Finite Group Databasebeta

← Group #507750

Character table — Group #507750

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888844444444888888888888161616161616161616161616161616162244444444444444
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
χ5111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ6111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ7111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-11111
χ8111111111111-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1
χ1011111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111
χ1111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1511111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-111-1-1
χ1611111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-200000000-2-2-2-2-2-22200000000000022−2−222−2−222−2−222−2−20000000000000000
χ192222222222222222-2-2-2-200000000-2-2-2-2-2-222000000000000−2−222−2−222−2−222−2−2220000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-20000000022-2-222-2-200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2522222222-2-2-2-22222-2-2-2-20000000022-2-222-2-2000000000000−2−22222−2−2−2−22222−2−20000000000000000
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
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ2922-22-2-22-200002i2i−2i−2i22-2-22222-2-2-2-2002i−2i000000002i2i−2i−2i000000000000000000000000002-20000002i−2i
χ3022-22-2-22-200002i2i−2i−2i22-2-22222-2-2-2-2002i−2i000000002i2i−2i−2i00000000000000000000000000-22000000−2i2i
χ3122-22-2-22-200002i2i−2i−2i22-2-2-2-2-2-22222002i−2i00000000−2i−2i2i2i0000000000000000000000002i−2i0000002-200
χ3222-22-2-22-200002i2i−2i−2i22-2-2-2-2-2-22222002i−2i00000000−2i−2i2i2i000000000000000000000000−2i2i000000-2200
χ3322-22-2-22-20000−2i−2i2i2i22-2-22222-2-2-2-200−2i2i00000000−2i−2i2i2i000000000000000000000000002-2000000−2i2i
χ3422-22-2-22-20000−2i−2i2i2i22-2-22222-2-2-2-200−2i2i00000000−2i−2i2i2i00000000000000000000000000-220000002i−2i
χ3522-22-2-22-20000−2i−2i2i2i22-2-2-2-2-2-2222200−2i2i000000002i2i−2i−2i0000000000000000000000002i−2i000000-2200
χ3622-22-2-22-20000−2i−2i2i2i22-2-2-2-2-2-2222200−2i2i000000002i2i−2i−2i000000000000000000000000−2i2i0000002-200
χ3722-2-22-2-222i2i−2i−2i00002-22-222-2-222-2-22i−2i0000002i2i−2i−2i0000000000000000000000002-20000002i−2i000000
χ3822-2-22-2-222i2i−2i−2i00002-22-222-2-222-2-22i−2i0000002i2i−2i−2i000000000000000000000000-22000000−2i2i000000
χ3922-2-22-2-222i2i−2i−2i00002-22-2-2-222-2-2222i−2i000000−2i−2i2i2i000000000000000000000000002i−2i0000002-20000
χ4022-2-22-2-222i2i−2i−2i00002-22-2-2-222-2-2222i−2i000000−2i−2i2i2i00000000000000000000000000−2i2i000000-220000
χ4122-2-22-2-22−2i−2i2i2i00002-22-222-2-222-2-2−2i2i000000−2i−2i2i2i0000000000000000000000002-2000000−2i2i000000
χ4222-2-22-2-22−2i−2i2i2i00002-22-222-2-222-2-2−2i2i000000−2i−2i2i2i000000000000000000000000-220000002i−2i000000
χ4322-2-22-2-22−2i−2i2i2i00002-22-2-2-222-2-222−2i2i0000002i2i−2i−2i000000000000000000000000002i−2i000000-220000
χ4422-2-22-2-22−2i−2i2i2i00002-22-2-2-222-2-222−2i2i0000002i2i−2i−2i00000000000000000000000000−2i2i0000002-20000
