Finite Group Databasebeta

← Group #346645

Character table — Group #346645

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442244444444444444222222444444444444444888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111
χ611111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ711111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ811111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ172222222222-2-222-2-222220000-2-20000-2-2000022-2-2-200-2-200000022000000000000000000
χ182222222222-2-222-2-222220000-2-20000-2-20000-2-222-20022000000-2-2000000000000000000
χ192222222222-2-222-2-2-2-2-2-20000220000-2-200002222200-2-2000000-2-2000000000000000000
χ202222222222-2-222-2-2-2-2-2-20000220000-2-20000-2-2-2-22002200000022000000000000000000
χ2122222222-2-222-2-22222-2-22222-2-2-2-2-2-2-2-20000000022200-2-2000000000000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-22222-2-2000000002-2-20022000000000000000000000000
χ2322222222-2-222-2-222-2-2222222222222-2-200000000-2-2-200-2-2000000000000000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-222-2-2-2-2-2-200000000-2220022000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-200002200002222-2-20000-200000022-2-200000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2000022000022-2-2220000-2000000-2-22200000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000-2-200002222-2-200002000000-2-22200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000-2-2000022-2-2220000200000022-2-200000000000000000000
χ29222-2-2-22-2002-2002-2002i−2i22-2-22i−2i2i2i−2i−2i0000000000000000000000022−2−2i2i2−i2−i22−2i2−i2000000
χ30222-2-2-22-2002-2002-2002i−2i22-2-22i−2i2i2i−2i−2i00000000000000000000000−2−222−i2−i2i2i2−22−i2i2000000
χ31222-2-2-22-2002-2002-2002i−2i-2-2222i−2i−2i−2i2i2i0000000000000000000000022−2−2i2i2−i2−i2−22−i2i2000000
χ32222-2-2-22-2002-2002-2002i−2i-2-2222i−2i−2i−2i2i2i00000000000000000000000−2−222−i2−i2i2i22−2i2−i2000000
χ33222-2-2-22-2002-2002-200−2i2i22-2-2−2i2i−2i−2i2i2i0000000000000000000000022−2−2−i2−i2i2i22−2−i2i2000000
χ34222-2-2-22-2002-2002-200−2i2i22-2-2−2i2i−2i−2i2i2i00000000000000000000000−2−222i2i2−i2−i2−22i2−i2000000
χ35222-2-2-22-2002-2002-200−2i2i-2-222−2i2i2i2i−2i−2i0000000000000000000000022−2−2−i2−i2i2i2−22i2−i2000000
χ36222-2-2-22-2002-2002-200−2i2i-2-222−2i2i2i2i−2i−2i00000000000000000000000−2−222i2i2−i2−i22−2−i2i2000000
χ372-2-2-22-2222-22-22-2-2200000000002-22-22-200002-20002-22-2002-22-200000000000000000000
χ382-2-2-22-2222-22-22-2-2200000000002-22-22-20000-220002-2-2200-22-2200000000000000000000
χ392-2-2-22-2222-22-22-2-220000000000-22-222-200002-2000-222-200-22-2200000000000000000000
χ402-2-2-22-2222-22-22-2-220000000000-22-222-20000-22000-22-22002-22-200000000000000000000
χ412-2-2-22-2222-2-222-22-200002-22-2000000-222-22-22-200000-222-2000000000000000000000000
χ422-2-2-22-2222-2-222-22-200002-22-2000000-22-22-22-22000002-22-2000000000000000000000000
χ432-2-2-22-2222-2-222-22-20000-22-22000000-222-22-2-22000002-2-22000000000000000000000000
χ442-2-2-22-2222-2-222-22-20000-22-22000000-22-22-222-200000-22-22000000000000000000000000
χ452-2-2-22-222-222-2-22-2200000000002-22-2-222-2-22002-20-22000000002-2000000000000000000
χ462-2-2-22-222-222-2-22-2200000000002-22-2-22-222-200-220-2200000000-22000000000000000000
χ472-2-2-22-222-222-2-22-220000000000-22-22-222-2-2200-2202-200000000-22000000000000000000
χ482-2-2-22-222-222-2-22-220000000000-22-22-22-222-2002-202-2000000002-2000000000000000000
χ492-2-2-22-222-22-22-222-200002-22-20000002-20000002-200000-222-2-22-22000000000000000000
χ502-2-2-22-222-22-22-222-200002-22-20000002-2000000-2200000-22-222-22-2000000000000000000
χ512-2-2-22-222-22-22-222-20000-22-220000002-20000002-2000002-2-222-2-22000000000000000000
χ522-2-2-22-222-22-22-222-20000-22-220000002-2000000-22000002-22-2-222-2000000000000000000
χ53444-4-4-44-400-4400-44004i−4i0000−4i4i000000000000000000000000000000000000000000000
χ54444-4-4-44-400-4400-4400−4i4i00004i−4i000000000000000000000000000000000000000000000
χ5544-444-4-4-44400-4-400000000000000000000000000000000000000022−2222−2200000000000000
χ5644-444-4-4-44400-4-4000000000000000000000000000000000000000−2222−222200000000000000
χ5744-444-4-4-4-4-4004400000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ5844-444-4-4-4-4-400440000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5944-4-4-44-44000000004-4000000000000000000000000000000000002-2-222-2-220000000000
χ6044-4-4-44-44000000004-400000000000000000000000000000000000-222-2-222-20000000000
χ6144-4-4-44-4400000000-44000000000000000000000000000000000002-2-22-222-20000000000
χ6244-4-4-44-4400000000-4400000000000000000000000000000000000-222-22-2-220000000000
χ634-44-444-4-44-400-440000000000000000000000000000000000000000000000000002i2−2i20000
χ644-44-444-4-44-400-44000000000000000000000000000000000000000000000000000−2i22i20000
χ654-44-444-4-4-44004-4000000000000000000000000000000000000000000000000000002i2−2i200
χ664-44-444-4-4-44004-400000000000000000000000000000000000000000000000000000−2i22i200
χ674-4-44-444-4004400-4-400000000004i−4i−4i4i00000000000000000000000000000000000000000
χ684-4-44-444-4004400-4-40000000000−4i4i4i−4i00000000000000000000000000000000000000000
χ694-4-44-444-400-4-4004400004-4-4400000000000000000000000000000000000000000000000
χ704-4-44-444-400-4-400440000-444-400000000000000000000000000000000000000000000000
χ718-888-8-8-88000000000000000000000000000000000000000000000000000000000000000

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