Finite Group Databasebeta

← Group #270225

Character table — Group #270225

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888244444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-11111-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ101111111111111111-1-1-1-1111111-1-1111111-1-1111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1111-1-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-11111-1-111-1-111-1
χ172222222222-22-2-2-220000-2-222220022-2-2-2-200-2-2000000000000200000000000000
χ182222222222-22-2-2-220000-2-2222200-2-2222200-2-2000000000000-200000000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-20022-2-2220022000000000000-200000000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-200-2-222-2-20022000000000000200000000000000
χ2122222222-2-22-2222-22222-2-20000-2-20000002200-2-222000000000-20000000000000
χ2222222222-2-22-2222-22222-2-20000-2-2000000-2-20022-2-200000000020000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-2000022000000220022-2-2000000000-20000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000022000000-2-200-2-22200000000020000000000000
χ2522-2-2-222-200202-2-202i2i−2i−2i0022−2−2000000002-22−2002i−2ii2i2−i2−i2i2i2−i2−i20000000000002−20
χ2622-2-2-222-200202-2-202i2i−2i−2i0022−2−200000000-222−200−2i2ii2i2−i2−i2−i2−i2i2i2000000000000−220
χ2722-2-2-222-200202-2-202i2i−2i−2i00−2−222000000002-2−22002i−2i−i2−i2i2i2−i2−i2i2i2000000000000−220
χ2822-2-2-222-200202-2-202i2i−2i−2i00−2−22200000000-22−2200−2i2i−i2−i2i2i2i2i2−i2−i20000000000002−20
χ2922-2-2-222-200202-2-20−2i−2i2i2i0022−2−2000000002-22−200−2i2i−i2−i2i2i2−i2−i2i2i20000000000002−20
χ3022-2-2-222-200202-2-20−2i−2i2i2i0022−2−200000000-222−2002i−2i−i2−i2i2i2i2i2−i2−i2000000000000−220
χ3122-2-2-222-200202-2-20−2i−2i2i2i00−2−222000000002-2−2200−2i2ii2i2−i2−i2i2i2−i2−i2000000000000−220
χ3222-2-2-222-200202-2-20−2i−2i2i2i00−2−22200000000-22−22002i−2ii2i2−i2−i2−i2−i2i2i20000000000002−20
χ332-2-2-222-22222-2-22-2-22-22-22-200002-20000000000000000000000002i−2i0000002i−2i000
χ342-2-2-222-22222-2-22-2-22-22-22-200002-2000000000000000000000000−2i2i000000−2i2i000
χ352-2-2-222-22222-2-22-2-2-22-222-20000-220000000000000000000000002i−2i000000−2i2i000
χ362-2-2-222-22222-2-22-2-2-22-222-20000-22000000000000000000000000−2i2i0000002i−2i000
χ372-2-2-222-22-2-222-22-222-22-2-220000-222-22-200000000000000000000002-2000000000
χ382-2-2-222-22-2-222-22-222-22-2-220000-22-22-220000000000000000000000-22000000000
χ392-2-2-222-22-2-222-22-22-22-22-2200002-22-22-20000000000000000000000-22000000000
χ402-2-2-222-22-2-222-22-22-22-22-2200002-2-22-2200000000000000000000002-2000000000
χ412-2-2-222-22-2-2-222-22200002-20000002-2-2200000000002-22-200000000002-20000000
χ422-2-2-222-22-2-2-222-22200002-20000002-2-220000000000-22-220000000000-220000000
χ432-2-2-222-22-2-2-222-22200002-2000000-222-200000000002-22-20000000000-220000000
χ442-2-2-222-22-2-2-222-22200002-2000000-222-20000000000-22-2200000000002-20000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-44-404000-400000000000000000000000000000000000000000022−2200000
χ47444-44-4-4-44-404000-4000000000000000000000000000000000000000000−222200000
χ48444-44-4-4-4-440-4000400000000000000004i−4i0000000000000000000000000000000
χ49444-44-4-4-4-440-400040000000000000000−4i4i0000000000000000000000000000000
χ5044-4-4-444-400-40-44400000002222−22−220000000000−2222000000000000000000000000000
χ5144-4-4-444-400-40-4440000000−22−222222000000000022−22000000000000000000000000000
χ524-444-44-4-40040-4-4404i−4i−4i4i000000000000000000000000000000000000000000000
χ534-444-44-4-40040-4-440−4i4i4i−4i000000000000000000000000000000000000000000000
χ544-444-44-4-400-4044-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ554-444-44-4-400-4044-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ564-44-4-4-4440000000000000022−2222−2200000000000022−220000002-22-2000000000000000
χ574-44-4-4-4440000000000000022−2222−22000000000000−2222000000-22-22000000000000000
χ584-44-4-4-44400000000000000−2222−222200000000000022−22000000-22-22000000000000000
χ594-44-4-4-44400000000000000−2222−2222000000000000−22220000002-22-2000000000000000
χ604-4-444-44-44-40-400040000004-4-44000000000000000000000000000000000000000
χ614-4-444-44-44-40-40004000000-444-4000000000000000000000000000000000000000
χ624-4-444-44-4-4404000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ634-4-444-44-4-4404000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ644-4-4-444-4444-4-44-44-40000-440000000000000000000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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