Finite Group Databasebeta

← Group #422889

Character table — Group #422889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444888888882244444444448888888888882222244444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-111
χ7111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-111-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111111-1-1-1-1-11111
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-111111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111111
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-111-1-1111-1-1-1-1
χ1722222222-2-2-2-222-2-22-22-2000022220022-2-200000000-2-200000000000002-2000000000
χ1822222222-2-2-2-222-2-22-22-20000222200-2-22200000000-2-20000000000000-22000000000
χ1922222222-2-2-2-222-2-22-22-20000-2-2-2-20022-2-200000000220000000000000-22000000000
χ2022222222-2-2-2-222-2-22-22-20000-2-2-2-200-2-222000000002200000000000002-2000000000
χ2122222222-2-2-2-2-2-222-22-2222220000220000-2-20000-2-20000000000200000000-2000000
χ2222222222-2-2-2-2-2-222-22-2222220000-2-20000220000-2-20000000000-2000000002000000
χ2322222222-2-2-2-2-2-222-22-22-2-2-2-20000220000-2-20000220000000000-2000000002000000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-20000-2-20000220000220000000000200000000-2000000
χ2522-2-2-2-22222-2-2222-2-22-2-222-2-200000000000000002-2002i2i−2i−2i00000000000000002i−2i00
χ2622-2-2-2-22222-2-2222-2-22-2-222-2-200000000000000002-200−2i−2i2i2i0000000000000000−2i2i00
χ2722-2-2-2-22222-2-2222-2-22-2-2-2-2220000000000000000-22002i2i−2i−2i0000000000000000−2i2i00
χ2822-2-2-2-22222-2-2222-2-22-2-2-2-2220000000000000000-2200−2i−2i2i2i00000000000000002i−2i00
χ2922-2-2-2-22222-2-2-2-2-222-222000022-2-2000000000000002-2000022-2-2000000000000002-2
χ3022-2-2-2-22222-2-2-2-2-222-222000022-2-2000000000000002-20000-2-22200000000000000-22
χ3122-2-2-2-22222-2-2-2-2-222-2220000-2-22200000000000000-22000022-2-200000000000000-22
χ3222-2-2-2-22222-2-2-2-2-222-2220000-2-22200000000000000-220000-2-222000000000000002-2
χ3322-2-2-2-222-2-222-2-22-2222-222-2-222-2-20000000022-2-2-22-22000000000000000000000000
χ3422-2-2-2-222-2-222-2-22-2222-222-2-2-2-22200000000-2-222-222-2000000000000000000000000
χ3522-2-2-2-222-2-222-2-22-2222-2-2-22222-2-200000000-2-2222-2-22000000000000000000000000
χ3622-2-2-2-222-2-222-2-22-2222-2-2-222-2-2220000000022-2-22-22-2000000000000000000000000
χ372-222-2-2-222-22-22-2222-2-2-200000000002-22-200000000002i−2i2i−2i000000000002i−2i0000000
χ382-222-2-2-222-22-22-2222-2-2-200000000002-22-20000000000−2i2i−2i2i00000000000−2i2i0000000
χ392-222-2-2-222-22-22-2222-2-2-20000000000-22-2200000000002i−2i2i−2i00000000000−2i2i0000000
χ402-222-2-2-222-22-22-2222-2-2-20000000000-22-220000000000−2i2i−2i2i000000000002i−2i0000000
χ412-222-2-2-222-22-2-22-2-2-2222000000002-200002-20000000000002-22-20002-200000000000
χ422-222-2-2-222-22-2-22-2-2-2222000000002-200002-2000000000000-22-22000-2200000000000
χ432-222-2-2-222-22-2-22-2-2-222200000000-220000-220000000000002-22-2000-2200000000000
χ442-222-2-2-222-22-2-22-2-2-222200000000-220000-22000000000000-22-220002-200000000000
χ452-222-2-2-22-22-222-2-2-222-22000000002-22-2-22-22000000000000000002-20000000000000
χ462-222-2-2-22-22-222-2-2-222-22000000002-2-222-2-2200000000000000000-220000000000000
χ472-222-2-2-22-22-222-2-2-222-2200000000-222-2-222-200000000000000000-220000000000000
χ482-222-2-2-22-22-222-2-2-222-2200000000-22-222-22-2000000000000000002-20000000000000
χ492-2-2-222-222-2-222-22-2-2-2220000000000000000000000002-2-222-2-2200000000002-20000
χ502-2-2-222-222-2-222-22-2-2-2220000000000000000000000002-2-22-222-20000000000-220000
χ512-2-2-222-222-2-222-22-2-2-222000000000000000000000000-222-22-2-220000000000-220000
χ522-2-2-222-222-2-222-22-2-2-222000000000000000000000000-222-2-222-200000000002-20000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-44-4-4-400000000000022−2222−222i2−2i22i2−2i2000000002i−2i2i−2i0000000000000000000000000000
χ55444-44-4-4-400000000000022−2222−22−2i22i2−2i22i200000000−2i2i−2i2i0000000000000000000000000000
χ56444-44-4-4-4000000000000−2222−22222i2−2i22i2−2i200000000−2i2i−2i2i0000000000000000000000000000
χ57444-44-4-4-4000000000000−2222−2222−2i22i2−2i22i2000000002i−2i2i−2i0000000000000000000000000000
χ5844-44-44-4-400000000000022−22−22222i2−2i2−2i22i2000000002i−2i−2i2i0000000000000000000000000000
χ5944-44-44-4-400000000000022−22−2222−2i22i22i2−2i200000000−2i2i2i−2i0000000000000000000000000000
χ6044-44-44-4-4000000000000−222222−222i2−2i2−2i22i200000000−2i2i2i−2i0000000000000000000000000000
χ6144-44-44-4-4000000000000−222222−22−2i22i22i2−2i2000000002i−2i−2i2i0000000000000000000000000000
χ6244-4-4-4-444-4-44444-44-4-4-44000000000000000000000000000000000000000000000000
χ634-444-4-4-44-44-44-4444-4-44-4000000000000000000000000000000000000000000000000
χ644-4-4-444-444-4-44-44-4444-4-4000000000000000000000000000000000000000000000000
χ654-4-4-444-44-444-44-4-44-444-4000000000000000000000000000000000000000000000000
χ664-4-4-444-44-444-4-444-44-4-44000000000000000000000000000000000000000000000000
χ678-88-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-88-8000000000000000000000000000000000000000000000000000000000000

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