χ452-222-2-2-222i−2i2i−2i2-22-200002−22−22−22−20000002i−2ii2−i2i2−i22−22−2i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ462-222-2-2-222i−2i2i−2i2-22-200002−22−22−22−20000002i−2ii2−i2i2−i22−22−2i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ472-222-2-2-222i−2i2i−2i2-22-20000−22−22−22−220000002i−2i−i2i2−i2i2−22−22−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ482-222-2-2-222i−2i2i−2i2-22-20000−22−22−22−220000002i−2i−i2i2−i2i2−22−22−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ492-222-2-2-222i−2i2i−2i-22-2200002−22−22−22−2000000−2i2ii2−i2i2−i2−22−22−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ502-222-2-2-222i−2i2i−2i-22-2200002−22−22−22−2000000−2i2ii2−i2i2−i2−22−22−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ512-222-2-2-222i−2i2i−2i-22-220000−22−22−22−22000000−2i2i−i2i2−i2i22−22−2i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ522-222-2-2-222i−2i2i−2i-22-220000−22−22−22−22000000−2i2i−i2i2−i2i22−22−2i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ532-222-2-2-22−2i2i−2i2i2-22-200002−22−22−22−2000000−2i2i−i2i2−i2i22−22−2−i2−i2i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ542-222-2-2-22−2i2i−2i2i2-22-200002−22−22−22−2000000−2i2i−i2i2−i2i22−22−2−i2−i2i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ552-222-2-2-22−2i2i−2i2i2-22-20000−22−22−22−22000000−2i2ii2−i2i2−i2−22−22i2i2−i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ562-222-2-2-22−2i2i−2i2i2-22-20000−22−22−22−22000000−2i2ii2−i2i2−i2−22−22i2i2−i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ572-222-2-2-22−2i2i−2i2i-22-2200002−22−22−22−20000002i−2i−i2i2−i2i2−22−22i2i2−i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000000000
χ582-222-2-2-22−2i2i−2i2i-22-2200002−22−22−22−20000002i−2i−i2i2−i2i2−22−22i2i2−i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000000000
χ592-222-2-2-22−2i2i−2i2i-22-220000−22−22−22−220000002i−2ii2−i2i2−i22−22−2−i2−i2i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000000000
χ602-222-2-2-22−2i2i−2i2i-22-220000−22−22−22−220000002i−2ii2−i2i2−i22−22−2−i2−i2i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000000000
χ61444-4-44-4-4000000004-4-4444-4-4-4-4440000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4000000004-4-44-4-44444-4-40000000000000000000000000000000000000000000000000000
χ63444-4-44-4-400000000-444-40000000000000000000000004-44-400000000000000000000000000000000
χ64444-4-44-4-400000000-444-4000000000000000000000000-44-4400000000000000000000000000000000
χ6544-44-4-44-400004i4i−4i−4i-4-4440000000000−4i4i000000000000000000000000000000000000000000000000
χ6644-44-4-44-40000−4i−4i4i4i-4-44400000000004i−4i000000000000000000000000000000000000000000000000
χ6744-4-44-4-444i4i−4i−4i0000-44-4400000000−4i4i00000000000000000000000000000000000000000000000000
χ6844-4-44-4-44−4i−4i4i4i0000-44-44000000004i−4i00000000000000000000000000000000000000000000000000
χ694-44-44-44-400000000000022−22−2222−222222−2200004i−4i00000000002i2−2i2−2i22i200000000000000000000000000000000
χ704-44-44-44-400000000000022−22−2222−222222−220000−4i4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ714-44-44-44-4000000000000−222222−2222−22−222200004i−4i0000000000−2i22i22i2−2i200000000000000000000000000000000
χ724-44-44-44-4000000000000−222222−2222−22−22220000−4i4i00000000002i2−2i2−2i22i200000000000000000000000000000000
χ734-4-4444-4-400004i−4i−4i4i000022−2222−22−2222−22220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ744-4-4444-4-400004i−4i−4i4i0000−2222−222222−2222−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ754-4-4444-4-40000−4i4i4i−4i000022−2222−22−2222−2222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ764-4-4444-4-40000−4i4i4i−4i0000−2222−222222−2222−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ774-4-4-4-44444-4-440000000022−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ784-4-4-4-44444-4-4400000000−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ794-4-4-4-4444-444-40000000022−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ804-4-4-4-4444-444-400000000−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000

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