Finite Group Databasebeta

← Group #316319

Character table — Group #316319

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888222444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1111111-1-1-1-111
χ9111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1111-1-1-1-1-1-1-111-1-111-1-111
χ10111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-1-1111-1-111-1-111-1-1
χ11111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-1-1-111111-1-1-1-1-111-1-11111
χ12111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1111111111-1-111-1-1-1-1
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-11-1-111-11111-1-1-1-111-1-1
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-1-1-1-1111-1-1-1-11111-1-111
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111111-1-1-111-1-11111-1-1-1-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-111-1-11-1-111-1-1-1-11111
χ17222222222222222-2-2-2-22-2-2-2-222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2222-2-2-2-22222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ20222222222-2-2-2-222-2-2-2-2222-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ2122222222-22222-2-22222-222-2-2-2-2-2-20000000000000000002-200-200002000000000000
χ2222222222-22222-2-22222-222-2-2-2-2-2-2000000000000000000-220020000-2000000000000
χ2322222222-22222-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000002i−2i000000002i−2i
χ2422222222-22222-2-2-2-2-2-2-2-2-222-2-2220000000000000000000000000000−2i2i00000000−2i2i
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-222220000000000000000002200-20000-2000000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-22222000000000000000000-2-200200002000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000002i−2i00000000−2i2i
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-20000000000000000000000000000−2i2i000000002i−2i
χ2922-2-222-2-222i2i−2i−2i-2-20000200002i−2i0000002i2i−2i−2i22-2-20000000000000000002−2i2−i22−2i2−i200
χ3022-2-222-2-222i2i−2i−2i-2-20000200002i−2i0000002i2i−2i−2i22-2-2000000000000000000−22−i2i2−22−i2i200
χ3122-2-222-2-222i2i−2i−2i-2-20000200002i−2i000000−2i−2i2i2i-2-2220000000000000000002−2i2−i2−22−i2i200
χ3222-2-222-2-222i2i−2i−2i-2-20000200002i−2i000000−2i−2i2i2i-2-222000000000000000000−22−i2i22−2i2−i200
χ3322-2-222-2-22−2i−2i2i2i-2-2000020000−2i2i0000002i2i−2i−2i-2-2220000000000000000002−2−i2i2−22i2−i200
χ3422-2-222-2-22−2i−2i2i2i-2-2000020000−2i2i0000002i2i−2i−2i-2-222000000000000000000−22i2−i22−2−i2i200
χ3522-2-222-2-22−2i−2i2i2i-2-2000020000−2i2i000000−2i−2i2i2i22-2-20000000000000000002−2−i2i22−2−i2i200
χ3622-2-222-2-22−2i−2i2i2i-2-2000020000−2i2i000000−2i−2i2i2i22-2-2000000000000000000−22i2−i2−22i2−i200
χ372-22-22-22-2200002-222-2-2-2002-200002i2i−2i−2i00002i−2i2i−2i000000000002-22i−2i0000000000000
χ382-22-22-22-2200002-222-2-2-2002-200002i2i−2i−2i00002i−2i2i−2i00000000000-22−2i2i0000000000000
χ392-22-22-22-2200002-222-2-2-2002-20000−2i−2i2i2i0000−2i2i−2i2i000000000002-2−2i2i0000000000000
χ402-22-22-22-2200002-222-2-2-2002-20000−2i−2i2i2i0000−2i2i−2i2i00000000000-222i−2i0000000000000
χ412-22-22-22-2200002-2-2-222-200-2200002i2i−2i−2i0000−2i2i−2i2i00002-2002i−2i000000000000000000
χ422-22-22-22-2200002-2-2-222-200-2200002i2i−2i−2i0000−2i2i−2i2i0000-2200−2i2i000000000000000000
χ432-22-22-22-2200002-2-2-222-200-220000−2i−2i2i2i00002i−2i2i−2i00002-200−2i2i000000000000000000
χ442-22-22-22-2200002-2-2-222-200-220000−2i−2i2i2i00002i−2i2i−2i0000-22002i−2i000000000000000000
χ45444-4-4-4-440000000000000000004i−4i2i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ46444-4-4-4-440000000000000000004i−4i−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ47444-4-4-4-44000000000000000000−4i4i2i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ48444-4-4-4-44000000000000000000−4i4i−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ4944-44-4-44-400000004-44-400000000000002i2−2i2−2i22i200002i22i2−2i2−2i2000000000000000000000000
χ5044-44-4-44-400000004-44-40000000000000−2i22i22i2−2i20000−2i2−2i22i22i2000000000000000000000000
χ5144-44-4-44-40000000-44-4400000000000002i2−2i2−2i22i20000−2i2−2i22i22i2000000000000000000000000
χ5244-44-4-44-40000000-44-440000000000000−2i22i22i2−2i200002i22i2−2i2−2i2000000000000000000000000
χ5344-4-444-4-4-44i4i−4i−4i440000-40000−4i4i000000000000000000000000000000000000000000
χ5444-4-444-4-4-4−4i−4i4i4i440000-400004i−4i000000000000000000000000000000000000000000
χ554-444-44-4-404i−4i4i−4i00000000000000022−22−2222000000002i2−2i22i2−2i2000000000000000000000000
χ564-444-44-4-404i−4i4i−4i000000000000000−222222−2200000000−2i22i2−2i22i2000000000000000000000000
χ574-444-44-4-40−4i4i−4i4i00000000000000022−22−222200000000−2i22i2−2i22i2000000000000000000000000
χ584-444-44-4-40−4i4i−4i4i000000000000000−222222−22000000002i2−2i22i2−2i2000000000000000000000000
χ594-44-44-44-4-40000-4444-4-4400-4400000000000000000000000000000000000000000000
χ604-44-44-44-4-40000-44-4-4444004-400000000000000000000000000000000000000000000
χ614-4-444-4-4440000-440000-400000000000000004i−4i−4i4i0000000000000000000000000000
χ624-4-444-4-4440000-440000-40000000000000000−4i4i4i−4i0000000000000000000000000000
χ634-4-444-4-44-400004-400004000000000000000000004-4-44000000000000000000000000
χ644-4-444-4-44-400004-40000400000000000000000000-444-4000000000000000000000000
χ654-4-4-4-444404-4-44004-4-4404-40000000000000000000000000000000000000000000000
χ664-4-4-4-444404-4-4400-444-40-440000000000000000000000000000000000000000000000
χ674-4-4-4-44440-444-4004-4-440-440000000000000000000000000000000000000000000000
χ684-4-4-4-44440-444-400-444-404-40000000000000000000000000000000000000000000000

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