Finite Group Databasebeta

← Group #423975

Character table — Group #423975

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222222224444444488888888888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444444448888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-111-1-1111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-1
χ31111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1
χ5111111111111111111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-111111-1-1-1-11111
χ911111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1
χ1011111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-1-11-1-111-1-111
χ1111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ1411111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-111-1-111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1111-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111-1-1111-1-111-1-1-1-1
χ1722222222-2-2-2-222-22-2-2-22000022222200-2-200000000-2-2000000002000000-200000000
χ1822222222-2-2-2-222-22-2-2-2200002222-2-2002200000000-2-200000000-2000000200000000
χ1922222222-2-2-2-222-22-2-2-220000-2-2-2-22200-2-2000000002200000000-2000000200000000
χ2022222222-2-2-2-222-22-2-2-220000-2-2-2-2-2-200220000000022000000002000000-200000000
χ2122222222-2-2-2-2-2-22-2222-222220000002200-2-20000-2-2000000000002-20000000000000
χ2222222222-2-2-2-2-2-22-2222-22222000000-2-200220000-2-200000000000-220000000000000
χ2322222222-2-2-2-2-2-22-2222-2-2-2-2-20000002200-2-200002200000000000-220000000000000
χ2422222222-2-2-2-2-2-22-2222-2-2-2-2-2000000-2-20022000022000000000002-20000000000000
χ25222-2-2-2-2222-2-22-2-2-222-2222-2-22i2i−2i−2i000000002i2i−2i−2i2-22i−2i000000000000000000000000
χ26222-2-2-2-2222-2-22-2-2-222-2222-2-2−2i−2i2i2i00000000−2i−2i2i2i2-2−2i2i000000000000000000000000
χ27222-2-2-2-2222-2-22-2-2-222-22-2-2222i2i−2i−2i00000000−2i−2i2i2i-222i−2i000000000000000000000000
χ28222-2-2-2-2222-2-22-2-2-222-22-2-222−2i−2i2i2i000000002i2i−2i−2i-22−2i2i000000000000000000000000
χ29222-2-2-2-22-2-2222-22-2-2-22200002i2i−2i−2i00000000000000−2i2i22-2-200000000000000002i−2i00
χ30222-2-2-2-22-2-2222-22-2-2-22200002i2i−2i−2i00000000000000−2i2i-2-2220000000000000000−2i2i00
χ31222-2-2-2-22-2-2222-22-2-2-2220000−2i−2i2i2i000000000000002i−2i22-2-20000000000000000−2i2i00
χ32222-2-2-2-22-2-2222-22-2-2-2220000−2i−2i2i2i000000000000002i−2i-2-22200000000000000002i−2i00
χ33222-2-2-2-22-2-222-22-2222-2-222-2-20000000000000000-220000002i2i−2i−2i000000000000002i−2i
χ34222-2-2-2-22-2-222-22-2222-2-222-2-20000000000000000-22000000−2i−2i2i2i00000000000000−2i2i
χ35222-2-2-2-22-2-222-22-2222-2-2-2-22200000000000000002-20000002i2i−2i−2i00000000000000−2i2i
χ36222-2-2-2-22-2-222-22-2222-2-2-2-22200000000000000002-2000000−2i−2i2i2i000000000000002i−2i
χ372-2-22-22-222-22-22-2222-2-2-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000002-20000
χ382-2-22-22-222-22-22-2222-2-2-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000-220000
χ392-2-22-22-222-22-22-2222-2-2-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000-220000
χ402-2-22-22-222-22-22-2222-2-2-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000002-20000
χ412-2-2-22-2222-2-22-2-222-22-22000000002-22-22-22-20000000000000000000002-2000000000
χ422-2-2-22-2222-2-22-2-222-22-22000000002-2-222-2-22000000000000000000000-22000000000
χ432-2-2-22-2222-2-22-2-222-22-2200000000-222-2-222-2000000000000000000000-22000000000
χ442-2-2-22-2222-2-22-2-222-22-2200000000-22-22-22-220000000000000000000002-2000000000
χ452-2-2-22-222-222-2222-2-22-2-200000000002-200-22000000002i−2i−2i2i00000002i−2i00000000000
χ462-2-2-22-222-222-2222-2-22-2-200000000002-200-2200000000−2i2i2i−2i0000000−2i2i00000000000
χ472-2-2-22-222-222-2222-2-22-2-20000000000-22002-2000000002i−2i−2i2i0000000−2i2i00000000000
χ482-2-2-22-222-222-2222-2-22-2-20000000000-22002-200000000−2i2i2i−2i00000002i−2i00000000000
χ492-2-2-22-222-222-2-2-2-222-222000000002-200-22000000000000002-2-22000000002-2000000
χ502-2-2-22-222-222-2-2-2-222-222000000002-200-2200000000000000-222-200000000-22000000
χ512-2-2-22-222-222-2-2-2-222-22200000000-22002-2000000000000002-2-2200000000-22000000
χ522-2-2-22-222-222-2-2-2-222-22200000000-22002-200000000000000-222-2000000002-2000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-4-4444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ5544-444-4-4-400000000000022−2222−2222−2222−22000000002-22-20000000000000000000000000000
χ5644-444-4-4-400000000000022−2222−22−2222−222200000000-22-220000000000000000000000000000
χ5744-444-4-4-4000000000000−2222−222222−2222−2200000000-22-220000000000000000000000000000
χ5844-444-4-4-4000000000000−2222−2222−2222−2222000000002-22-20000000000000000000000000000
χ5944-4-4-444-400000000000022−22−22222i2−2i2−2i22i2000000002i−2i−2i2i0000000000000000000000000000
χ6044-4-4-444-400000000000022−22−2222−2i22i22i2−2i200000000−2i2i2i−2i0000000000000000000000000000
χ6144-4-4-444-4000000000000−222222−222i2−2i2−2i22i200000000−2i2i2i−2i0000000000000000000000000000
χ6244-4-4-444-4000000000000−222222−22−2i22i22i2−2i2000000002i−2i−2i2i0000000000000000000000000000
χ634-4-44-44-444-44-4-44-4-4-4444000000000000000000000000000000000000000000000000
χ644-4-44-44-44-44-444-4-44-444-4000000000000000000000000000000000000000000000000
χ654-4-44-44-44-44-44-444-44-4-44000000000000000000000000000000000000000000000000
χ664-4-4-44-4444-4-4444-4-44-44-4000000000000000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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