Finite Group Databasebeta

← Group #305719

Character table — Group #305719

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-11111-1-11111-1-111-1-1-1-111-1-1-1-111-1-1-1111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-11111-1-1111111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-111111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111-1-11-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-11111-1-111-1
χ172222222222-2-22-22-2-22222-20000-2-20000220000220000-2-2000000000-2000000000
χ182222222222-2-22-22-2-22222-20000-2-20000-2-20000-2-20000220000000002000000000
χ192222222222-2-22-22-2-2-2-2-2-2-20000220000220000-2-2000022000000000-2000000000
χ202222222222-2-22-22-2-2-2-2-2-2-20000220000-2-20000220000-2-20000000002000000000
χ2122222222-2-222-22-22-20000-222220022-2-200-2-2-2-2000000000000002000000000000
χ2222222222-2-222-22-22-20000-2222200-2-2220022-2-200000000000000-2000000000000
χ2322222222-2-222-22-22-20000-2-2-2-2-200222200-2-22200000000000000-2000000000000
χ2422222222-2-222-22-22-20000-2-2-2-2-200-2-2-2-2002222000000000000002000000000000
χ2522-22-22-2-22222-2-2-2-2222-2-2-200002-22-200002-2000000000000002-20000000000000
χ2622-22-22-2-22222-2-2-2-2222-2-2-200002-2-220000-2200000000000000-220000000000000
χ2722-22-22-2-22222-2-2-2-22-2-222-20000-222-200002-200000000000000-220000000000000
χ2822-22-22-2-22222-2-2-2-22-2-222-20000-22-220000-22000000000000002-20000000000000
χ2922-22-22-2-222-2-2-22-22-222-2-220000-2200000000000000000000000000002i−2i002i−2i000
χ3022-22-22-2-222-2-2-22-22-222-2-220000-220000000000000000000000000000−2i2i00−2i2i000
χ3122-22-22-2-222-2-2-22-22-2-2-222200002-200000000000000000000000000002i−2i00−2i2i000
χ3222-22-22-2-222-2-2-22-22-2-2-222200002-20000000000000000000000000000−2i2i002i−2i000
χ3322-22-22-2-2-2-2222-22-2-2000020000002-20000-2200002i2i−2i−2i0000000002i−2i0000000000
χ3422-22-22-2-2-2-2222-22-2-2000020000002-20000-220000−2i−2i2i2i000000000−2i2i0000000000
χ3522-22-22-2-2-2-2222-22-2-200002000000-2200002-200002i2i−2i−2i000000000−2i2i0000000000
χ3622-22-22-2-2-2-2222-22-2-200002000000-2200002-20000−2i−2i2i2i0000000002i−2i0000000000
χ3722-2-2-2-2222-20020-2002i−2i2i−2i022−2−20000002i−2i002−22-2i2−i2i2−i20022−2−200000000i2−i200000
χ3822-2-2-2-2222-20020-2002i−2i2i−2i022−2−2000000−2i2i002−2-22i2−i2i2−i200−2−22200000000−i2i200000
χ3922-2-2-2-2222-20020-2002i−2i2i−2i0−2−2220000002i−2i00−222-2−i2i2−i2i200−2−22200000000−i2i200000
χ4022-2-2-2-2222-20020-2002i−2i2i−2i0−2−222000000−2i2i00−22-22−i2i2−i2i20022−2−200000000i2−i200000
χ4122-2-2-2-2222-20020-200−2i2i−2i2i022−2−20000002i−2i002−2-22−i2i2−i2i200−2−22200000000i2−i200000
χ4222-2-2-2-2222-20020-200−2i2i−2i2i022−2−2000000−2i2i002−22-2−i2i2−i2i20022−2−200000000−i2i200000
χ4322-2-2-2-2222-20020-200−2i2i−2i2i0−2−2220000002i−2i00−22-22i2−i2i2−i20022−2−200000000−i2i200000
χ4422-2-2-2-2222-20020-200−2i2i−2i2i0−2−222000000−2i2i00−222-2i2−i2i2−i200−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-44-400-404004i−4i−4i4i00000000000000000000000000000000000000000000
χ47444-44-4-4-44-400-40400−4i4i4i−4i00000000000000000000000000000000000000000000
χ48444-44-4-4-4-440040-4000000000000000000000000022−22−2222000000000000000000000
χ49444-44-4-4-4-440040-40000000000000000000000000−222222−22000000000000000000000
χ5044-44-44-4-4-4-4-4-4444440000-40000000000000000000000000000000000000000000
χ5144-4-4-4-444-4400-40400000002222−22−220000000000−2222000000000000000000000000000
χ5244-4-4-4-444-4400-4040000000−22−222222000000000022−22000000000000000000000000000
χ534-444-4-44-40000000000000022−2222−220000000000000000002i2−2i22i−2i2i−2i000000000000000
χ544-444-4-44-40000000000000022−2222−22000000000000000000−2i22i2−2i2i−2i2i000000000000000
χ554-444-4-44-400000000000000−2222−22220000000000000000002i2−2i2−2i2i−2i2i000000000000000
χ564-444-4-44-400000000000000−2222−2222000000000000000000−2i22i22i−2i2i−2i000000000000000
χ574-44-4-44-44004-4040-4000000000000004i−4i000000000000000000000000000000000
χ584-44-4-44-44004-4040-400000000000000−4i4i000000000000000000000000000000000
χ594-44-4-44-4400-440-404000000000000000000000000000000000000000000000022−220
χ604-44-4-44-4400-440-4040000000000000000000000000000000000000000000000−22220
χ614-4-4-4444-4004-40-4040000004-4-44000000000000000000000000000000000000000
χ624-4-4-4444-4004-40-404000000-444-4000000000000000000000000000000000000000
χ634-4-4-4444-400-44040-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-4-4444-400-44040-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-888-8-88000000000000000000000000000000000000000000000000000000000

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