Finite Group Databasebeta

← Group #314750

Character table — Group #314750

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888244444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ311111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ9111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1
χ10111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1
χ11111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111
χ12111111111-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111
χ13111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-11111
χ14111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-11111-1-111
χ15111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11111-1-11111-1-1-1-1
χ16111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1
χ172222222222222-2-2-2-222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2122222222-222222222-2-2-2-2-2-2-222-2-200000000000000002-200002-20000000000000000
χ2222222222-222222222-2-2-2-2-2-2-222-2-20000000000000000-220000-220000000000000000
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
χ2522222222-2-2-2-2-22222-2-2-222-2-2-2-22200000000000000002-20000-220000000000000000
χ2622222222-2-2-2-2-22222-2-2-222-2-2-2-2220000000000000000-2200002-20000000000000000
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
χ292222-2-2-2-2-2000022-2-22-22002-20000000022-2-2000022-2-200002i−2i002i−2i00000000000000
χ302222-2-2-2-2-2000022-2-22-22002-20000000022-2-2000022-2-20000−2i2i00−2i2i00000000000000
χ312222-2-2-2-2-2000022-2-22-22002-200000000-2-2220000-2-22200002i−2i00−2i2i00000000000000
χ322222-2-2-2-2-2000022-2-22-22002-200000000-2-2220000-2-2220000−2i2i002i−2i00000000000000
χ332222-2-2-2-2-20000-2-2222-2200-220000000022-2-20000-2-222002i−2i0000002i−2i000000000000
χ342222-2-2-2-2-20000-2-2222-2200-220000000022-2-20000-2-22200−2i2i000000−2i2i000000000000
χ352222-2-2-2-2-20000-2-2222-2200-2200000000-2-222000022-2-2002i−2i000000−2i2i000000000000
χ362222-2-2-2-2-20000-2-2222-2200-2200000000-2-222000022-2-200−2i2i0000002i−2i000000000000
χ372-2-22-2-222222-2-200002-2-22-2000000000000002i2i−2i−2i2i−2i2i−2i00000000000000i2−i2i2−i22−22−200
χ382-2-22-2-222222-2-200002-2-22-2000000000000002i2i−2i−2i2i−2i2i−2i00000000000000−i2i2−i2i2−22−2200
χ392-2-22-2-222222-2-200002-2-22-200000000000000−2i−2i2i2i−2i2i−2i2i00000000000000i2−i2i2−i2−22−2200
χ402-2-22-2-222222-2-200002-2-22-200000000000000−2i−2i2i2i−2i2i−2i2i00000000000000−i2i2−i2i22−22−200
χ412-2-22-2-2222-2-22200002-2-2-22000000000000002i2i−2i−2i−2i2i−2i2i00000000000000i2−i2−i2i22−2−2200
χ422-2-22-2-2222-2-22200002-2-2-22000000000000002i2i−2i−2i−2i2i−2i2i00000000000000−i2i2i2−i2−222−200
χ432-2-22-2-2222-2-22200002-2-2-2200000000000000−2i−2i2i2i2i−2i2i−2i00000000000000i2−i2−i2i2−222−200
χ442-2-22-2-2222-2-22200002-2-2-2200000000000000−2i−2i2i2i2i−2i2i−2i00000000000000−i2i2i2−i22−2−2200
χ454444-4-4-4-44000044-4-4-44-400-4400000000000000000000000000000000000000000000
χ464444-4-4-4-440000-4-444-44-4004-400000000000000000000000000000000000000000000
χ4744-4-44-44-40000000000000000004i−4i00002i2−2i22i2−2i222−2222−220000000000000000000000000000
χ4844-4-44-44-40000000000000000004i−4i0000−2i22i2−2i22i2−2222−22220000000000000000000000000000
χ4944-4-44-44-4000000000000000000−4i4i00002i2−2i22i2−2i2−2222−22220000000000000000000000000000
χ5044-4-44-44-4000000000000000000−4i4i0000−2i22i2−2i22i222−2222−220000000000000000000000000000
χ5144-4-4-44-4404i−4i4i−4i0000000000000002222−22−222i2−2i2−2i22i200000000000000000000000000000000
χ5244-4-4-44-4404i−4i4i−4i000000000000000−22−222222−2i22i22i2−2i200000000000000000000000000000000
χ5344-4-4-44-440−4i4i−4i4i0000000000000002222−22−22−2i22i22i2−2i200000000000000000000000000000000
χ5444-4-4-44-440−4i4i−4i4i000000000000000−22−2222222i2−2i2−2i22i200000000000000000000000000000000
χ554-44-44-4-4404i−4i−4i4i4-44-400000004i−4i000000000000000000000000000000000000000000
χ564-44-44-4-4404i−4i−4i4i-44-440000000−4i4i000000000000000000000000000000000000000000
χ574-44-44-4-440−4i4i4i−4i4-44-40000000−4i4i000000000000000000000000000000000000000000
χ584-44-44-4-440−4i4i4i−4i-44-4400000004i−4i000000000000000000000000000000000000000000
χ594-44-4-444-4000004-4-44000000000002i2−2i22i2−2i200002i2−2i2−2i22i20000000000000000000000000000
χ604-44-4-444-4000004-4-4400000000000−2i22i2−2i22i20000−2i22i22i2−2i20000000000000000000000000000
χ614-44-4-444-400000-444-4000000000002i2−2i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ624-44-4-444-400000-444-400000000000−2i22i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ634-4-4444-4-4400000000-4-44000000004i−4i−4i4i000000000000000000000000000000000000
χ644-4-4444-4-4400000000-4-4400000000−4i4i4i−4i000000000000000000000000000000000000
χ654-4-4444-4-4-40000000044-4000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4444-4-4-40000000044-400000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-44-4-444-444-4-40000-444-440000000000000000000000000000000000000000000000
χ684-4-44-4-444-4-4-4440000-4444-40000000000000000000000000000000000000000000000

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