Finite Group Databasebeta

← Group #346722

Character table — Group #346722

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
χ31111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-1111111-1-1-1-111-1-11111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1111111-1-1-1-111-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-22200002000000-2-2000000000000000000000000
χ182222222222-2-222-2-22222-2-222222222-2-2-2-20000-2000000-2-2000000000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2-2-20000200000022000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2220000-200000022000000000000000000000000
χ2122222222-2-222-2-222000022-2-2220000-2-2002222-2-2-2000000-2-20000000000000000000000
χ2222222222-2-222-2-222000022-2-2220000-2-200-2-2-2-2-222000000220000000000000000000000
χ2322222222-2-222-2-2220000-2-222-2-20000-2-20022-2-22-2-2000000220000000000000000000000
χ2422222222-2-222-2-2220000-2-222-2-20000-2-200-2-222222000000-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-2000022000000-20022-2-2000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-2000022000000-200-2-2220000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2-2-22200002200000020022-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2-2-222000022000000200-2-222000022-2-2000000000000000000
χ2922-2-22-22-22-2002-20022-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ3022-2-22-22-22-2002-20022-2-2002i−2i2i−2i2i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ3122-2-22-22-22-2002-20022-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ3222-2-22-22-22-2002-20022-2-200−2i2i−2i2i−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ3322-2-22-22-22-2002-200-2-222002i−2i2i−2i−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ3422-2-22-22-22-2002-200-2-222002i−2i2i−2i−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ3522-2-22-22-22-2002-200-2-22200−2i2i−2i2i2i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ3622-2-22-22-22-2002-200-2-22200−2i2i−2i2i2i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ372-2-2-2-22222-22-2-222-22-22-200000000002-200002-200000002-22-22-22-2000000000000000000
χ382-2-2-2-22222-22-2-222-22-22-200000000002-20000-2200000002-2-22-22-22000000000000000000
χ392-2-2-2-22222-22-2-222-2-22-2200000000002-200002-20000000-222-2-22-22000000000000000000
χ402-2-2-2-22222-22-2-222-2-22-2200000000002-20000-220000000-22-222-22-2000000000000000000
χ412-2-2-2-22222-2-22-22-222-22-20000000000-22002-20002-22-22-2-22000000000000000000000000
χ422-2-2-2-22222-2-22-22-222-22-20000000000-2200-22000-22-22-22-22000000000000000000000000
χ432-2-2-2-22222-2-22-22-22-22-220000000000-22002-20002-2-22-222-2000000000000000000000000
χ442-2-2-2-22222-2-22-22-22-22-220000000000-2200-22000-222-22-22-2000000000000000000000000
χ452-2-2-2-2222-222-22-22-200000000002-22-2-222-2002-20002-2-2200-220000000000000000000000
χ462-2-2-2-2222-222-22-22-200000000002-22-2-222-200-22000-222-2002-20000000000000000000000
χ472-2-2-2-2222-222-22-22-20000000000-22-22-22-22002-2000-222-200-220000000000000000000000
χ482-2-2-2-2222-222-22-22-20000000000-22-22-22-2200-220002-2-22002-20000000000000000000000
χ492-2-2-2-2222-22-222-2-2200000000002-22-22-2-222-2000-2200000000-222-2000000000000000000
χ502-2-2-2-2222-22-222-2-2200000000002-22-22-2-22-220002-2000000002-2-22000000000000000000
χ512-2-2-2-2222-22-222-2-220000000000-22-222-22-22-2000-22000000002-2-22000000000000000000
χ522-2-2-2-2222-22-222-2-220000000000-22-222-22-2-220002-200000000-222-2000000000000000000
χ53444-4-44-4-40000000000004-400000000000000000000000000000002-22-22-22-20000000000
χ54444-4-44-4-40000000000004-40000000000000000000000000000000-22-22-22-220000000000
χ55444-4-44-4-4000000000000-4400000000000000000000000000000002-22-2-22-220000000000
χ56444-4-44-4-4000000000000-440000000000000000000000000000000-22-222-22-20000000000
χ5744-44-4-4-44004400-4-4000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ5844-44-4-4-44004400-4-400000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ5944-44-4-4-4400-4-40044000000000000000000000000000000000000022−22−222200000000000000
χ6044-44-4-4-4400-4-400440000000000000000000000000000000000000−222222−2200000000000000
χ6144-4-44-44-4-4400-44000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ6244-4-44-44-4-4400-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ634-444-4-44-44400-4-4004-4-44000000000000000000000000000000000000000000000000000
χ644-444-4-44-44400-4-400-444-4000000000000000000000000000000000000000000000000000
χ654-444-4-44-4-4-400440000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ664-444-4-44-4-4-40044000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ674-44-44-4-44004-400-44000000000000000000000000000000000000000000000000022−220000
χ684-44-44-4-44004-400-440000000000000000000000000000000000000000000000000−22220000
χ694-44-44-4-4400-44004-400000000000000000000000000000000000000000000000000022−2200
χ704-44-44-4-4400-44004-4000000000000000000000000000000000000000000000000000−222200
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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