Finite Group Databasebeta

← Group #232713

Character table — Group #232713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444888888888888888822224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-111111-1-1-1-1
χ9111111-1-1-1-1-1-11-1-1111-111-1-1-1111111-1-1-1-11111-1-1-1-11-1111-11-11-1-1-111-1-111-1-1
χ10111111-1-1-1-1-1-11-1-1111-111-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-1-11-111-111-1-111-1-111
χ11111111-1-1-1-1-1-11-1-1111-111-1-1-1111111-1-1-1-1-1-1-1-11111-111-11-1-11-11-1111-1-1-1-111
χ12111111-1-1-1-1-1-11-1-1111-111-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-111-1-111-1-1-11111-1-1
χ13111111-1-1-1-1-1-11-1-1111-111-1-1-111-1-1-1-111111111-1-1-1-1-11111-11-1-11-1-1-1-111-1-111
χ14111111-1-1-1-1-1-11-1-1111-111-1-1-111-1-1-1-111111111-1-1-1-1-11-1-1-11-11-111111-1-111-1-1
χ15111111-1-1-1-1-1-11-1-1111-111-1-1-111-1-1-1-11111-1-1-1-111111-11-11-1-111-1-11-1-11111-1-1
χ16111111-1-1-1-1-1-11-1-1111-111-1-1-111-1-1-1-11111-1-1-1-111111-1-11-111-11-11-111-1-1-1-111
χ17222222222222-2-2-2-2-2-22-2-2-2-2-22200000000000000002-2000000-220000000000
χ18222222222222-2-2-2-2-2-22-2-2-2-2-2220000000000000000-220000002-20000000000
χ1922222222-2-2-2-22222222-2-2-2-22-2-20000000022-2-222-2-200000000000000000000
χ2022222222-2-2-2-22222222-2-2-2-22-2-200000000-2-222-2-22200000000000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-222222-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-222222-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ23222222-2-222222-2-2222-2-2-222-2-2-20000000022-2-2-2-22200000000000000000000
χ24222222-2-222222-2-2222-2-2-222-2-2-200000000-2-22222-2-200000000000000000000
χ25222222-2-22222-222-2-2-2-222-2-22-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ26222222-2-22222-222-2-2-2-222-2-22-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ27222222-2-2-2-2-2-2-222-2-2-2-2-2-222222000000000000000022000000-2-20000000000
χ28222222-2-2-2-2-2-2-222-2-2-2-2-2-2222220000000000000000-2-2000000220000000000
χ292222-2-22222-2-2222-2-22-22-22-2-22-20000000000000000000200-2-2000200000000
χ302222-2-22222-2-2222-2-22-22-22-2-22-20000000000000000000-20022000-200000000
χ312222-2-22222-2-2-2-2-222-2-2-22-2222-200000000000000000000000000002-22-20000
χ322222-2-22222-2-2-2-2-222-2-2-22-2222-20000000000000000000000000000-22-220000
χ332222-2-222-2-222222-2-22-2-22-22-2-2200000000000000000020-2-200002000000000
χ342222-2-222-2-222222-2-22-2-22-22-2-22000000000000000000-20220000-2000000000
χ352222-2-222-2-222-2-2-222-2-22-22-22-22000000000000000000000000000000002-22-2
χ362222-2-222-2-222-2-2-222-2-22-22-22-2200000000000000000000000000000000-22-22
χ372222-2-2-2-222-2-22-2-2-2-222-222-22-2200000000000000000020-220000-2000000000
χ382222-2-2-2-222-2-22-2-2-2-222-222-22-22000000000000000000-202-200002000000000
χ392222-2-2-2-222-2-2-22222-222-2-22-2-22000000000000000000000000000000002-2-22
χ402222-2-2-2-222-2-2-22222-222-2-22-2-2200000000000000000000000000000000-222-2
χ412222-2-2-2-2-2-2222-2-2-2-2222-2-2222-20000000000000000000200-22000-200000000
χ422222-2-2-2-2-2-2222-2-2-2-2222-2-2222-20000000000000000000-2002-2000200000000
χ432222-2-2-2-2-2-222-22222-22-222-2-22-200000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-222-22222-22-222-2-22-20000000000000000000000000000-222-20000
χ4544-4-44-4004i−4i4i−4i00000000000000000000000022−222i2−2i20000000000000000000000
χ4644-4-44-4004i−4i4i−4i000000000000000000000000−2222−2i22i20000000000000000000000
χ4744-4-44-400−4i4i−4i4i00000000000000000000000022−22−2i22i20000000000000000000000
χ4844-4-44-400−4i4i−4i4i000000000000000000000000−22222i2−2i20000000000000000000000
χ4944-4-4-44004i−4i−4i4i000000000000000000000022−2200002i2−2i200000000000000000000
χ5044-4-4-44004i−4i−4i4i0000000000000000000000−22220000−2i22i200000000000000000000
χ5144-4-4-4400−4i4i4i−4i000000000000000000000022−220000−2i22i200000000000000000000
χ5244-4-4-4400−4i4i4i−4i0000000000000000000000−222200002i2−2i200000000000000000000
χ534-4-44004-4000044-400-4000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ544-4-44004-4000044-400-400000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ554-4-44004-40000-4-44004000000002-2-222-2-220000000000000000000000000000
χ564-4-44004-40000-4-4400400000000-222-2-222-20000000000000000000000000000
χ574-4-4400-4400004-4400-4000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ584-4-4400-4400004-4400-400000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ594-4-4400-440000-44-4004000000002-2-22-222-20000000000000000000000000000
χ604-4-4400-440000-44-400400000000-222-22-2-220000000000000000000000000000
χ618-88-8000000000008i−8i000000000000000000000000000000000000000000000
χ628-88-800000000000−8i8i000000000000000000000000000000000000000000000

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