Finite Group Databasebeta

← Group #285124

Character table — Group #285124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888884444488888888888844444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1
χ4111111111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1111-1-1-111-1-11-1-11-1
χ611111111111111111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-1111-11
χ711111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-111-1-1-111111-1-1-1-1-11-1
χ91111111111111-1-11111111111-111-1-111111111-1-111-1-11-1-11-1-111-1-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-1-11111-1-111-1-111-1-1-111-111-1-1-1-1-1-1-111
χ111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1111-1-11-1-1-1-1-1-11-1-111
χ121111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-11111-1-1111-1-1
χ131111111111111-1-111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-1-11
χ141111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1111-1-1-1-111-1111-1
χ151111111111111-1-111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11-1-1-111-1-1111111-1
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1111-1-111111-1-1-11
χ172222222-22-2-2-2222-2-22i2i−2i−2i0000200-2-20000002i−2i000000000000002i−2i00000
χ182222222-22-2-2-2222-2-2−2i−2i2i2i0000200-2-2000000−2i2i00000000000000−2i2i00000
χ192222222-22-2-2-22-2-2-2-22i2i−2i−2i0000-200220000002i−2i00000000000000−2i2i00000
χ202222222-22-2-2-22-2-2-2-2−2i−2i2i2i0000-20022000000−2i2i000000000000002i−2i00000
χ21222222-22-2222-200-2-22222000002200000022-2-2000000-200-200000000000
χ22222222-22-2222-200-2-2222200000-2-2000000-2-2-2-2000000200200000000000
χ23222222-22-2222-200-2-2-2-2-2-20000022000000-2-222000000-200200000000000
χ24222222-22-2222-200-2-2-2-2-2-200000-2-20000002222000000200-200000000000
χ25222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i00000002-202i−2i000000000
χ26222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i0000000-220−2i2i000000000
χ27222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i00000002-20−2i2i000000000
χ28222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i0000000-2202i−2i000000000
χ292222-2-2222-2-22-2222-200002222-2002-20000000022-2-2000000000000-20000
χ302222-2-2222-2-22-2222-20000-2-2-2-2-2002-200000000-2-22200000000000020000
χ312222-2-2222-2-22-2-2-22-200002222200-2200000000-2-2-2-200000000000020000
χ322222-2-2222-2-22-2-2-22-20000-2-2-2-2200-22000000002222000000000000-20000
χ332222-2-22-2222-2-222-2200000000-200-2222-2-2000000002-2000000000000000
χ342222-2-22-2222-2-222-2200000000-200-22-2-22200000000-22000000000000000
χ352222-2-22-2222-2-2-2-2-22000000002002-222-2-200000000-22000000000000000
χ362222-2-22-2222-2-2-2-2-22000000002002-2-2-222000000002-2000000000000000
χ372-22-22-20-202-22000002i−2i2i−2ii2i2−i2−i202-2002−22−22i−2i0000i2−i200000000i2−i20002−200
χ382-22-22-20-202-22000002i−2i2i−2ii2i2−i2−i20-22002−22−2−2i2i0000i2−i200000000−i2i2000−2200
χ392-22-22-20-202-22000002i−2i2i−2i−i2−i2i2i202-200−22−222i−2i0000−i2i200000000−i2i2000−2200
χ402-22-22-20-202-22000002i−2i2i−2i−i2−i2i2i20-2200−22−22−2i2i0000−i2i200000000i2−i20002−200
χ412-22-22-20-202-2200000−2i2i−2i2ii2i2−i2−i202-200−22−22−2i2i0000i2−i200000000i2−i2000−2200
χ422-22-22-20-202-2200000−2i2i−2i2ii2i2−i2−i20-2200−22−222i−2i0000i2−i200000000−i2i20002−200
χ432-22-22-20-202-2200000−2i2i−2i2i−i2−i2i2i202-2002−22−2−2i2i0000−i2i200000000−i2i20002−200
χ442-22-22-20-202-2200000−2i2i−2i2i−i2−i2i2i20-22002−22−22i−2i0000−i2i200000000i2−i2000−2200
χ454444-4-4-44-4-4-44400-44000000000000000000000000000000000000000000
χ464444-4-4-4-4-444-44004-4000000000000000000000000000000000000000000
χ4744-4-40040-400004-400000022−2222−22000000000000022−220000000000000000000
χ4844-4-40040-400004-4000000−2222−22220000000000000−22220000000000000000000
χ4944-4-40040-40000-4400000022−2222−220000000000000−22220000000000000000000
χ5044-4-40040-40000-44000000−2222−2222000000000000022−220000000000000000000
χ514-44-44-4040-44-4000004-4-4400000000000000000000000000000000000000
χ524-44-44-4040-44-400000-444-400000000000000000000000000000000000000
χ534-44-4-440404-4-400000000000000000022−22−22220000000000000000000000000
χ544-44-4-440404-4-4000000000000000000−222222−220000000000000000000000000
χ554-44-4-440-40-4440000000002i22i2−2i2−2i2000000000000000−2i22i200000000000000000
χ564-44-4-440-40-444000000000−2i2−2i22i22i20000000000000002i2−2i200000000000000000
χ5788-8-800-80800000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-8-8800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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