Finite Group Databasebeta

← Group #428395

Character table — Group #428395

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444224444444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ911111111111111111111-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ1011111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ1311111111111111111111-1-1-1-111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-1-1-1-1-1
χ1722222222-2-2-2-222-2-22-22-20022000022-2-2000000-2-200000000000022-2-2000000000000
χ1822222222-2-2-2-222-2-22-22-200220000-2-222000000-2-2000000000000-2-222000000000000
χ1922222222-2-2-2-222-2-22-22-200-2-2000022-2-200000022000000000000-2-222000000000000
χ2022222222-2-2-2-222-2-22-22-200-2-20000-2-2220000002200000000000022-2-2000000000000
χ2122222222-2-2-2-2-2-222-22-22220022-2-20000-2-20000000000000022-2-20000000000000000
χ2222222222-2-2-2-2-2-222-22-222200-2-2220000-2-200000000000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-222-22-22-2-20022-2-200002200000000000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-222-22-22-2-200-2-2220000220000000000000022-2-20000000000000000
χ2522-22-2-22-222-2-22-2-2-222-220000000000000022-2-2002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622-22-2-22-222-2-22-2-2-222-220000000000000022-2-200−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2722-22-2-22-222-2-22-2-2-222-2200000000000000-2-222002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2822-22-2-22-222-2-22-2-2-222-2200000000000000-2-22200−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292-22-2-2-2222-22-2222-2-2-2-222-20000002i−2i2i−2i2-200000000000000000000002i−2i0000000000
χ302-22-2-2-2222-22-2222-2-2-2-222-2000000−2i2i−2i2i2-20000000000000000000000−2i2i0000000000
χ312-22-2-2-2222-22-2222-2-2-2-22-220000002i−2i2i−2i-220000000000000000000000−2i2i0000000000
χ322-22-2-2-2222-22-2222-2-2-2-22-22000000−2i2i−2i2i-2200000000000000000000002i−2i0000000000
χ332-22-2-2-222-22-2222-22-22-2-2000000002i−2i−2i2i000000002-22-200000000000000002i−2i000000
χ342-22-2-2-222-22-2222-22-22-2-2000000002i−2i−2i2i00000000-22-220000000000000000−2i2i000000
χ352-22-2-2-222-22-2222-22-22-2-200000000−2i2i2i−2i000000002-22-20000000000000000−2i2i000000
χ362-22-2-2-222-22-2222-22-22-2-200000000−2i2i2i−2i00000000-22-2200000000000000002i−2i000000
χ372-22-2-2-222-22-22-2-22-22-2222-20000000000-222-22-2000000000000000000000000002-200
χ382-22-2-2-222-22-22-2-22-22-2222-20000000000-22-22-2200000000000000000000000000-2200
χ392-22-2-2-222-22-22-2-22-22-222-2200000000002-22-22-200000000000000000000000000-2200
χ402-22-2-2-222-22-22-2-22-22-222-2200000000002-2-22-22000000000000000000000000002-200
χ412-2-2-2222-22-2-22-222-222-2-2002i−2i2-22-200000000002i−2i0000000000000000002i−2i00000000
χ422-2-2-2222-22-2-22-222-222-2-2002i−2i-22-2200000000002i−2i000000000000000000−2i2i00000000
χ432-2-2-2222-22-2-22-222-222-2-200−2i2i2-22-20000000000−2i2i000000000000000000−2i2i00000000
χ442-2-2-2222-22-2-22-222-222-2-200−2i2i-22-220000000000−2i2i0000000000000000002i−2i00000000
χ452-2-2-2222-2-222-22-22-2-222-200002-2-220000000000002i−2i−2i2i0000000000000000002i−2i0000
χ462-2-2-2222-2-222-22-22-2-222-200002-2-22000000000000−2i2i2i−2i000000000000000000−2i2i0000
χ472-2-2-2222-2-222-22-22-2-222-20000-222-20000000000002i−2i−2i2i000000000000000000−2i2i0000
χ482-2-2-2222-2-222-22-22-2-222-20000-222-2000000000000−2i2i2i−2i0000000000000000002i−2i0000
χ492-2-2-2222-2-222-2-22-222-2-22002i−2i00000000002-2-22−2i2i000000000000000000000000002i−2i
χ502-2-2-2222-2-222-2-22-222-2-22002i−2i0000000000-222-2−2i2i00000000000000000000000000−2i2i
χ512-2-2-2222-2-222-2-22-222-2-2200−2i2i00000000002-2-222i−2i00000000000000000000000000−2i2i
χ522-2-2-2222-2-222-2-22-222-2-2200−2i2i0000000000-222-22i−2i000000000000000000000000002i−2i
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-44-4-4-40000000000000000000000000000000000002-22-222−220022−2200000000000000
χ55444-44-4-4-40000000000000000000000000000000000002-22-2−222200−222200000000000000
χ56444-44-4-4-4000000000000000000000000000000000000-22-2222−2200−222200000000000000
χ57444-44-4-4-4000000000000000000000000000000000000-22-22−22220022−2200000000000000
χ5844-44-4-44-444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ5944-44-4-44-4-4-4444-4444-4-4-4000000000000000000000000000000000000000000000000
χ6044-44-4-44-4-4-444-44-4-4-4444000000000000000000000000000000000000000000000000
χ6144-4-4-44-440000000000000000000000000000000000002i−2i−2i2i0022−22002i2−2i2000000000000
χ6244-4-4-44-440000000000000000000000000000000000002i−2i−2i2i00−222200−2i22i2000000000000
χ6344-4-4-44-44000000000000000000000000000000000000−2i2i2i−2i0022−2200−2i22i2000000000000
χ6444-4-4-44-44000000000000000000000000000000000000−2i2i2i−2i00−2222002i2−2i2000000000000
χ654-44-4-4-4444-44-4-4-4-44444-4000000000000000000000000000000000000000000000000
χ664-4-4-4444-44-4-444-4-44-4-444000000000000000000000000000000000000000000000000
χ678-888-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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