Finite Group Databasebeta

← Group #405613

Character table — Group #405613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888822444444888888882224444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-11111111-1-11-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1111-1-1-1-111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-11111-1-1-1-1-11111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-111-1-11-1-1-1111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11-1-111-1111-1-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111111-1-1-11-1-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1111-111111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-111-11-1-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111-1-1-11-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1111-111-1-1
χ1722222222-2-2-2-222-22-2-2-22222222220000000000000000-2-2-2-200000000000000000020000-2-20020000
χ1822222222-2-2-2-222-22-2-2-22222222220000000000000000-2-2-2-2000000000000000000-200002200-20000
χ1922222222-2-2-2-222-22-2-2-22-2-2-2-2-2-2-2-200000000000000002222000000000000000000200002-200-20000
χ2022222222-2-2-2-222-22-2-2-22-2-2-2-2-2-2-2-200000000000000002222000000000000000000-20000-220020000
χ2122222222-2-2-2-2-2-22-2222-200000000000000002222-2-2-2-200002222-2-2-2-2000000000000000000000000
χ2222222222-2-2-2-2-2-22-2222-200000000000000002222-2-2-2-20000-2-2-2-22222000000000000000000000000
χ2322222222-2-2-2-2-2-22-2222-20000000000000000-2-2-2-22222000022-2-2-2-222000000000000000000000000
χ2422222222-2-2-2-2-2-22-2222-20000000000000000-2-2-2-222220000-2-22222-2-2000000000000000000000000
χ2522-22-2-22-222-2-22-22-22-2-2200000000000000002i2i−2i−2i2i2i−2i−2i0000000000002i2i−2i−2i22-2-20000000000000000
χ2622-22-2-22-222-2-22-22-22-2-2200000000000000002i2i−2i−2i2i2i−2i−2i000000000000−2i−2i2i2i-2-2220000000000000000
χ2722-22-2-22-222-2-22-22-22-2-220000000000000000−2i−2i2i2i−2i−2i2i2i0000000000002i2i−2i−2i-2-2220000000000000000
χ2822-22-2-22-222-2-22-22-22-2-220000000000000000−2i−2i2i2i−2i−2i2i2i000000000000−2i−2i2i2i22-2-20000000000000000
χ2922-22-2-22-222-2-2-22-22-222-22i2i2i2i−2i−2i−2i−2i00000000000000002i2i−2i−2i00000000000000000000000000002-22i−2i
χ3022-22-2-22-222-2-2-22-22-222-22i2i2i2i−2i−2i−2i−2i00000000000000002i2i−2i−2i0000000000000000000000000000-22−2i2i
χ3122-22-2-22-222-2-2-22-22-222-2−2i−2i−2i−2i2i2i2i2i0000000000000000−2i−2i2i2i00000000000000000000000000002-2−2i2i
χ3222-22-2-22-222-2-2-22-22-222-2−2i−2i−2i−2i2i2i2i2i0000000000000000−2i−2i2i2i0000000000000000000000000000-222i−2i
χ3322-22-2-22-2-2-222-22222-2-2-22i2i2i2i−2i−2i−2i−2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3422-22-2-22-2-2-222-22222-2-2-22i2i2i2i−2i−2i−2i−2i-2-2-2-22222−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3522-22-2-22-2-2-222-22222-2-2-2−2i−2i−2i−2i2i2i2i2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3622-22-2-22-2-2-222-22222-2-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2-222222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ372-22-22-22-22-22-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i00000000000000000002i−2i2-2000000000
χ382-22-22-22-22-22-22-2-2222-2-22i2i−2i−2i2i2i−2i−2i00000000000000002i−2i2i−2i0000000000000000000−2i2i-22000000000
χ392-22-22-22-22-22-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i00000000000000000002i−2i-22000000000
χ402-22-22-22-22-22-22-2-2222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000−2i2i−2i2i0000000000000000000−2i2i2-2000000000
χ412-22-22-22-22-22-2-222-2-2-222000000002i2i−2i−2i2i2i−2i−2i0000000000002-2002-2002i−2i2i−2i00000000000000000000
χ422-22-22-22-22-22-2-222-2-2-222000000002i2i−2i−2i2i2i−2i−2i000000000000-2200-2200−2i2i−2i2i00000000000000000000
χ432-22-22-22-22-22-2-222-2-2-22200000000−2i−2i2i2i−2i−2i2i2i0000000000002-2002-200−2i2i−2i2i00000000000000000000
χ442-22-22-22-22-22-2-222-2-2-22200000000−2i−2i2i2i−2i−2i2i2i000000000000-2200-22002i−2i2i−2i00000000000000000000
χ452-22-22-22-2-22-222-222-2-22-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i2-200-220000002i−2i2i−2i0000000000000000
