Finite Group Databasebeta

← Group #419713

Character table — Group #419713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222222244448888888888888888888888888888881616161616161616161616161616
order12222222222222222222444422222244444444444444444444444424444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1
χ31111111111111111111111111111-1-111111111-1-1-1-111-1-111111111-1-1-111-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-111111-1-1-1-1
χ911111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-111111-1-1-1-111
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111-1-111
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ1411111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1111-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1111-1-111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-222222000000000022-2-20000-2-200000000000002-2000000000
χ1822222222222-2-2-2-2-2-2-2-2222220000000000-2-2220000-2-20000000000000-22000000000
χ1922222222222-2-2-2-2-2-2-2-22-2-2-2-2000000000022-2-20000220000000000000-22000000000
χ2022222222222-2-2-2-2-2-2-2-22-2-2-2-20000000000-2-22200002200000000000002-2000000000
χ2122222222-2-2-222-2-222-2-2-222-2-20000000000000022-2-22-2000000000020000-200000000
χ2222222222-2-2-222-2-222-2-2-222-2-200000000000000-2-2222-20000000000-20000200000000
χ2322222222-2-2-222-2-222-2-2-2-2-2220000000000000022-2-2-220000000000-20000200000000
χ2422222222-2-2-222-2-222-2-2-2-2-22200000000000000-2-222-22000000000020000-200000000
χ2522222222-2-2-2-2-222-2-222-222-2-2000022000000000000-22-2-20000000002-200000000000
χ2622222222-2-2-2-2-222-2-222-222-2-20000-2-2000000000000-2222000000000-2200000000000
χ2722222222-2-2-2-2-222-2-222-2-2-2220000220000000000002-2-2-2000000000-2200000000000
χ2822222222-2-2-2-2-222-2-222-2-2-2220000-2-20000000000002-2220000000002-200000000000
χ29222-2-2-2-2222-22-22-22-22-2-2000000000022-2-22i−2i2i−2i0000000000002i2i−2i−2i00000000000000
χ30222-2-2-2-2222-22-22-22-22-2-2000000000022-2-2−2i2i−2i2i000000000000−2i−2i2i2i00000000000000
χ31222-2-2-2-2222-22-22-22-22-2-20000000000-2-2222i−2i2i−2i000000000000−2i−2i2i2i00000000000000
χ32222-2-2-2-2222-22-22-22-22-2-20000000000-2-222−2i2i−2i2i0000000000002i2i−2i−2i00000000000000
χ33222-2-2-2-2222-2-22-22-22-22-2000022-2-20000002i−2i−2i2i000000002i2i−2i−2i000000000000000000
χ34222-2-2-2-2222-2-22-22-22-22-2000022-2-2000000−2i2i2i−2i00000000−2i−2i2i2i000000000000000000
χ35222-2-2-2-2222-2-22-22-22-22-20000-2-2220000002i−2i−2i2i00000000−2i−2i2i2i000000000000000000
χ36222-2-2-2-2222-2-22-22-22-22-20000-2-222000000−2i2i2i−2i000000002i2i−2i−2i000000000000000000
χ372-2-222-2-222-22222-2-2-2-22-2000000002-2000000000000002-22i−2i2i−2i000000000000002i−2i00
χ382-2-222-2-222-22222-2-2-2-22-2000000002-2000000000000002-2−2i2i−2i2i00000000000000−2i2i00
χ392-2-222-2-222-22222-2-2-2-22-200000000-2200000000000000-222i−2i2i−2i00000000000000−2i2i00
χ402-2-222-2-222-22222-2-2-2-22-200000000-2200000000000000-22−2i2i−2i2i000000000000002i−2i00
χ412-2-222-2-22-22-2-2-22-222-222000000002-200000000000000-2200002-22-20000000000002-2
χ422-2-222-2-22-22-2-2-22-222-222000000002-200000000000000-220000-22-22000000000000-22
χ432-2-222-2-22-22-2-2-22-222-22200000000-22000000000000002-200002-22-2000000000000-22
χ442-2-222-2-22-22-2-2-22-222-22200000000-22000000000000002-20000-22-220000000000002-2
χ452-2-2-2-22222-2-2-22-2-22-22220000000000000000002-22-200002-2-2200000000002-2000000
χ462-2-2-2-22222-2-2-22-2-22-22220000000000000000002-22-20000-222-20000000000-22000000
χ472-2-2-2-22222-2-2-22-2-22-2222000000000000000000-22-2200002-2-220000000000-22000000
χ482-2-2-2-22222-2-2-22-2-22-2222000000000000000000-22-220000-222-200000000002-2000000
χ492-2-2-2-2222-222-22222-2-2-2-20000000000000000002-2-22000000002i−2i−2i2i000000002i−2i0000
χ502-2-2-2-2222-222-22222-2-2-2-20000000000000000002-2-2200000000−2i2i2i−2i00000000−2i2i0000
χ512-2-2-2-2222-222-22222-2-2-2-2000000000000000000-222-2000000002i−2i−2i2i00000000−2i2i0000
χ522-2-2-2-2222-222-22222-2-2-2-2000000000000000000-222-200000000−2i2i2i−2i000000002i−2i0000
χ53444-4-4-4-44-4-444-4-444-4-444000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-44-444-4-444-44000000000000000000000000000000000000000000000000
χ5544-44-44-4-4000000000000004i−4i2-22-2002i−2i2i−2i0000000000000000000000000000000000
χ5644-44-44-4-4000000000000004i−4i-22-2200−2i2i−2i2i0000000000000000000000000000000000
χ5744-44-44-4-400000000000000−4i4i2-22-200−2i2i−2i2i0000000000000000000000000000000000
χ5844-44-44-4-400000000000000−4i4i-22-22002i−2i2i−2i0000000000000000000000000000000000
χ5944-4-44-44-40000000000004i−4i002-2-22002i−2i−2i2i0000000000000000000000000000000000
χ6044-4-44-44-40000000000004i−4i00-222-200−2i2i2i−2i0000000000000000000000000000000000
χ6144-4-44-44-4000000000000−4i4i002-2-2200−2i2i2i−2i0000000000000000000000000000000000
χ6244-4-44-44-4000000000000−4i4i00-222-2002i−2i−2i2i0000000000000000000000000000000000
χ634-4-444-4-444-44-4-4-44444-4-4000000000000000000000000000000000000000000000000
χ644-4-444-4-44-44-444-44-4-44-44000000000000000000000000000000000000000000000000
χ654-4-4-4-44444-4-44-444-44-4-44000000000000000000000000000000000000000000000000
χ664-4-4-4-4444-4444-4-4-4-4444-4000000000000000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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