Finite Group Databasebeta

← Group #267748

Character table — Group #267748

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-11-1-11111-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11-11111111-1-1-1-1
χ91111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-111-111-1-1111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-11-1-111-1-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1111-1-111
χ121111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-1111-1-1-111-1-1
χ131111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-111-1111-1-1-1-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11111-111-1-11-1-1-111111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-11-1-111-11-1-111-111-1-1
χ161111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-111-1-11-111-1-11-1-111
χ17222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-22200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-222-2-200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-22-222-2-200002-2000000000000000000000022-20-200000000000
χ2222222222-2-22222-2-2-2-22-222-2-200002-20000000000000000000000-2-220200000000000
χ2322222222-2-22222-2-2-2-2-22-2-2220000-22000000000000000000000000020-2-2000020000
χ2422222222-2-22222-2-2-2-2-22-2-2220000-220000000000000000000000000-20220000-20000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-22200002-200000000000000000000002-220-200000000000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-22200002-20000000000000000000000-22-20200000000000
χ2722222222-2-2-2-2-2-2-2-222-2222-2-20000-220000000000000000000000000202-20000-20000
χ2822222222-2-2-2-2-2-2-2-222-2222-2-20000-220000000000000000000000000-20-22000020000
χ29222-22-2-2-2-2-222-2-2222-20000002i2i−2i−2i0000002i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−20000000000000000
χ30222-22-2-2-2-2-222-2-2222-20000002i2i−2i−2i0000002i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−2220000000000000000
χ31222-22-2-2-2-2-222-2-2222-2000000−2i−2i2i2i000000−2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−2220000000000000000
χ32222-22-2-2-2-2-222-2-2222-2000000−2i−2i2i2i000000−2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−20000000000000000
χ33222-22-2-2-2-2-2-2-22222-220000002i2i−2i−2i000000−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ34222-22-2-2-2-2-2-2-22222-220000002i2i−2i−2i000000−2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ35222-22-2-2-2-2-2-2-22222-22000000−2i−2i2i2i0000002i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ36222-22-2-2-2-2-2-2-22222-22000000−2i−2i2i2i0000002i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ372-2-2222-2-22-200002-200002i−2i2i−2i2i−2i2i−2i00002-200i2−i2i2−i22−22−22−22−2i2−i2i2−i20000000000000000
χ382-2-2222-2-22-200002-200002i−2i2i−2i2i−2i2i−2i00002-200−i2i2−i2i2−22−22−22−22−i2i2−i2i20000000000000000
χ392-2-2222-2-22-200002-200002i−2i2i−2i−2i2i−2i2i0000-2200i2−i2i2−i22−22−2−22−22−i2i2−i2i20000000000000000
χ402-2-2222-2-22-200002-200002i−2i2i−2i−2i2i−2i2i0000-2200−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
χ412-2-2222-2-22-200002-20000−2i2i−2i2i2i−2i2i−2i0000-2200i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ422-2-2222-2-22-200002-20000−2i2i−2i2i2i−2i2i−2i0000-2200−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ432-2-2222-2-22-200002-20000−2i2i−2i2i−2i2i−2i2i00002-200i2−i2i2−i2−22−22−22−22i2−i2i2−i20000000000000000
χ442-2-2222-2-22-200002-20000−2i2i−2i2i−2i2i−2i2i00002-200−i2i2−i2i22−22−22−22−2−i2i2−i2i20000000000000000
χ452-2-2-22-222-2200002-2002200002-2-22-2-22-2000000002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ462-2-2-22-222-2200002-2002200002-2-22-2-22-200000000−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ472-2-2-22-222-2200002-200220000-222-2-2-2-22000000002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ482-2-2-22-222-2200002-200220000-222-2-2-2-2200000000−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ492-2-2-22-222-2200002-200-2-200002-2-2222-2200002-2-2200002-2-2200000000000000000000
χ502-2-2-22-222-2200002-200-2-200002-2-2222-220000-222-20000-222-200000000000000000000
χ512-2-2-22-222-2200002-200-2-20000-222-2222-200002-2-220000-222-200000000000000000000
χ522-2-2-22-222-2200002-200-2-20000-222-2222-20000-222-200002-2-2200000000000000000000
χ53444-44-4-4-44444-4-4-4-4-4400000000000000000000000000000000000000000000000000
χ54444-44-4-4-444-4-444-4-44-400000000000000000000000000000000000000000000000000
χ5544-44-4-4-44004-44-40000000000000000000000000000000000000000000002i−2i2i−2i00000
χ5644-44-4-4-44004-44-4000000000000000000000000000000000000000000000−2i2i−2i2i00000
χ5744-44-4-4-4400-44-440000000000000000000000000000000000000000000002i−2i−2i2i00000
χ5844-44-4-4-4400-44-44000000000000000000000000000000000000000000000−2i2i2i−2i00000
χ5944-4-4-444-4004-4-44000000000000000000000000000000000000000000000000002i−2i2i−2i
χ6044-4-4-444-4004-4-4400000000000000000000000000000000000000000000000000−2i2i−2i2i
χ6144-4-4-444-400-444-4000000000000000000000000000000000000000000000000002i−2i−2i2i
χ6244-4-4-444-400-444-400000000000000000000000000000000000000000000000000−2i2i2i−2i
χ634-4-4444-4-4-440000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ644-4-4444-4-4-440000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ654-4-4-44-4444-40000-44004-400000000-4400000000000000000000000000000000000000
χ664-4-4-44-4444-40000-4400-44000000004-400000000000000000000000000000000000000
χ678-888-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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