Finite Group Databasebeta

← Group #346716

Character table — Group #346716

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222224444444444222222224444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ611111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-111-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ101111111111111111-1-1-1-1111111-1-1-1-111-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111-1-11111111111-1-1-1-11111-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ131111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-2222222-2-2-2-2-2-2-2-2-2-222000000200000000-2-200000000000000000000
χ182222222222-2-222-2-22222-2-222222222-2-2-2-2000000-200000000-2-200000000000000000000
χ192222222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2-2-20000002000000002200000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-222000000-2000000002200000000000000000000
χ2122222222-2-222-2-222000022-2-2220000-2-200000022-2-2-200002200-2-2000000000000000000
χ2222222222-2-222-2-222000022-2-2220000-2-2000000-2-2-2220000-2-20022000000000000000000
χ2322222222-2-222-2-2220000-2-222-2-20000-2-2000000222-2-20000-2-20022000000000000000000
χ2422222222-2-222-2-2220000-2-222-2-20000-2-2000000-2-222200002200-2-2000000000000000000
χ2522222222-2-2-2-2-2-2-2-200002222-2-20000220022-2-200-20022-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-200002222-2-200002200-2-22200-200-2-222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-20000-2-2-2-2220000220022-2-200200-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-20000-2-2-2-22200002200-2-2220020022-2-2000000000000000000000000
χ2922-2-222-2-22-2002-20022-2-2002i−2i2i−2i2i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ3022-2-222-2-22-2002-20022-2-2002i−2i2i−2i2i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ3122-2-222-2-22-2002-20022-2-200−2i2i−2i2i−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ3222-2-222-2-22-2002-20022-2-200−2i2i−2i2i−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ3322-2-222-2-22-2002-200-2-222002i−2i2i−2i−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ3422-2-222-2-22-2002-200-2-222002i−2i2i−2i−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ3522-2-222-2-22-2002-200-2-22200−2i2i−2i2i2i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ3622-2-222-2-22-2002-200-2-22200−2i2i−2i2i2i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ372-2-2-22-2222-22-2-222-22-22-200000000002-2000000000002-22-22-22-22-2000000000000000000
χ382-2-2-22-2222-22-2-222-22-22-200000000002-200000000000-22-22-222-2-22000000000000000000
χ392-2-2-22-2222-22-2-222-2-22-2200000000002-2000000000002-22-2-22-22-22000000000000000000
χ402-2-2-22-2222-22-2-222-2-22-2200000000002-200000000000-22-222-2-222-2000000000000000000
χ412-2-2-22-2222-2-22-22-222-22-20000000000-22002-22-22-202-2000000-2200000000000000000000
χ422-2-2-22-2222-2-22-22-222-22-20000000000-2200-22-22-220-22000000-2200000000000000000000
χ432-2-2-22-2222-2-22-22-22-22-220000000000-22002-22-2-220-220000002-200000000000000000000
χ442-2-2-22-2222-2-22-22-22-22-220000000000-2200-22-222-202-20000002-200000000000000000000
χ452-2-2-22-222-222-22-22-200000000002-22-2-222-22-2-220000000002-200-22000000000000000000
χ462-2-2-22-222-222-22-22-200000000002-22-2-222-2-222-2000000000-22002-2000000000000000000
χ472-2-2-22-222-222-22-22-20000000000-22-22-22-222-2-22000000000-22002-2000000000000000000
χ482-2-2-22-222-222-22-22-20000000000-22-22-22-22-222-20000000002-200-22000000000000000000
χ492-2-2-22-222-22-222-2-2200000000002-22-22-2-2200002-20-22-222-2000000000000000000000000
χ502-2-2-22-222-22-222-2-2200000000002-22-22-2-220000-2202-22-2-22000000000000000000000000
χ512-2-2-22-222-22-222-2-220000000000-22-222-22-200002-20-222-2-22000000000000000000000000
χ522-2-2-22-222-22-222-2-220000000000-22-222-22-20000-2202-2-222-2000000000000000000000000
χ53444-4-4-44-40000000000004-400000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000
χ54444-4-4-44-40000000000004-40000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000
χ55444-4-4-44-4000000000000-4400000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000
χ56444-4-4-44-4000000000000-440000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000
χ5744-44-4-4-44004400-4-400000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ5844-44-4-4-44004400-4-40000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ5944-44-4-4-4400-4-400440000000000000000000000000000000000000000022−22−22220000000000
χ6044-44-4-4-4400-4-4004400000000000000000000000000000000000000000−222222−220000000000
χ6144-4-444-4-4-4400-44000000004i−4i−4i4i000000000000000000000000000000000000000000000
χ6244-4-444-4-4-4400-4400000000−4i4i4i−4i000000000000000000000000000000000000000000000
χ634-4444-4-4-44400-4-4004-4-44000000000000000000000000000000000000000000000000000
χ644-4444-4-4-44400-4-400-444-4000000000000000000000000000000000000000000000000000
χ654-4444-4-4-4-4-400440000000000004i−4i−4i4i00000000000000000000000000000000000000000
χ664-4444-4-4-4-4-40044000000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ674-44-4-44-44004-400-4400000000000000000000000000000000000000000000000000022−2200
χ684-44-4-44-44004-400-44000000000000000000000000000000000000000000000000000−222200
χ694-44-4-44-4400-44004-4000000000000000000000000000000000000000000000000022−220000
χ704-44-4-44-4400-44004-40000000000000000000000000000000000000000000000000−22220000
χ718-8-88-888-8000000000000000000000000000000000000000000000000000000000000000

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