Finite Group Databasebeta

← Group #346724

Character table — Group #346724

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222224444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-1111111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2000022-2-2-2-20000-2-222-2-200002-2-20000220000000000000000000000
χ182222222222-2-222-2-2000022-2-2-2-20000-2-2-2-22200002220000-2-20000000000000000000000
χ192222222222-2-222-2-20000-2-222220000-2-222220000-2-2-20000-2-20000000000000000000000
χ202222222222-2-222-2-20000-2-222220000-2-2-2-2-2-20000-2220000220000000000000000000000
χ2122222222-2-222-2-222222222-2-2222222-2-20000-2-2-2-2-2000000000000000000000000000000
χ2222222222-2-222-2-2222222-2-222-2-2-2-2-2-2-2-2000022-2-22000000000000000000000000000000
χ2322222222-2-222-2-222-2-2-2-222-2-222-2-2-2-2-2-200002222-2000000000000000000000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-222-2-22222-2-20000-2-2222000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-200002200000000-20022-2-20022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-200002200000000-200-2-22200-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2-2-2220000220000000020022-2-200-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2-2-22200002200000000200-2-2220022-2-2000000000000000000
χ29222-2-2-2-22002200-2-222-2-22-2002-222-2-200000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-2-2-2-22002200-2-222-2-22-2002-222-2-200000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-2-2-2-22002200-2-222-2-2-2200-22-2-22200000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ32222-2-2-2-22002200-2-222-2-2-2200-22-2-22200000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ33222-2-2-2-22002200-2-2-2-2222-2002-2-2-22200000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ34222-2-2-2-22002200-2-2-2-2222-2002-2-2-22200000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ35222-2-2-2-22002200-2-2-2-222-2200-2222-2-200000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-2-2-2-22002200-2-2-2-222-2200-2222-2-200000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ372-2-2-22-2222-22-22-22-200000000002-22-22-2002-22-2000002-22-22-20000000000000000000000
χ382-2-2-22-2222-22-22-22-200000000002-22-22-200-222-200000-22-22-220000000000000000000000
χ392-2-2-22-2222-22-22-22-20000000000-22-222-2002-2-2200000-22-222-20000000000000000000000
χ402-2-2-22-2222-22-22-22-20000000000-22-222-200-22-22000002-22-2-220000000000000000000000
χ412-2-2-22-2222-2-222-2-222-22-20000000000-22002-2002-20000000-222-22-2000000000000000000
χ422-2-2-22-2222-2-222-2-222-22-20000000000-2200-22002-200000002-2-22-22000000000000000000
χ432-2-2-22-2222-2-222-2-22-22-220000000000-22002-200-220000000-22-22-22000000000000000000
χ442-2-2-22-2222-2-222-2-22-22-220000000000-2200-2200-2200000002-22-22-2000000000000000000
χ452-2-2-22-222-222-2-222-200000000002-22-2-222-200-220002-20000002-2-22000000000000000000
χ462-2-2-22-222-222-2-222-200000000002-22-2-22-2200-22000-22000000-222-2000000000000000000
χ472-2-2-22-222-222-2-222-20000000000-22-22-222-2002-20002-2000000-222-2000000000000000000
χ482-2-2-22-222-222-2-222-20000000000-22-22-22-22002-2000-220000002-2-22000000000000000000
χ492-2-2-22-222-22-22-22-222-22-200000000002-22-20000-220-22-222-2000000000000000000000000
χ502-2-2-22-222-22-22-22-222-22-200000000002-2-220000-2202-22-2-22000000000000000000000000
χ512-2-2-22-222-22-22-22-22-22-2200000000002-22-200002-20-222-2-22000000000000000000000000
χ522-2-2-22-222-22-22-22-22-22-2200000000002-2-2200002-202-2-222-2000000000000000000000000
χ53444-4-4-4-4400-4-4004400004-400-44000000000000000000000000000000000000000000000
χ54444-4-4-4-4400-4-400440000-44004-4000000000000000000000000000000000000000000000
χ5544-444-4-4-4000000000000004-4000000000000000000000000000002-22-22-22-20000000000
χ5644-444-4-4-4000000000000004-400000000000000000000000000000-22-22-22-220000000000
χ5744-444-4-4-400000000000000-44000000000000000000000000000002-22-2-22-220000000000
χ5844-444-4-4-400000000000000-4400000000000000000000000000000-22-222-22-20000000000
χ5944-4-4-444-44-400-440000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ6044-4-4-444-44-400-44000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ6144-4-4-444-4-44004-400000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ6244-4-4-444-4-44004-40000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ634-444-4-44-44400-4-40000000000000000000000000000000000000000000000000000022−2200
χ644-444-4-44-44400-4-400000000000000000000000000000000000000000000000000000−222200
χ654-444-4-44-4-4-400440000000000000000000000000000000000000000000000000002i2−2i20000
χ664-444-4-44-4-4-40044000000000000000000000000000000000000000000000000000−2i22i20000
χ674-4-44-44-44004-400-4400000000004-4-4400000000000000000000000000000000000000000
χ684-4-44-44-44004-400-440000000000-444-400000000000000000000000000000000000000000
χ694-4-44-44-4400-44004-44-4-44000000000000000000000000000000000000000000000000000
χ704-4-44-44-4400-44004-4-444-4000000000000000000000000000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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