Finite Group Databasebeta

← Group #305755

Character table — Group #305755

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1-1-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ101111111111111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1111-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-111-1
χ172222222222-2-22-22-20000-2-222220022-2-2-2-200-2-2000000000000200000000000000
χ182222222222-2-22-22-20000-2-2222200-2-2222200-2-2000000000000-200000000000000
χ192222222222-2-22-22-20000-2-2-2-2-2-2002222-2-20022000000000000-200000000000000
χ202222222222-2-22-22-20000-2-2-2-2-2-200-2-2-2-2220022000000000000200000000000000
χ2122222222-2-222-22-222222-2-20000-2-20000002200-2-20000220000000-200000000000
χ2222222222-2-222-22-222222-2-20000-2-2000000-2-200220000-2-20000000200000000000
χ2322222222-2-222-22-22-2-2-2-2-2-20000220000002200220000-2-20000000-200000000000
χ2422222222-2-222-22-22-2-2-2-2-2-2000022000000-2-200-2-20000220000000200000000000
χ25222-22-2-2-2002-20-2022i2i−2i−2i0022−2−2000000002i−2i2−200i2i2−i2−i22-222−2−200000000i2−i200000
χ26222-22-2-2-2002-20-2022i2i−2i−2i0022−2−200000000−2i2i2−200i2i2−i2−i2-22−2−22200000000−i2i200000
χ27222-22-2-2-2002-20-2022i2i−2i−2i00−2−222000000002i−2i−2200−i2−i2i2i22-2−2−22200000000−i2i200000
χ28222-22-2-2-2002-20-2022i2i−2i−2i00−2−22200000000−2i2i−2200−i2−i2i2i2-2222−2−200000000i2−i200000
χ29222-22-2-2-2002-20-202−2i−2i2i2i0022−2−2000000002i−2i2−200−i2−i2i2i2-22−2−22200000000i2−i200000
χ30222-22-2-2-2002-20-202−2i−2i2i2i0022−2−200000000−2i2i2−200−i2−i2i2i22-222−2−200000000−i2i200000
χ31222-22-2-2-2002-20-202−2i−2i2i2i00−2−222000000002i−2i−2200i2i2−i2−i2-2222−2−200000000−i2i200000
χ32222-22-2-2-2002-20-202−2i−2i2i2i00−2−22200000000−2i2i−2200i2i2−i2−i22-2−2−22200000000i2−i200000
χ332-222-2-22-22222-2-2-2-22-22-22-200002-22-2002-2000000000000000000002-2000000000
χ342-222-2-22-22222-2-2-2-22-22-22-200002-2-2200-2200000000000000000000-22000000000
χ352-222-2-22-22222-2-2-2-2-22-222-20000-222-2002-200000000000000000000-22000000000
χ362-222-2-22-22222-2-2-2-2-22-222-20000-22-2200-22000000000000000000002-2000000000
χ372-222-2-22-222-2-2-22-220000-220000002-200-220000002i−2i2i−2i00000002i−2i000000000000
χ382-222-2-22-222-2-2-22-220000-220000002-200-22000000−2i2i−2i2i0000000−2i2i000000000000
χ392-222-2-22-222-2-2-22-220000-22000000-22002-20000002i−2i2i−2i0000000−2i2i000000000000
χ402-222-2-22-222-2-2-22-220000-22000000-22002-2000000−2i2i−2i2i00000002i−2i000000000000
χ412-222-2-22-2-2-2222-22-22-22-2-220000-2200000000000000000000000000002i−2i002i−2i000
χ422-222-2-22-2-2-2222-22-22-22-2-220000-220000000000000000000000000000−2i2i00−2i2i000
χ432-222-2-22-2-2-2222-22-2-22-22-2200002-200000000000000000000000000002i−2i00−2i2i000
χ442-222-2-22-2-2-2222-22-2-22-22-2200002-20000000000000000000000000000−2i2i002i−2i000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-400-44040-40000002222−22−220000000000−2222000000000000000000000000000
χ47444-44-4-4-400-44040-4000000−22−222222000000000022−22000000000000000000000000000
χ4844-44-44-4-44-40040-40000000000000004-4000000000000000000000000000000000
χ4944-44-44-4-44-40040-4000000000000000-44000000000000000000000000000000000
χ5044-44-44-4-4-4400-404000000000000000000000000000000000000000000000002i2−2i20
χ5144-44-44-4-4-4400-40400000000000000000000000000000000000000000000000−2i22i20
χ524-444-4-44-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ534-44-4-44-44004-4040-44i−4i−4i4i000000000000000000000000000000000000000000000
χ544-44-4-44-44004-4040-4−4i4i4i−4i000000000000000000000000000000000000000000000
χ554-44-4-44-4400-440-40400000000000000000000000022−22−2222000000000000000000000
χ564-44-4-44-4400-440-404000000000000000000000000−222222−22000000000000000000000
χ574-4-444-4-444-400-40400000004-44-4000000000000000000000000000000000000000
χ584-4-444-4-444-400-4040000000-44-44000000000000000000000000000000000000000
χ594-4-444-4-44-440040-400000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ604-4-444-4-44-440040-40000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ614-4-4-4444-40000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ624-4-4-4444-40000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ634-4-4-4444-400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ644-4-4-4444-400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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