Finite Group Databasebeta

← Group #317340

Character table — Group #317340

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888224444888888888822224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ17222222222-2-222-2-22-2-222-2-20000222-2-2-2000000000000002-200000000000000
χ18222222222-2-222-2-22-2-222-2-20000-2-22-22200000000000000-2200000000000000
χ19222222222-2-222-2-22-2-2-2-222000022-22-2-200000000000000-2200000000000000
χ20222222222-2-222-2-22-2-2-2-2220000-2-2-2222000000000000002-200000000000000
χ2122222222-222-2-222-2-2-22222222200-2-20022-2-2-2-2000000000000000000000000
χ2222222222-222-2-222-2-2-22222-2-2-2-200-2-200-2-22222000000000000000000000000
χ2322222222-222-2-222-2-2-2-2-2-2-22222002200-2-222-2-2000000000000000000000000
χ2422222222-222-2-222-2-2-2-2-2-2-2-2-2-2-200220022-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000-22000000002i2i−2i−2i000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000-2200000000−2i−2i2i2i00000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-2220000002-2000000002i2i−2i−2i00000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-2220000002-200000000−2i−2i2i2i000000000000002i−2i0000
χ292222-2-2-2-202-2002-20002i−2i2i−2i2i2i−2i−2i0000002-20000000000000000002−2i2−i200i2−i22−2
χ302222-2-2-2-202-2002-20002i−2i2i−2i2i2i−2i−2i0000002-2000000000000000000−22−i2i200−i2i2−22
χ312222-2-2-2-202-2002-20002i−2i2i−2i−2i−2i2i2i000000-220000000000000000002−2i2−i200−i2i2−22
χ322222-2-2-2-202-2002-20002i−2i2i−2i−2i−2i2i2i000000-22000000000000000000−22−i2i200i2−i22−2
χ332222-2-2-2-202-2002-2000−2i2i−2i2i2i2i−2i−2i000000-220000000000000000002−2−i2i200i2−i2−22
χ342222-2-2-2-202-2002-2000−2i2i−2i2i2i2i−2i−2i000000-22000000000000000000−22i2−i200−i2i22−2
χ352222-2-2-2-202-2002-2000−2i2i−2i2i−2i−2i2i2i0000002-20000000000000000002−2−i2i200−i2i22−2
χ362222-2-2-2-202-2002-2000−2i2i−2i2i−2i−2i2i2i0000002-2000000000000000000−22i2−i200i2−i2−22
χ372-2-2222-2-2222-2-2-2-222-200002i−2i2i−2i00000000002i−2i0000002-2002i−2i000000000000
χ382-2-2222-2-2222-2-2-2-222-200002i−2i2i−2i00000000002i−2i000000-2200−2i2i000000000000
χ392-2-2222-2-2222-2-2-2-222-20000−2i2i−2i2i0000000000−2i2i0000002-200−2i2i000000000000
χ402-2-2222-2-2222-2-2-2-222-20000−2i2i−2i2i0000000000−2i2i000000-22002i−2i000000000000
χ412-2-2222-2-2-22222-2-2-2-2200002i−2i2i−2i0000000000−2i2i00002-20000002i−2i0000000000
χ422-2-2222-2-2-22222-2-2-2-2200002i−2i2i−2i0000000000−2i2i0000-22000000−2i2i0000000000
χ432-2-2222-2-2-22222-2-2-2-220000−2i2i−2i2i00000000002i−2i00002-2000000−2i2i0000000000
χ442-2-2222-2-2-22222-2-2-2-220000−2i2i−2i2i00000000002i−2i0000-220000002i−2i0000000000
χ454444-4-4-4-40-4400-440004i−4i−4i4i0000000000000000000000000000000000000000
χ464444-4-4-4-40-4400-44000−4i4i4i−4i0000000000000000000000000000000000000000
χ4744-4-44-44-44004-400-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ4844-4-44-44-44004-400-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ4944-4-44-44-4-400-44004000000000000000000000022−22−222200000000000000000000
χ5044-4-44-44-4-400-440040000000000000000000000−222222−2200000000000000000000
χ514-44-44-4-44400-4400-4000000000000004i−4i000000000000000000000000000000
χ524-44-44-4-44400-4400-400000000000000−4i4i000000000000000000000000000000
χ534-44-44-4-44-4004-400400000000004-40000000000000000000000000000000000
χ544-44-44-4-44-4004-40040000000000-440000000000000000000000000000000000
χ554-4-4444-4-44-4-4-4-4444-4400000000000000000000000000000000000000000000
χ564-4-4444-4-4-4-4-44444-44-400000000000000000000000000000000000000000000
χ574-4-44-4-44404-400-4400000004-4-44000000000000000000000000000000000000
χ584-4-44-4-44404-400-440000000-444-4000000000000000000000000000000000000
χ594-4-44-4-4440-44004-400000000000000000004-400000000000000000000000000
χ604-4-44-4-4440-44004-40000000000000000000-4400000000000000000000000000
χ6188-8-8-88-88000000000000000000000000000000000000000000000000000000
χ628-88-8-888-8000000000000000000000000000000000000000000000000000000

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