2−i2i2i2i2−i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ4822-2-22-22-2-2-2220002i−2i2i−2i0−2−222−2−222000000−2i2i22−2−2−i2i2−i2i2i2i2−i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ4922-2-22-22-2-2-222000−2i2i−2i2i022−2−222−2−20000002i−2i−2−222−i2i2−i2i2i2i2−i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ70000000000000000
χ5022-2-22-22-2-2-222000−2i2i−2i2i022−2−222−2−20000002i−2i−2−222−i2i2−i2i2i2i2−i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ70000000000000000
χ5122-2-22-22-2-2-222000−2i2i−2i2i0−2−222−2−2220000002i−2i22−2−2i2−i2i2−i2−i2−i2i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ5222-2-22-22-2-2-222000−2i2i−2i2i0−2−222−2−2220000002i−2i22−2−2i2−i2i2−i2−i2−i2i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ532-2-2-222-222-22-2-22-2000022-22-22-22-200002-2002-22-200000000000000000000000000002-200002-20000
χ542-2-2-222-222-22-2-22-2000022-22-22-22-200002-2002-22-20000000000000000000000000000-220000-220000
χ552-2-2-222-222-22-2-22-200002-22-22-22-2200002-200-22-220000000000000000000000002-22-2000000000000
χ562-2-2-222-222-22-2-22-200002-22-22-22-2200002-200-22-22000000000000000000000000-22-22000000000000
χ572-2-2-222-22-22-22-22-2000022-22-22-22-20000-2200-22-2200000000000000000000000000002-20000-220000
χ582-2-2-222-22-22-22-22-2000022-22-22-22-20000-2200-22-220000000000000000000000000000-2200002-20000
χ592-2-2-222-22-22-22-22-200002-22-22-22-220000-22002-22-20000000000000000000000002-2-22000000000000
χ602-2-2-222-22-22-22-22-200002-22-22-22-220000-22002-22-2000000000000000000000000-222-2000000000000
χ61444-4-44-4-40000-44444-4-4-400000000-4400000000000000000000000000000000000000000000000000
χ62444-4-44-4-40000-444-4-444-4000000004-400000000000000000000000000000000000000000000000000
χ6344-44-4-4-4400000004i−4i−4i4i02222−22−22−22−2222220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ6444-44-4-4-4400000004i−4i−4i4i0−22−2222222222−22−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6544-44-4-4-440000000−4i4i4i−4i02222−22−22−22−222222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6644-44-4-4-440000000−4i4i4i−4i0−22−2222222222−22−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ674-4444-4-4-44-4-440000000022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ684-4444-4-4-44-4-4400000000−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ694-4444-4-4-4-444-40000000022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ704-4444-4-4-4-444-400000000−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ714-44-4-4-44400000000000022−22−2222−222222−22004-400000000000022−2222−2200000000000000000000000000000000
χ724-44-4-4-44400000000000022−22−2222−222222−2200-44000000000000−2222−222200000000000000000000000000000000
χ734-44-4-4-444000000000000−222222−2222−22−2222004-4000000000000−2222−222200000000000000000000000000000000
χ744-44-4-4-444000000000000−222222−2222−22−222200-4400000000000022−2222−2200000000000000000000000000000000
χ754-4-44-444-4000044-40000-40000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ764-4-44-444-4000044-40000-4000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ774-4-44-444-40000-4-44000044-44-4-44-440000000000000000000000000000000000000000000000000000
χ784-4-44-444-40000-4-4400004-44-444-44-40000000000000000000000000000000000000000000000000000
χ794-4-4-444-444-44-44-440000-4000000000000-440000000000000000000000000000000000000000000000
χ804-4-4-444-44-44-444-440000-40000000000004-40000000000000000000000000000000000000000000000

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