Finite Group Databasebeta

← Group #419601

Character table — Group #419601

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222244444444888822444444444444444444888888888822444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111
χ5111111111111111111111111-1-11111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ6111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ1011111111111111111111-1-1-1-11111-1-111111111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ1211111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1
χ1311111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111
χ1722222222-2-2-2-222-22-2-2-22000000222200-2-20000-2-2000000000022-2-200000000000000
χ1822222222-2-2-2-222-22-2-2-2200000022-2-200-2-20000220000000000-2-22200000000000000
χ1922222222-2-2-2-222-22-2-2-22000000-2-22200220000-2-20000000000-2-22200000000000000
χ2022222222-2-2-2-222-22-2-2-22000000-2-2-2-20022000022000000000022-2-200000000000000
χ2122222222-2-2-2-2-2-22-2222-22222220000-2-2000000000000-2-20000000000-220000000000
χ2222222222-2-2-2-2-2-22-2222-22222-2-2000022000000000000-2-200000000002-20000000000
χ2322222222-2-2-2-2-2-22-2222-2-2-2-2-2220000-2-20000000000002200000000002-20000000000
χ2422222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2000022000000000000220000000000-220000000000
χ25222-2-2-22-222-2-22-2-2-222-222i2i−2i−2i002i−2i00002i−2i00000000002i−2i00000000000000002-20000
χ26222-2-2-22-222-2-22-2-2-222-222i2i−2i−2i00−2i2i0000−2i2i00000000002i−2i0000000000000000-220000
χ27222-2-2-22-222-2-22-2-2-222-22−2i−2i2i2i002i−2i00002i−2i0000000000−2i2i0000000000000000-220000
χ28222-2-2-22-222-2-22-2-2-222-22−2i−2i2i2i00−2i2i0000−2i2i0000000000−2i2i00000000000000002-20000
χ29222-2-2-22-2-2-2222-22-2-2-2220000002i−2i0000−2i2i00000022-2-2002i2i−2i−2i000000000000000000
χ30222-2-2-22-2-2-2222-22-2-2-2220000002i−2i0000−2i2i000000-2-22200−2i−2i2i2i000000000000000000
χ31222-2-2-22-2-2-2222-22-2-2-222000000−2i2i00002i−2i00000022-2-200−2i−2i2i2i000000000000000000
χ32222-2-2-22-2-2-2222-22-2-2-222000000−2i2i00002i−2i000000-2-222002i2i−2i−2i000000000000000000
χ33222-2-2-22-2-2-222-22-2222-2-22i2i−2i−2i00000000002i2i−2i−2i000000−2i2i000000000000002-2000000
χ34222-2-2-22-2-2-222-22-2222-2-22i2i−2i−2i0000000000−2i−2i2i2i000000−2i2i00000000000000-22000000
χ35222-2-2-22-2-2-222-22-2222-2-2−2i−2i2i2i00000000002i2i−2i−2i0000002i−2i00000000000000-22000000
χ36222-2-2-22-2-2-222-22-2222-2-2−2i−2i2i2i0000000000−2i−2i2i2i0000002i−2i000000000000002-2000000
χ372-2-22-222-22-22-22-2222-2-2-2000000000000002i−2i2i−2i000000002-22-200000000000000002i−2i
χ382-2-22-222-22-22-22-2222-2-2-2000000000000002i−2i2i−2i00000000-22-220000000000000000−2i2i
χ392-2-22-222-22-22-22-2222-2-2-200000000000000−2i2i−2i2i000000002-22-20000000000000000−2i2i
χ402-2-22-222-22-22-22-2222-2-2-200000000000000−2i2i−2i2i00000000-22-2200000000000000002i−2i
χ412-2-2-22-2222-2-22-2-222-22-2200002-2002-22-20000002-2000000000000002-2000000000000
χ422-2-2-22-2222-2-22-2-222-22-2200002-200-222-2000000-2200000000000000-22000000000000
χ432-2-2-22-2222-2-22-2-222-22-220000-22002-2-220000002-200000000000000-22000000000000
χ442-2-2-22-2222-2-22-2-222-22-220000-2200-22-22000000-22000000000000002-2000000000000
χ452-2-2-22-222-222-2222-2-22-2-200002-20000-22000000000000002i−2i−2i2i000000002i−2i00000000
χ462-2-2-22-222-222-2222-2-22-2-200002-20000-2200000000000000−2i2i2i−2i00000000−2i2i00000000
χ472-2-2-22-222-222-2222-2-22-2-20000-2200002-2000000000000002i−2i−2i2i00000000−2i2i00000000
χ482-2-2-22-222-222-2222-2-22-2-20000-2200002-200000000000000−2i2i2i−2i000000002i−2i00000000
χ492-2-2-22-222-222-2-2-2-222-222000000002-200002-2-22-220000000000000000000000002-200
χ502-2-2-22-222-222-2-2-2-222-222000000002-20000-222-2-22000000000000000000000000-2200
χ512-2-2-22-222-222-2-2-2-222-22200000000-2200002-2-222-2000000000000000000000000-2200
χ522-2-2-22-222-222-2-2-2-222-22200000000-220000-222-22-20000000000000000000000002-200
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ5544-44-4-4-440000000000002i2−2i22i2−2i200000000000000002i−2i2i−2i00000022−220000000000000000
χ5644-44-4-4-440000000000002i2−2i22i2−2i20000000000000000−2i2i−2i2i000000−22220000000000000000
χ5744-44-4-4-44000000000000−2i22i2−2i22i200000000000000002i−2i2i−2i000000−22220000000000000000
χ5844-44-4-4-44000000000000−2i22i2−2i22i20000000000000000−2i2i−2i2i00000022−220000000000000000
χ5944-4-444-4-400000000000022−22−222200000000000000002i−2i−2i2i000000002i2−2i200000000000000
χ6044-4-444-4-400000000000022−22−22220000000000000000−2i2i2i−2i00000000−2i22i200000000000000
χ6144-4-444-4-4000000000000−222222−2200000000000000002i−2i−2i2i00000000−2i22i200000000000000
χ6244-4-444-4-4000000000000−222222−220000000000000000−2i2i2i−2i000000002i2−2i200000000000000
χ634-4-44-444-44-44-4-44-4-4-4444000000000000000000000000000000000000000000000000
χ644-4-44-444-4-44-444-4-44-444-4000000000000000000000000000000000000000000000000
χ654-4-44-444-4-44-44-444-44-4-44000000000000000000000000000000000000000000000000
χ664-4-4-44-4444-4-4444-4-44-44-4000000000000000000000000000000000000000000000000
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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