Finite Group Databasebeta

← Group #406006

Character table — Group #406006

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888822444444888888882244444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-1-111-1-11-1-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1111-1-111-1111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-11-1-111-1-1-1111-1-1
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11-111-1-1111-1-1-111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1111-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11-11111-1-11-111-1-1
χ1722222222-2-2-2-222-2-22-22-2000000000000000000002222-2-2-2-22222-2-2-2-2000000000000000000000000
χ1822222222-2-2-2-222-2-22-22-2000000000000000000002222-2-2-2-2-2-2-2-22222000000000000000000000000
χ1922222222-2-2-2-222-2-22-22-200000000000000000000-2-2-2-2222222-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-222-2-22-22-200000000000000000000-2-2-2-22222-2-22222-2-2000000000000000000000000
χ2122222222-2-2-2-2-2-222-22-222222222200000000-2-2-2-20000000000000000000000000022000000-2-20000
χ2222222222-2-2-2-2-2-222-22-222222222200000000-2-2-2-200000000000000000000000000-2-2000000220000
χ2322222222-2-2-2-2-2-222-22-22-2-2-2-2-2-2-2-2000000002222000000000000000000000000002-2000000-220000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-2-2-2-2-200000000222200000000000000000000000000-220000002-20000
χ2522-2-222-2-222-2-222-2-2-22-222222-2-2-2-20000000022-2-20000000000000000000000000000002i−2i2i−2i000000
χ2622-2-222-2-222-2-222-2-2-22-222222-2-2-2-20000000022-2-2000000000000000000000000000000−2i2i−2i2i000000
χ2722-2-222-2-222-2-222-2-2-22-22-2-2-2-2222200000000-2-2220000000000000000000000000000002i−2i−2i2i000000
χ2822-2-222-2-222-2-222-2-2-22-22-2-2-2-2222200000000-2-222000000000000000000000000000000−2i2i2i−2i000000
χ2922-2-222-2-222-2-2-2-2222-22-2000000002i2i2i2i−2i−2i−2i−2i000000000000002-2002-200002i2i−2i−2i0000000000000000
χ3022-2-222-2-222-2-2-2-2222-22-2000000002i2i2i2i−2i−2i−2i−2i00000000000000-2200-220000−2i−2i2i2i0000000000000000
χ3122-2-222-2-222-2-2-2-2222-22-200000000−2i−2i−2i−2i2i2i2i2i000000000000002-2002-20000−2i−2i2i2i0000000000000000
χ3222-2-222-2-222-2-2-2-2222-22-200000000−2i−2i−2i−2i2i2i2i2i00000000000000-2200-2200002i2i−2i−2i0000000000000000
χ3322-2-222-2-2-2-222-2-2-2-222222222-2-2-2-200000000-2-22200000000002-200-2222-2-200000000000000000000
χ3422-2-222-2-2-2-222-2-2-2-222222222-2-2-2-200000000-2-2220000000000-22002-2-2-22200000000000000000000
χ3522-2-222-2-2-2-222-2-2-2-22222-2-2-2-222220000000022-2-200000000002-200-22-2-22200000000000000000000
χ3622-2-222-2-2-2-222-2-2-2-22222-2-2-2-222220000000022-2-20000000000-22002-222-2-200000000000000000000
χ372-22-22-22-22-22-22-22-22-2-22000000000000000000002i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i2-22-20000000000000000
χ382-22-22-22-22-22-22-22-22-2-22000000000000000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i−2i2i-22-220000000000000000
χ392-22-22-22-22-22-22-22-22-2-2200000000000000000000−2i−2i2i2i−2i−2i2i2i000000002i−2i2i−2i-22-220000000000000000
χ402-22-22-22-22-22-22-22-22-2-2200000000000000000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i2-22-20000000000000000
χ412-22-22-22-22-22-2-22-22-222-22i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i0000000000000000000000000000000000002i−2i2-2
χ422-22-22-22-22-22-2-22-22-222-22i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i000000000000000000000000000000000000−2i2i-22
χ432-22-22-22-22-22-2-22-22-222-2−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i0000000000000000000000000000000000002i−2i-22
χ442-22-22-22-22-22-2-22-22-222-2−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i000000000000000000000000000000000000−2i2i2-2
χ452-22-22-22-2-22-222-2-2222-2-22i2i−2i−2i2i2i−2i−2i22-2-222-2-2−2i2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462-22-22-22-2-22-222-2-2222-2-22i2i−2i−2i2i2i−2i−2i-2-222-2-222−2i2i−2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472-22-22-22-2-22-222-2-2222-2-2−2i−2i2i2i−2i−2i2i2i22-2-222-2-22i−2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ482-22-22-22-2-22-222-2-2222-2-2−2i−2i2i2i−2i−2i2i2i-2-222-2-2222i−2i2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ492-2-222-2-222-2-22-222-222-2-22i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i000000002-2002-20000002i−2i−2i2i0000000000000000
