Finite Group Databasebeta

← Group #305682

Character table — Group #305682

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-1-11-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-11
χ91111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11-1-111-1111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-111-1-1111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-111-1-1-1-1-111-1-1111
χ172222222222-2-22-22-22222-2-200000022-2-2000022000000-2-2000000000-2000000000
χ182222222222-2-22-22-22222-2-2000000-2-2-2-20000-2-2000000220000000002000000000
χ192222222222-2-22-22-2-2-2-2-2-2-200000022220000-2-200000022000000000-2000000000
χ202222222222-2-22-22-2-2-2-2-2-2-2000000-2-222000022000000-2-20000000002000000000
χ2122222222-2-222-22-220000-2-2222222000022-2-200-2-20000000000-200000000000000
χ2222222222-2-222-22-220000-2-22222-2-20000-2-22200-2-20000000000200000000000000
χ2322222222-2-222-22-220000-2-2-2-2-2-2220000-2-22200220000000000-200000000000000
χ2422222222-2-222-22-220000-2-2-2-2-2-2-2-2000022-2-200220000000000200000000000000
χ25222-2-2-2-222-200-202022-2-20022−2−2002i−2i0000002i−2i2−222−2−200i2i2−i2−i200000000i2−i200000
χ26222-2-2-2-222-200-202022-2-20022−2−200−2i2i000000−2i2i2−222−2−200−i2−i2i2i200000000−i2i200000
χ27222-2-2-2-222-200-202022-2-200−2−222002i−2i0000002i−2i−22−2−22200−i2−i2i2i200000000−i2i200000
χ28222-2-2-2-222-200-202022-2-200−2−22200−2i2i000000−2i2i−22−2−22200i2i2−i2−i200000000i2−i200000
χ29222-2-2-2-222-200-2020-2-2220022−2−2002i−2i000000−2i2i2−2−2−22200−i2−i2i2i200000000i2−i200000
χ30222-2-2-2-222-200-2020-2-2220022−2−200−2i2i0000002i−2i2−2−2−22200i2i2−i2−i200000000−i2i200000
χ31222-2-2-2-222-200-2020-2-22200−2−222002i−2i000000−2i2i−2222−2−200i2i2−i2−i200000000−i2i200000
χ32222-2-2-2-222-200-2020-2-22200−2−22200−2i2i0000002i−2i−2222−2−200−i2−i2i2i200000000i2−i200000
χ332-22-22-22-22222-2-2-2-22-22-22-2000000002-22-22-2000000000000000002-20000000000
χ342-22-22-22-22222-2-2-2-22-22-22-2000000002-2-22-2200000000000000000-220000000000
χ352-22-22-22-22222-2-2-2-2-22-222-200000000-222-22-200000000000000000-220000000000
χ362-22-22-22-22222-2-2-2-2-22-222-200000000-22-22-22000000000000000002-20000000000
χ372-22-22-22-222-2-2-22-222-22-2-2200000000-220000000000000000000000002i−2i00002i−2i0
χ382-22-22-22-222-2-2-22-222-22-2-2200000000-22000000000000000000000000−2i2i0000−2i2i0
χ392-22-22-22-222-2-2-22-22-22-22-22000000002-20000000000000000000000002i−2i0000−2i2i0
χ402-22-22-22-222-2-2-22-22-22-22-22000000002-2000000000000000000000000−2i2i00002i−2i0
χ412-22-22-22-2-2-2222-22-20000-2200000000002-2-2200002i−2i2i−2i00000002i−2i000000000000
χ422-22-22-22-2-2-2222-22-20000-2200000000002-2-220000−2i2i−2i2i0000000−2i2i000000000000
χ432-22-22-22-2-2-2222-22-20000-220000000000-222-200002i−2i2i−2i0000000−2i2i000000000000
χ442-22-22-22-2-2-2222-22-20000-220000000000-222-20000−2i2i−2i2i00000002i−2i000000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-44-440040-400000002222−22−22000000000000−22220000000000000000000000000
χ47444-4-4-4-44-440040-40000000−22−22222200000000000022−220000000000000000000000000
χ4844-444-4-4-40000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ4944-444-4-4-40000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ5044-444-4-4-400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ5144-444-4-4-400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ5244-4-4-444-4004-4040-40000004-4-44000000000000000000000000000000000000000
χ5344-4-4-444-4004-4040-4000000-444-4000000000000000000000000000000000000000
χ5444-4-4-444-400-440-4040000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ5544-4-4-444-400-440-404000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ564-444-44-4-44-40040-404-4-44000000000000000000000000000000000000000000000
χ574-444-44-4-44-40040-40-444-4000000000000000000000000000000000000000000000
χ584-444-44-4-4-4400-40400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ594-444-44-4-4-4400-4040000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ604-44-44-44-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ614-4-44-4-444004-40-40400000000004-40000000000000000000000000000000000000
χ624-4-44-4-444004-40-4040000000000-440000000000000000000000000000000000000
χ634-4-44-4-44400-44040-4000000000000000000000000000000000000000000002i2−2i2000
χ644-4-44-4-44400-44040-400000000000000000000000000000000000000000000−2i22i2000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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