Finite Group Databasebeta

← Group #346309

Character table — Group #346309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444422224444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1-1-1-111
χ1722222222222222222222222222-2-2-2-200000000-2-2-2-20000-2-200000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000-2-200000000000000000000
χ192222222222-2-2-2-222-2-22222-2-2-2-2-2-2-2-200000000-2-22200002200000000000000000000
χ202222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-20000000022-2-200002200000000000000000000
χ2122222222-2-22222-2-2-2-20000000022-2-200002222000000002-2-2-2-2-20000000000000000
χ2222222222-2-22222-2-2-2-20000000022-2-20000-2-2-2-2000000002-222220000000000000000
χ2322222222-2-22222-2-2-2-200000000-2-222222200000000-2-2-2-2-2200000000000000000000
χ2422222222-2-22222-2-2-2-200000000-2-222-2-2-2-2000000002222-2200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-2000022-2-200000000-22-2-2220000000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-20000-2-22200000000-2222-2-20000000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-22222-2-200000000-2-2222-200000000000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-222-2-2220000000022-2-22-200000000000000000000
χ29222-2-2-22-2-2-222-2-2222-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000i2−i2i2−i22−22−2
χ30222-2-2-22-2-2-222-2-2222-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000−i2i2−i2i2−22−22
χ31222-2-2-22-2-2-222-2-2222-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000i2−i2i2−i2−22−22
χ32222-2-2-22-2-2-222-2-2222-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000−i2i2−i2i22−22−2
χ33222-2-2-22-2-2-2-2-22222-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000i2−i2−i2i22−2−22
χ34222-2-2-22-2-2-2-2-22222-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000−i2i2i2−i2−222−2
χ35222-2-2-22-2-2-2-2-22222-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000i2−i2−i2i2−222−2
χ36222-2-2-22-2-2-2-2-22222-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000−i2i2i2−i22−2−22
χ372-2-2-22-2222-200002-20000002-22-22-22-2002-22-200002-2002-2002-2000000000000000000
χ382-2-2-22-2222-200002-20000002-22-22-22-200-22-2200002-200-2200-22000000000000000000
χ392-2-2-22-2222-200002-20000002-22-2-22-222-200002-200-222-20000002-20000000000000000
χ402-2-2-22-2222-200002-20000002-22-2-22-22-220000-2200-22-22000000-220000000000000000
χ412-2-2-22-2222-200002-2000000-22-222-22-2002-2-220000-22002-200-22000000000000000000
χ422-2-2-22-2222-200002-2000000-22-222-22-200-222-20000-2200-22002-2000000000000000000
χ432-2-2-22-2222-200002-2000000-22-22-22-222-20000-22002-22-2000000-220000000000000000
χ442-2-2-22-2222-200002-2000000-22-22-22-22-2200002-2002-2-220000002-20000000000000000
χ452-2-2-22-222-220000-22002-22-200002-2-222-2002-2002-200-220000-22000000000000000000
χ462-2-2-22-222-220000-22002-22-200002-2-22-2200-22002-2002-200002-2000000000000000000
χ472-2-2-22-222-220000-22002-22-20000-222-2002-2002-2-220000-220000-220000000000000000
χ482-2-2-22-222-220000-22002-22-20000-222-200-2200-22-2200002-200002-20000000000000000
χ492-2-2-22-222-220000-2200-22-2200002-2-222-200-2200-2200-2200002-2000000000000000000
χ502-2-2-22-222-220000-2200-22-2200002-2-22-22002-200-22002-20000-22000000000000000000
χ512-2-2-22-222-220000-2200-22-220000-222-2002-200-222-20000-2200002-20000000000000000
χ522-2-2-22-222-220000-2200-22-220000-222-200-22002-22-200002-20000-220000000000000000
χ53444-4-4-44-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ5544-444-4-4-4004-44-40000000000000000000000000000000000000000002-22-200000000
χ5644-444-4-4-4004-44-4000000000000000000000000000000000000000000-22-2200000000
χ5744-444-4-4-400-44-440000000000000000000000000000000000000000002-2-2200000000
χ5844-444-4-4-400-44-44000000000000000000000000000000000000000000-222-200000000
χ5944-4-4-44-44004-4-44000000000000000000000000000000000000002-22-2000000000000
χ6044-4-4-44-44004-4-4400000000000000000000000000000000000000-22-22000000000000
χ6144-4-4-44-4400-444-4000000000000000000000000000000000000002-2-22000000000000
χ6244-4-4-44-4400-444-400000000000000000000000000000000000000-222-2000000000000
χ634-4-44-444-44-40000-44004i−4i−4i4i0000000000000000000000000000000000000000000000
χ644-4-44-444-44-40000-4400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ654-4-44-444-4-4400004-40000004i−4i−4i4i000000000000000000000000000000000000000000
χ664-4-44-444-4-4400004-4000000−4i4i4i−4i000000000000000000000000000000000000000000
χ678-888-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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