Finite Group Databasebeta

← Group #285178

Character table — Group #285178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888884444488888888888822444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111111111-1-111-1-1-1111-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-111-1-111-1-1-1-111-1-11-1-111-1111-1-1-1-1
χ4111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1111-1-11-1-1-1-1-11-1
χ611111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-11
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
χ811111111111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1-111-111-1-1-1111-1-11-1
χ91111111111111-1-11111111111-1-1-11111111111-1-111-1-1-1-1111-1-1-11-1-111-1-1
χ101111111111111-1-11111111111-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-111-1-111
χ111111111111111-1-1111111-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-1-1-111
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
χ131111111111111-1-111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111111-1-111-1-1-11
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
χ151111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11-1-1111-111111-1
χ161111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1111111-1-1-1-1-11
χ172222222-2-22-2-2222-2-22i2i−2i−2i0000-2-22000000002i−2i000000000002i−2i00000000
χ182222222-2-22-2-2222-2-2−2i−2i2i2i0000-2-2200000000−2i2i00000000000−2i2i00000000
χ192222222-2-22-2-22-2-2-2-22i2i−2i−2i000022-2000000002i−2i00000000000−2i2i00000000
χ202222222-2-22-2-22-2-2-2-2−2i−2i2i2i000022-200000000−2i2i000000000002i−2i00000000
χ21222222-222-222-200-2-22222000000022002200-2-200000000-200000-2000000
χ22222222-222-222-200-2-222220000000-2-200-2-200-2-2000000002000002000000
χ23222222-222-222-200-2-2-2-2-2-200000002200-2-2002200000000-2000002000000
χ24222222-222-222-200-2-2-2-2-2-20000000-2-20022002200000000200000-2000000
χ25222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i00002-20000000002i−2i0000
χ26222222-2-2-2-2-2-2-200222i2i−2i−2i000000000000000−2i2i0000-22000000000−2i2i0000
χ27222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i00002-2000000000−2i2i0000
χ28222222-2-2-2-2-2-2-20022−2i−2i2i2i0000000000000002i−2i0000-220000000002i−2i0000
χ292222-2-222-222-2-2222-2000022222-2-2000000000022-2-2000000000-20000000
χ302222-2-222-222-2-2222-20000-2-2-2-22-2-20000000000-2-22200000000020000000
χ312222-2-222-222-2-2-2-22-200002222-2220000000000-2-2-2-200000000020000000
χ322222-2-222-222-2-2-2-22-20000-2-2-2-2-22200000000002222000000000-20000000
χ332222-2-22-222-22-222-2200000000-22-2002200-2-2000000002-20000000000000
χ342222-2-22-222-22-222-2200000000-22-200-2-2002200000000-220000000000000
χ352222-2-22-222-22-2-2-2-22000000002-22002200-2-200000000-220000000000000
χ362222-2-22-222-22-2-2-2-22000000002-2200-2-20022000000002-20000000000000
χ372-22-22-202-20-22000002-22-222−2−20002i−2i2−22i−2i2−200002−200000i2−i2000000i2−i200
χ382-22-22-202-20-22000002-22-222−2−2000−2i2i2−2−2i2i2−200002−200000−i2i2000000−i2i200
χ392-22-22-202-20-22000002-22-2−2−2220002i−2i−222i−2i−220000−2200000−i2i2000000−i2i200
χ402-22-22-202-20-22000002-22-2−2−222000−2i2i−22−2i2i−220000−2200000i2−i2000000i2−i200
χ412-22-22-202-20-2200000-22-2222−2−20002i−2i−22−2i2i−2200002−200000i2−i2000000−i2i200
χ422-22-22-202-20-2200000-22-2222−2−2000−2i2i−222i−2i−2200002−200000−i2i2000000i2−i200
χ432-22-22-202-20-2200000-22-22−2−2220002i−2i2−2−2i2i2−20000−2200000−i2i2000000i2−i200
χ442-22-22-202-20-2200000-22-22−2−222000−2i2i2−22i−2i2−20000−2200000i2−i2000000−i2i200
χ454444-4-4-44-4-44-4400-44000000000000000000000000000000000000000000
χ464444-4-4-4-44-4-444004-4000000000000000000000000000000000000000000
χ4744-4-400-40040004i−4i0000002i2−2i22i2−2i2000000000000022−220000000000000000000
χ4844-4-400-40040004i−4i000000−2i22i2−2i22i20000000000000−22220000000000000000000
χ4944-4-400-4004000−4i4i0000002i2−2i22i2−2i20000000000000−22220000000000000000000
χ5044-4-400-4004000−4i4i000000−2i22i2−2i22i2000000000000022−220000000000000000000
χ514-44-44-40-4404-4000004i−4i−4i4i00000000000000000000000000000000000000
χ524-44-44-40-4404-400000−4i4i4i−4i00000000000000000000000000000000000000
χ534-44-4-440440-4-40000000002222−22−22000000000000000−222200000000000000000
χ544-44-4-440440-4-4000000000−22−22222200000000000000022−2200000000000000000
χ554-44-4-440-4-404400000000000000000022−2200−222200000000000000000000000
χ564-44-4-440-4-4044000000000000000000−22220022−2200000000000000000000000
χ5788-8-800800-80000000000000000000000000000000000000000000000000
χ588-8-88000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ598-8-8800000000000000000−4i4i4i−4i0000000000000000000000000000000000

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