Finite Group Databasebeta

← Group #414980

Character table — Group #414980

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12224444222222444444888888882222444444448888888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-111-1-1-1-111
χ172222222222-2-2-2-22-2-2-2-222222-2-2-2-20000000000000000000000002i−2i2i−2i000000000000
χ182222222222-2-2-2-22-2-2-2-222222-2-2-2-2000000000000000000000000−2i2i−2i2i000000000000
χ192222222222-2-2-2-22-2-2-2-22-2-2-2-222220000000000000000000000002i−2i−2i2i000000000000
χ202222222222-2-2-2-22-2-2-2-22-2-2-2-22222000000000000000000000000−2i2i2i−2i000000000000
χ2122222222-2-222-2-2-22-2-22-20000000000000000000022-2-22i2i−2i−2i2i2i−2i−2i0000000000000000
χ2222222222-2-222-2-2-22-2-22-20000000000000000000022-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-222-2-2-22-2-22-200000000000000000000-2-2222i2i−2i−2i−2i−2i2i2i0000000000000000
χ2422222222-2-222-2-2-22-2-22-200000000000000000000-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000
χ252222-2-2-2-222-2-2-2-2-22222-2000000002222-2-2-2-200002-22-2000000000000000000000000
χ262222-2-2-2-222-2-2-2-2-22222-20000000022-2-2-2-2220000-22-22000000000000000000000000
χ272222-2-2-2-222-2-2-2-2-22222-200000000-2-22222-2-20000-22-22000000000000000000000000
χ282222-2-2-2-222-2-2-2-2-22222-200000000-2-2-2-2222200002-22-2000000000000000000000000
χ292222-2-2-2-2-2-222-2-22-222-2222-2-222-2-20000000000000000000000000000000000002i−2i2i−2i
χ302222-2-2-2-2-2-222-2-22-222-2222-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i
χ312222-2-2-2-2-2-222-2-22-222-22-2-222-2-2220000000000000000000000000000000000002i−2i−2i2i
χ322222-2-2-2-2-2-222-2-22-222-22-2-222-2-222000000000000000000000000000000000000−2i2i2i−2i
χ332222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2220000000022-2-22-2-22000000000000000000000000
χ342222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-22200000000-2-222-222-2000000000000000000000000
χ352222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-20000000022-2-2-222-2000000000000000000000000
χ362222-2-2-2-2-2-2-2-22222-2-222-2-22222-2-200000000-2-2222-2-22000000000000000000000000
χ372-2-2222-2-22-22-22-2-222-2-222-22-22-22-2000000000000000000000000000000002i−2i2i−2i0000
χ382-2-2222-2-22-22-22-2-222-2-222-22-22-22-200000000000000000000000000000000−2i2i−2i2i0000
χ392-2-2222-2-22-22-22-2-222-2-22-22-22-22-22000000000000000000000000000000002i−2i−2i2i0000
χ402-2-2222-2-22-22-22-2-222-2-22-22-22-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ412-2-2222-2-22-2-22-22-2-2-22222-22-2-22-22002-2002-20000000000002-22-20000000000000000
χ422-2-2222-2-22-2-22-22-2-2-22222-22-2-22-2200-2200-22000000000000-22-220000000000000000
χ432-2-2222-2-22-2-22-22-2-2-2222-22-222-22-2002-2002-2000000000000-22-220000000000000000
χ442-2-2222-2-22-2-22-22-2-2-2222-22-222-22-200-2200-220000000000002-22-20000000000000000
χ452-2-2222-2-2-22-222-22-22-22-2000000002-2002-2002i−2i2i−2i000000002i−2i−2i2i0000000000000000
χ462-2-2222-2-2-22-222-22-22-22-2000000002-2002-200−2i2i−2i2i00000000−2i2i2i−2i0000000000000000
χ472-2-2222-2-2-22-222-22-22-22-200000000-2200-22002i−2i2i−2i00000000−2i2i2i−2i0000000000000000
χ482-2-2222-2-2-22-222-22-22-22-200000000-2200-2200−2i2i−2i2i000000002i−2i−2i2i0000000000000000
χ492-2-22-2-2222-22-22-22-2-222-200000000002-200-222i−2i−2i2i00002i−2i2i−2i00000000000000000000
χ502-2-22-2-2222-22-22-22-2-222-200000000002-200-22−2i2i2i−2i0000−2i2i−2i2i00000000000000000000
χ512-2-22-2-2222-22-22-22-2-222-20000000000-22002-22i−2i−2i2i0000−2i2i−2i2i00000000000000000000
χ522-2-22-2-2222-22-22-22-2-222-20000000000-22002-2−2i2i2i−2i00002i−2i2i−2i00000000000000000000
χ532-2-22-2-222-222-2-22-2-22-2222-2-222-2-222-200-2200000000002-2-2200000000000000000000
χ542-2-22-2-222-222-2-22-2-22-2222-2-222-2-22-22002-20000000000-222-200000000000000000000
χ552-2-22-2-222-222-2-22-2-22-222-222-2-222-22-200-220000000000-222-200000000000000000000
χ562-2-22-2-222-222-2-22-2-22-222-222-2-222-2-22002-200000000002-2-2200000000000000000000
χ572-2-22-2-222-22-222-2-22-22-222-2-22-222-200000000000000000000000000002-22-200000000
χ582-2-22-2-222-22-222-2-22-22-222-2-22-222-20000000000000000000000000000-22-2200000000
χ592-2-22-2-222-22-222-2-22-22-22-222-22-2-2200000000000000000000000000002-2-2200000000
χ602-2-22-2-222-22-222-2-22-22-22-222-22-2-220000000000000000000000000000-222-200000000
χ6144444444-4-4-4-444-4-444-4-4000000000000000000000000000000000000000000000000
χ624444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ634-4-4444-4-4-444-4-4444-44-4-4000000000000000000000000000000000000000000000000
χ644-4-44-4-4444-4-44-44444-4-4-4000000000000000000000000000000000000000000000000
χ6588-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000
χ6688-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ678-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000
χ688-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000

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