Finite Group Databasebeta

← Group #275366

Character table — Group #275366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444442244444444444444888888884444488888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ91111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ101111111111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ111111111111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-11
χ121111111111111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-111-1-111-1-1-1-111-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ17222222222-2-222-2-2222-2-2-2-2222222-2-2-2-200000000-222-2-200000000000000000000000000
χ18222222222-2-222-2-2222-2-2-2-222-2-2-2-2222200000000-2-2-22200000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-222-2-22222-2-2-2-2000000002-2-22200000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-222-2-2-2-2-2-2222200000000222-2-200000000000000000000000000
χ2122222222-222-2-222-222-2-2-2-2-2-2000000002222-2-2-2-220000-2-2220000000000000000000000
χ2222222222-222-2-222-222-2-2-2-2-2-200000000-2-2-2-222222000022-2-20000000000000000000000
χ2322222222-222-2-222-2-2-2-2-222220000000022222222-20000-2-2-2-20000000000000000000000
χ2422222222-222-2-222-2-2-2-2-2222200000000-2-2-2-2-2-2-2-2-2000022220000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-20000000000000000-2000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-20000000000000000-200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000002000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000200000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ29222-2-22-2-2-22-22-22-22002-200002i2i−2i−2i2i2i−2i−2i0000000000000000000000000002i−2i0000002-200
χ30222-2-22-2-2-22-22-22-22002-200002i2i−2i−2i2i2i−2i−2i000000000000000000000000000−2i2i000000-2200
χ31222-2-22-2-2-22-22-22-22002-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000002i−2i000000-2200
χ32222-2-22-2-2-22-22-22-22002-20000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000−2i2i0000002-200
χ33222-2-22-2-2-2-222-2-22200-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000000002i−2i0000002-20000
χ34222-2-22-2-2-2-222-2-22200-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−2i2i000000-220000
χ35222-2-22-2-2-2-222-2-22200-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000000002i−2i000000-220000
χ36222-2-22-2-2-2-222-2-22200-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−2i2i0000002-20000
χ372-2-22-222-2200-2-20022-200002-200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20002i−2ii2−i2i2−i22−22−22−22−200000000000000
χ382-2-22-222-2200-2-20022-200002-200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20002i−2i−i2i2−i2i2−22−22−22−2200000000000000
χ392-2-22-222-2200-2-20022-200002-20000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000−2i2ii2−i2i2−i2−22−22−22−2200000000000000
χ402-2-22-222-2200-2-20022-200002-20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000−2i2i−i2i2−i2i22−22−22−22−200000000000000
χ412-2-22-222-2200-2-2002-220000-2200002i−2i2i−2ii2i2−i2−i2−i2−i2i2i2000−2i2ii2−i2−i2i22−22−2−22−2200000000000000
χ422-2-22-222-2200-2-2002-220000-2200002i−2i2i−2i−i2−i2i2i2i2i2−i2−i2000−2i2i−i2i2i2−i2−22−222−22−200000000000000
χ432-2-22-222-2200-2-2002-220000-220000−2i2i−2i2ii2i2−i2−i2−i2−i2i2i20002i−2ii2−i2−i2i2−22−222−22−200000000000000
χ442-2-22-222-2200-2-2002-220000-220000−2i2i−2i2i−i2−i2i2i2i2i2−i2−i20002i−2i−i2i2i2−i22−22−2−22−2200000000000000
χ452-2-22-222-2-2002200-22-20000-222-22-20000i2i2−i2−i2−i2−i2i2i202-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000000000
χ462-2-22-222-2-2002200-22-20000-222-22-20000−i2−i2i2i2i2i2−i2−i202-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000000000
χ472-2-22-222-2-2002200-22-20000-22-22-220000i2i2−i2−i2−i2−i2i2i20-2200−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000
χ482-2-22-222-2-2002200-22-20000-22-22-220000−i2−i2i2i2i2i2−i2−i20-2200i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000
χ492-2-22-222-2-2002200-2-2200002-22-22-20000i2i2−i2−i2i2i2−i2−i20-2200−i2i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000000
χ502-2-22-222-2-2002200-2-2200002-22-22-20000−i2−i2i2i2−i2−i2i2i20-2200i2−i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000000
χ512-2-22-222-2-2002200-2-2200002-2-22-220000i2i2−i2−i2i2i2−i2−i202-200−i2i2−i2i2−i2i2i2−i2i2−i2−i2i200000000000000
χ522-2-22-222-2-2002200-2-2200002-2-22-220000−i2−i2i2i2−i2−i2i2i202-200i2−i2i2−i2i2−i2−i2i2−i2i2i2−i200000000000000
χ53444-4-44-4-444-4-444-4-400-44000000000000000000000000000000000000000000000000000
χ54444-4-44-4-44-44-44-44-4004-4000000000000000000000000000000000000000000000000000
χ5544-444-4-4-404-400-440000000000000000000004-44-40000000000000000000000000000000
χ5644-444-4-4-404-400-44000000000000000000000-44-440000000000000000000000000000000
χ5744-444-4-4-40-44004-4000000000000000004-44-400000000000000000000000000000000000
χ5844-444-4-4-40-44004-400000000000000000-44-4400000000000000000000000000000000000
χ5944-4-4-4-44404400-4-400000000000000000000000000000000000000000000002i2−2i200000000
χ6044-4-4-4-44404400-4-40000000000000000000000000000000000000000000000−2i22i200000000
χ6144-4-4-4-4440-4-4004400000000000000000000000000000000000000000000000022−22000000
χ6244-4-4-4-4440-4-40044000000000000000000000000000000000000000000000000−2222000000
χ634-444-4-4-440000000000004-400000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000
χ644-444-4-4-440000000000004-40000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000
χ654-444-4-4-44000000000000-4400000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ664-444-4-4-44000000000000-440000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ674-4-4-444-444004-400-4000000004i−4i−4i4i0000000000000000000000000000000000000000000
χ684-4-4-444-444004-400-400000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ694-4-4-444-44-400-440040000000000004-4-44000000000000000000000000000000000000000
χ704-4-4-444-44-400-44004000000000000-444-4000000000000000000000000000000000000000
χ718-88-88-88-8000000000000000000000000000000000000000000000000000000000000000

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