χ502-2-222-2-222-2-22-222-222-2-22i2i−2i−2i−2i−2i2i2i000000002i−2i−2i2i00000000-2200-22000000−2i2i2i−2i0000000000000000
χ512-2-222-2-222-2-22-222-222-2-2−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i000000002-2002-2000000−2i2i2i−2i0000000000000000
χ522-2-222-2-222-2-22-222-222-2-2−2i−2i2i2i2i2i−2i−2i00000000−2i2i2i−2i00000000-2200-220000002i−2i−2i2i0000000000000000
χ532-2-222-2-22-222-22-22-2-222-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i0000000000000000000000002-2002i−2i0000000000
χ542-2-222-2-22-222-22-22-2-222-22i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i000000000000000000000000-2200−2i2i0000000000
χ552-2-222-2-22-222-22-22-2-222-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i0000000000000000000000002-200−2i2i0000000000
χ562-2-222-2-22-222-22-22-2-222-2−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i000000000000000000000000-22002i−2i0000000000
χ572-2-222-2-22-222-2-22-222-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000002-200-2200−2i2i2i−2i00000000000000000000
χ582-2-222-2-22-222-2-22-222-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000-22002-2002i−2i−2i2i00000000000000000000
χ592-2-222-2-22-222-2-22-222-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000002-200-22002i−2i−2i2i00000000000000000000
χ602-2-222-2-22-222-2-22-222-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000-22002-200−2i2i2i−2i00000000000000000000
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-440000000000002i2−2i22i2−2i22i2−2i22i2−2i22i−2i2i−2i2i−2i2i−2i000022−2222−22000000000000000000000000000000000000
χ63444-4-4-4-440000000000002i2−2i22i2−2i22i2−2i22i2−2i2−2i2i−2i2i−2i2i−2i2i0000−2222−2222000000000000000000000000000000000000
χ64444-4-4-4-44000000000000−2i22i2−2i22i2−2i22i2−2i22i22i−2i2i−2i2i−2i2i−2i0000−2222−2222000000000000000000000000000000000000
χ65444-4-4-4-44000000000000−2i22i2−2i22i2−2i22i2−2i22i2−2i2i−2i2i−2i2i−2i2i000022−2222−22000000000000000000000000000000000000
χ6644-44-4-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i22-22-2-22-22000000002i2−2i22i2−2i200000000000000000000000000000000
χ6744-44-4-44-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2-22-222-22-200000000−2i22i2−2i22i200000000000000000000000000000000
χ6844-44-4-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i22-22-2-22-2200000000−2i22i2−2i22i200000000000000000000000000000000
χ6944-44-4-44-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2-22-222-22-2000000002i2−2i22i2−2i200000000000000000000000000000000
χ7044-4-444-4-4-4-4444444-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ714-444-44-4-400000000000022−22−222222−22−22222i−2i−2i2i2i−2i−2i2i0000−2i22i22i2−2i2000000000000000000000000000000000000
χ724-444-44-4-400000000000022−22−222222−22−2222−2i2i2i−2i−2i2i2i−2i00002i2−2i2−2i22i2000000000000000000000000000000000000
χ734-444-44-4-4000000000000−222222−22−222222−222i−2i−2i2i2i−2i−2i2i00002i2−2i2−2i22i2000000000000000000000000000000000000
χ744-444-44-4-4000000000000−222222−22−222222−22−2i2i2i−2i−2i2i2i−2i0000−2i22i22i2−2i2000000000000000000000000000000000000
χ754-44-44-44-4-44-44-444-4-4-444000000000000000000000000000000000000000000000000000000000000
χ764-4-444-4-444-4-444-4-44-4-444000000000000000000000000000000000000000000000000000000000000
χ774-4-4-4-444400000000000022−22−2222−222222−222-2-22-222-200000000−222222−2200000000000000000000000000000000
χ784-4-4-4-444400000000000022−22−2222−222222−22-222-22-2-220000000022−22−222200000000000000000000000000000000
χ794-4-4-4-4444000000000000−222222−2222−22−22222-2-22-222-20000000022−22−222200000000000000000000000000000000
χ804-4-4-4-4444000000000000−222222−2222−22−2222-222-22-2-2200000000−222222−2200000000000000000000000000000000

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