Finite Group Databasebeta

← Group #270104

Character table — Group #270104

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888882
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11
χ91111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-111-1-11111-1-1-1-1111111-1-1-11-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-111-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-11-1-1111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111111-111-1-1-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ17222222222-2-22-222-20000-2-22222222200-2-20000-2-20000000000000-200000000000
χ18222222222-2-22-222-20000-2-22222-2-2-2-200220000-2-20000000000000200000000000
χ19222222222-2-22-222-20000-2-2-2-2-2-222-2-200220000220000000000000-200000000000
χ20222222222-2-22-222-20000-2-2-2-2-2-2-2-22200-2-20000220000000000000200000000000
χ2122222222-222-22-2-222222-2-200000000-2-2002222000000-2-2000000-2000000000000
χ2222222222-222-22-2-222222-2-200000000-2-200-2-2-2-2000000220000002000000000000
χ2322222222-222-22-2-22-2-2-2-2-2-200000000220022-2-200000022000000-2000000000000
χ2422222222-222-22-2-22-2-2-2-2-2-2000000002200-2-222000000-2-20000002000000000000
χ25222-2-22-2-202-20-200222-2-20022−2−2000000002i−2i2i−2i2−222−2−200i2i2−i2−i200000000i2−i200000
χ26222-2-22-2-202-20-200222-2-20022−2−200000000−2i2i−2i2i2−222−2−200−i2−i2i2i200000000−i2i200000
χ27222-2-22-2-202-20-200222-2-200−2−222000000002i−2i2i−2i−22−2−22200−i2−i2i2i200000000−i2i200000
χ28222-2-22-2-202-20-200222-2-200−2−22200000000−2i2i−2i2i−22−2−22200i2i2−i2−i200000000i2−i200000
χ29222-2-22-2-202-20-2002-2-2220022−2−2000000002i−2i−2i2i2−2−2−22200−i2−i2i2i200000000i2−i200000
χ30222-2-22-2-202-20-2002-2-2220022−2−200000000−2i2i2i−2i2−2−2−22200i2i2−i2−i200000000−i2i200000
χ31222-2-22-2-202-20-2002-2-22200−2−222000000002i−2i−2i2i−2222−2−200i2i2−i2−i200000000−i2i200000
χ32222-2-22-2-202-20-2002-2-22200−2−22200000000−2i2i2i−2i−2222−2−200−i2−i2i2i200000000i2−i200000
χ332-2-2-222-22222-2-22-2-200002-20000002-2002-20000002i−2i2i−2i00000000002i−2i000000000
χ342-2-2-222-22222-2-22-2-200002-20000002-2002-2000000−2i2i−2i2i0000000000−2i2i000000000
χ352-2-2-222-22222-2-22-2-200002-2000000-2200-220000002i−2i2i−2i0000000000−2i2i000000000
χ362-2-2-222-22222-2-22-2-200002-2000000-2200-22000000−2i2i−2i2i00000000002i−2i000000000
χ372-2-2-222-222-2-2-222-222-22-2-220000002-22-2-2200000000000000000000002-20000000
χ382-2-2-222-222-2-2-222-222-22-2-22000000-222-22-20000000000000000000000-220000000
χ392-2-2-222-222-2-2-222-22-22-22-220000002-2-22-220000000000000000000000-220000000
χ402-2-2-222-222-2-2-222-22-22-22-22000000-22-222-200000000000000000000002-20000000
χ412-2-2-222-22-2-2-222-2222-22-22-200000000-220000000000000000002-200000000002-20
χ422-2-2-222-22-2-2-222-2222-22-22-200000000-22000000000000000000-220000000000-220
χ432-2-2-222-22-2-2-222-222-22-222-2000000002-20000000000000000002-20000000000-220
χ442-2-2-222-22-2-2-222-222-22-222-2000000002-2000000000000000000-2200000000002-20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-40-440400-40000002222−22−22000000000000−22220000000000000000000000000
χ47444-4-44-4-40-440400-4000000−22−22222200000000000022−220000000000000000000000000
χ4844-444-4-4-440040-4-400000004-44-4000000000000000000000000000000000000000
χ4944-444-4-4-440040-4-40000000-44-44000000000000000000000000000000000000000
χ5044-444-4-4-4-400-404400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5144-444-4-4-4-400-40440000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ5244-4-4-4-4440000000000000022−22−222200000000000000000022−222-2-22000000000000000
χ5344-4-4-4-4440000000000000022−22−2222000000000000000000−2222-222-2000000000000000
χ5444-4-4-4-44400000000000000−222222−2200000000000000000022−22-222-2000000000000000
χ5544-4-4-4-44400000000000000−222222−22000000000000000000−22222-2-22000000000000000
χ564-44-44-44-4400-40-44000000000004i−4i0000000000000000000000000000000000000
χ574-44-44-44-4400-40-4400000000000−4i4i0000000000000000000000000000000000000
χ584-44-44-44-4-400404-40000000000000000000000000000000000000000000002i2−2i2000
χ594-44-44-44-4-400404-4000000000000000000000000000000000000000000000−2i22i2000
χ604-4-44-444-404-40400-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ614-4-44-444-404-40400-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ624-4-44-444-40-440-40044-4-44000000000000000000000000000000000000000000000
χ634-4-44-444-40-440-4004-444-4000000000000000000000000000000000000000000000
χ644-4-4-444-44-4444-4-44-40000-440000000000000000000000000000000000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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