Finite Group Databasebeta

← Group #285174

Character table — Group #285174

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888884444488888888888844444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-111111-1-1111111111-1-11-1-1-1111-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-111-1-111-1-1-1-1-111-11-1-111-1111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-111-1111-1-11-1-1-1-1-11-1
χ611111111111111111-1-1-1-11111-1-1111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-11
χ711111111111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-11-111-1-1-1111-1-11-1
χ91111111111111-1-1111111111111-1-1-111111111-1-111-1-1-1-1111-1-1-11-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-1-111-1-11111-1-111-111-1-1-1-1-1-1-1-111-1-111
χ111111111111111-1-1111111-1-1-1-111-1-1-1-1-111-1-11111-1-11-1-111-1-1-1-111-1-1-1-111
χ121111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-111-1-11-11111-1-1
χ131111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111111-1-111-1-1-11
χ141111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-111-11-1-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-111-1-1-111-1-111-1-111-1-1-1-1-1-11-1-1111-111111-1
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-111-1-1111111-1-1-1-1-11
χ1722222222-2-222-200-2-22222000022000002200-2-200000000-200000-2000000
χ1822222222-2-222-200-2-222220000-2-200000-2-200-2-2000000002000002000000
χ1922222222-2-222-200-2-2-2-2-2-200002200000-2-2002200000000-2000002000000
χ2022222222-2-222-200-2-2-2-2-2-20000-2-20000022002200000000200000-2000000
χ21222222-2-222-2-2222-2-22i2i−2i−2i000000-2-220000002i−2i000000000002i−2i00000000
χ22222222-2-222-2-2222-2-2−2i−2i2i2i000000-2-22000000−2i2i00000000000−2i2i00000000
χ23222222-2-222-2-22-2-2-2-22i2i−2i−2i00000022-20000002i−2i00000000000−2i2i00000000
χ24222222-2-222-2-22-2-2-2-2−2i−2i2i2i00000022-2000000−2i2i000000000002i−2i00000000
χ25222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i000002-2000000002i−2i0000
χ26222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i00000-2200000000−2i2i0000
χ27222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i000002-200000000−2i2i0000
χ28222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i00000-22000000002i−2i0000
χ292222-2-22-2222-2-2222-200002222002-2-20000000022-2-2000000000-20000000
χ302222-2-22-2222-2-2222-20000-2-2-2-2002-2-200000000-2-22200000000020000000
χ312222-2-22-2222-2-2-2-22-20000222200-22200000000-2-2-2-200000000020000000
χ322222-2-22-2222-2-2-2-22-20000-2-2-2-200-222000000002222000000000-20000000
χ332222-2-2-2222-22-222-220000000000-22-22200-2-2000000200-20000000000000
χ342222-2-2-2222-22-222-220000000000-22-2-2-20022000000-20020000000000000
χ352222-2-2-2222-22-2-2-2-2200000000002-222200-2-2000000-20020000000000000
χ362222-2-2-2222-22-2-2-2-2200000000002-22-2-20022000000200-20000000000000
χ3722-2-22-22200-2-2000002-22-222−2−22-20002−22-22−200002−2000002−20000002−200
χ3822-2-22-22200-2-2000002-22-222−2−2-220002−2-222−200002−200000−22000000−2200
χ3922-2-22-22200-2-2000002-22-2−2−2222-2000−222-2−220000−2200000−22000000−2200
χ4022-2-22-22200-2-2000002-22-2−2−222-22000−22-22−220000−22000002−20000002−200
χ4122-2-22-22200-2-200000-22-2222−2−22-2000−22-22−2200002−2000002−2000000−2200
χ4222-2-22-22200-2-200000-22-2222−2−2-22000−222-2−2200002−200000−220000002−200
χ4322-2-22-22200-2-200000-22-22−2−2222-20002−2-222−20000−2200000−220000002−200
χ4422-2-22-22200-2-200000-22-22−2−222-220002−22-22−20000−22000002−2000000−2200
χ454444-4-44-4-4-44-4400-44000000000000000000000000000000000000000000
χ464444-4-4-44-4-4-444004-4000000000000000000000000000000000000000000
χ4744-4-44-4-4-40044000004i−4i−4i4i00000000000000000000000000000000000000
χ4844-4-44-4-4-4004400000−4i4i4i−4i00000000000000000000000000000000000000
χ4944-4-4-444-400-440000000002222−22−22000000000000000−222200000000000000000
χ5044-4-4-444-400-44000000000−22−22222200000000000000022−2200000000000000000
χ5144-4-4-44-44004-400000000000000000022−2200−222200000000000000000000000
χ5244-4-4-44-44004-4000000000000000000−22220022−2200000000000000000000000
χ534-44-40000-440004i−4i0000002i2−2i22i2−2i2000000000000022−220000000000000000000
χ544-44-40000-440004i−4i000000−2i22i2−2i22i20000000000000−22220000000000000000000
χ554-44-40000-44000−4i4i0000002i2−2i22i2−2i20000000000000−22220000000000000000000
χ564-44-40000-44000−4i4i000000−2i22i2−2i22i2000000000000022−220000000000000000000
χ578-88-800008-80000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-8-8800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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