Finite Group Databasebeta

← Group #270329

Character table — Group #270329

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ31111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-11-1-1-1-11111-1-1-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111111-1-1-11111-1-1-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111111-1-111-1-111-1
χ172222222222-22-2-2-22-20000-2222200002222-2-2-2-2000000000000000-200000000000
χ182222222222-22-2-2-22-20000-222220000-2-2-2-222-2-2000000000000000200000000000
χ192222222222-22-2-2-22-20000-2-2-2-2-2000022-2-2-2-222000000000000000200000000000
χ202222222222-22-2-2-22-20000-2-2-2-2-20000-2-2222222000000000000000-200000000000
χ2122222222-2-22-2222-2-22222-20000-2-2220000000022-2-200000000-200000000000000
χ2222222222-2-22-2222-2-22222-20000-2-2-2-200000000-2-22200000000200000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-20000222200000000-2-22200000000-200000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-2000022-2-20000000022-2-200000000200000000000000
χ2522-2-2-22-2200202-2-2002i2i−2i−2i022−2−2002i−2i0000002−22-200i2i2−i2−i222−2−2000000000000i2−i20
χ2622-2-2-22-2200202-2-2002i2i−2i−2i022−2−200−2i2i0000002−2-2200i2i2−i2−i2−2−222000000000000−i2i20
χ2722-2-2-22-2200202-2-2002i2i−2i−2i0−2−222002i−2i000000−222-200−i2−i2i2i2−2−222000000000000−i2i20
χ2822-2-2-22-2200202-2-2002i2i−2i−2i0−2−22200−2i2i000000−22-2200−i2−i2i2i222−2−2000000000000i2−i20
χ2922-2-2-22-2200202-2-200−2i−2i2i2i022−2−2002i−2i0000002−2-2200−i2−i2i2i2−2−222000000000000i2−i20
χ3022-2-2-22-2200202-2-200−2i−2i2i2i022−2−200−2i2i0000002−22-200−i2−i2i2i222−2−2000000000000−i2i20
χ3122-2-2-22-2200202-2-200−2i−2i2i2i0−2−222002i−2i000000−22-2200i2i2−i2−i222−2−2000000000000−i2i20
χ3222-2-2-22-2200202-2-200−2i−2i2i2i0−2−22200−2i2i000000−222-200i2i2−i2−i2−2−222000000000000i2−i20
χ332-2-2-22-222222-2-22-2-222-22-2-200002-2000000000000000000000002i−2i00000002i−2i000
χ342-2-2-22-222222-2-22-2-222-22-2-200002-200000000000000000000000−2i2i0000000−2i2i000
χ352-2-2-22-222222-2-22-2-22-22-22-20000-22000000000000000000000002i−2i0000000−2i2i000
χ362-2-2-22-222222-2-22-2-22-22-22-20000-2200000000000000000000000−2i2i00000002i−2i000
χ372-2-2-22-222-2-222-22-22-22-22-220000-22002-2002-20000000000000000002-2000000000
χ382-2-2-22-222-2-222-22-22-22-22-220000-2200-2200-22000000000000000000-22000000000
χ392-2-2-22-222-2-222-22-22-2-22-22200002-2002-2002-2000000000000000000-22000000000
χ402-2-2-22-222-2-222-22-22-2-22-22200002-200-2200-220000000000000000002-2000000000
χ412-2-2-22-222-2-2-222-22220000-2000000002-200-220000002-22-200000000002-20000000
χ422-2-2-22-222-2-2-222-22220000-2000000002-200-22000000-22-220000000000-220000000
χ432-2-2-22-222-2-2-222-22220000-200000000-22002-20000002-22-20000000000-220000000
χ442-2-2-22-222-2-2-222-22220000-200000000-22002-2000000-22-2200000000002-20000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-44-44-404000-400000000000000000000000000000000000000000022−2200000
χ47444-4-4-44-44-404000-4000000000000000000000000000000000000000000−222200000
χ48444-4-4-44-4-440-4000400000000000000004i−4i0000000000000000000000000000000
χ49444-4-4-44-4-440-400040000000000000000−4i4i0000000000000000000000000000000
χ5044-4-4-44-4400-40-44400000002222−22−220000000000−2222000000000000000000000000000
χ5144-4-4-44-4400-40-4440000000−22−222222000000000022−22000000000000000000000000000
χ524-444-4-4-440040-4-44004i−4i−4i4i00000000000000000000000000000000000000000000
χ534-444-4-4-440040-4-4400−4i4i4i−4i00000000000000000000000000000000000000000000
χ544-444-4-4-4400-4044-40000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ554-444-4-4-4400-4044-4000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ564-44-444-4-40000000000000022−2222−22000000000000002i2−2i200002i−2i2i−2i000000000000000
χ574-44-444-4-40000000000000022−2222−2200000000000000−2i22i20000−2i2i−2i2i000000000000000
χ584-44-444-4-400000000000000−2222−2222000000000000002i2−2i20000−2i2i−2i2i000000000000000
χ594-44-444-4-400000000000000−2222−222200000000000000−2i22i200002i−2i2i−2i000000000000000
χ604-4-44-444-44-40-400040000004-4-44000000000000000000000000000000000000000
χ614-4-44-444-44-40-40004000000-444-4000000000000000000000000000000000000000
χ624-4-44-444-4-4404000-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ634-4-44-444-4-4404000-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ644-4-4-44-44444-4-44-44-4-4000040000000000000000000000000000000000000000000
χ6588-888-8-8-8000000000000000000000000000000000000000000000000000000000

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