χ462-22-22-22-2-22-222-222-2-22-22i2i−2i−2i2i2i−2i−2i0000000000000000−2i2i−2i2i-22002-2000000−2i2i−2i2i0000000000000000
χ472-22-22-22-2-22-222-222-2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i2-200-22000000−2i2i−2i2i0000000000000000
χ482-22-22-22-2-22-222-222-2-22-2−2i−2i2i2i−2i−2i2i2i00000000000000002i−2i2i−2i-22002-20000002i−2i2i−2i0000000000000000
χ492-2-2-2-22222-2-22-2-222-22-2222-2-2-2-22200000000000000002-2-22002-2002-22-2-2200000000000000000000
χ502-2-2-2-22222-2-22-2-222-22-2222-2-2-2-22200000000000000002-2-2200-2200-22-222-200000000000000000000
χ512-2-2-2-22222-2-22-2-222-22-22-2-22222-2-20000000000000000-222-2002-2002-2-222-200000000000000000000
χ522-2-2-2-22222-2-22-2-222-22-22-2-22222-2-20000000000000000-222-200-2200-222-2-2200000000000000000000
χ532-2-2-2-2222-222-2222-2-22-2-2000000002i2i−2i−2i−2i−2i2i2i000000000000002-200-220000−2i2i2i−2i0000000000000000
χ542-2-2-2-2222-222-2222-2-22-2-2000000002i2i−2i−2i−2i−2i2i2i00000000000000-22002-200002i−2i−2i2i0000000000000000
χ552-2-2-2-2222-222-2222-2-22-2-200000000−2i−2i2i2i2i2i−2i−2i000000000000002-200-2200002i−2i−2i2i0000000000000000
χ562-2-2-2-2222-222-2222-2-22-2-200000000−2i−2i2i2i2i2i−2i−2i00000000000000-22002-20000−2i2i2i−2i0000000000000000
χ572-2-2-2-2222-222-2-2-2-222-22222-2-2-2-2220000000000000000-222-200000000000000002-200000002-200000
χ582-2-2-2-2222-222-2-2-2-222-22222-2-2-2-2220000000000000000-222-20000000000000000-220000000-2200000
χ592-2-2-2-2222-222-2-2-2-222-222-2-22222-2-200000000000000002-2-2200000000000000002-20000000-2200000
χ602-2-2-2-2222-222-2-2-2-222-222-2-22222-2-200000000000000002-2-220000000000000000-2200000002-200000
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ62444-4-4-4-4400000000000022−2222−2222−2222−222i−2i2i−2i2i−2i2i−2i2i2−2i22i2−2i20000000000000000000000000000000000000000
χ63444-4-4-4-4400000000000022−2222−2222−2222−22−2i2i−2i2i−2i2i−2i2i−2i22i2−2i22i20000000000000000000000000000000000000000
χ64444-4-4-4-44000000000000−2222−2222−2222−22222i−2i2i−2i2i−2i2i−2i−2i22i2−2i22i20000000000000000000000000000000000000000
χ65444-4-4-4-44000000000000−2222−2222−2222−2222−2i2i−2i2i−2i2i−2i2i2i2−2i22i2−2i20000000000000000000000000000000000000000
χ6644-44-4-44-4-4-4444-4-4-4-4444000000000000000000000000000000000000000000000000000000000000
χ6744-4-444-4-40000000000002i2−2i22i2−2i2−2i22i2−2i22i22i−2i2i−2i−2i2i−2i2i−222222−220000000000000000000000000000000000000000
χ6844-4-444-4-40000000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i2i−2i2i2i−2i2i−2i22−22−22220000000000000000000000000000000000000000
χ6944-4-444-4-4000000000000−2i22i2−2i22i22i2−2i22i2−2i22i−2i2i−2i−2i2i−2i2i22−22−22220000000000000000000000000000000000000000
χ7044-4-444-4-4000000000000−2i22i2−2i22i22i2−2i22i2−2i2−2i2i−2i2i2i−2i2i−2i−222222−220000000000000000000000000000000000000000
χ714-444-44-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i22-2-222-2-2200002i2−2i22i2−2i2000000000000000000000000000000000000
χ724-444-44-4-40000000000002i2−2i2−2i22i22i2−2i2−2i22i2-222-2-222-20000−2i22i2−2i22i2000000000000000000000000000000000000
χ734-444-44-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i22-2-222-2-220000−2i22i2−2i22i2000000000000000000000000000000000000
χ744-444-44-4-4000000000000−2i22i22i2−2i2−2i22i22i2−2i2-222-2-222-200002i2−2i22i2−2i2000000000000000000000000000000000000
χ754-44-44-44-4-44-44-44-4-444-44000000000000000000000000000000000000000000000000000000000000
χ764-4-444-4-4400000000000022−22−2222−222222−222-2-22-222-20000−222222−22000000000000000000000000000000000000
χ774-4-444-4-4400000000000022−22−2222−222222−22-222-22-2-22000022−22−2222000000000000000000000000000000000000
χ784-4-444-4-44000000000000−222222−2222−22−22222-2-22-222-2000022−22−2222000000000000000000000000000000000000
χ794-4-444-4-44000000000000−222222−2222−22−2222-222-22-2-220000−222222−22000000000000000000000000000000000000
χ804-4-4-4-44444-4-4444-4-44-44-4000000000000000000000000000000000000000000000000000000000000

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