Finite Group Databasebeta

← Group #309953

Character table — Group #309953

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1111111-1-1-1
χ911111111111111111-1-1-1-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ1011111111111111111-1-1-1-11111111-1-111-1-111111111-1-1-1-11111-11-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111111-111-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111111-1-111-1-111-1
χ17222222222-222-2-22-2-22222-20000002200-2-2000022-2-200000000-200000000000000
χ18222222222-222-2-22-2-22222-2000000-2-200-2-20000-2-22200000000200000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-20000002200220000-2-22200000000-200000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2000000-2-20022000022-2-200000000200000000000000
χ2122222222-22-2-222-22-20000-222222200-2-200-2-2-2-2000000000000020000000000000
χ2222222222-22-2-222-22-20000-22222-2-200220022-2-20000000000000-20000000000000
χ2322222222-22-2-222-22-20000-2-2-2-2-222002200-2-2220000000000000-20000000000000
χ2422222222-22-2-222-22-20000-2-2-2-2-2-2-200-2-2002222000000000000020000000000000
χ252-222-22-2-2-202-20020022-2-2022−2−2002i−2i0000002−22i−2i0022−2−2i2i2−i2−i200000000i2−i200000
χ262-222-22-2-2-202-20020022-2-2022−2−200−2i2i0000002−2−2i2i0022−2−2−i2−i2i2i200000000−i2i200000
χ272-222-22-2-2-202-20020022-2-20−2−222002i−2i000000−222i−2i00−2−222−i2−i2i2i200000000−i2i200000
χ282-222-22-2-2-202-20020022-2-20−2−22200−2i2i000000−22−2i2i00−2−222i2i2−i2−i200000000i2−i200000
χ292-222-22-2-2-202-200200-2-222022−2−2002i−2i0000002−2−2i2i00−2−222−i2−i2i2i200000000i2−i200000
χ302-222-22-2-2-202-200200-2-222022−2−200−2i2i0000002−22i−2i00−2−222i2i2−i2−i200000000−i2i200000
χ312-222-22-2-2-202-200200-2-2220−2−222002i−2i000000−22−2i2i0022−2−2i2i2−i2−i200000000−i2i200000
χ322-222-22-2-2-202-200200-2-2220−2−22200−2i2i000000−222i−2i0022−2−2−i2−i2i2i200000000i2−i200000
χ332-22-22-22-222-2-2-2-22222i−2i2i−2i-200002i−2i00002i−2i2i−2i0000000000000000002-2000000000
χ342-22-22-22-222-2-2-2-22222i−2i2i−2i-20000−2i2i00002i−2i−2i2i000000000000000000-22000000000
χ352-22-22-22-222-2-2-2-2222−2i2i−2i2i-200002i−2i0000−2i2i2i−2i000000000000000000-22000000000
χ362-22-22-22-222-2-2-2-2222−2i2i−2i2i-20000−2i2i0000−2i2i−2i2i0000000000000000002-2000000000
χ372-22-22-22-22-2-2-2222-2-22i−2i2i−2i20000000000−2i2i0000000000000000002i−2i0000002-2000
χ382-22-22-22-22-2-2-2222-2-22i−2i2i−2i20000000000−2i2i000000000000000000−2i2i000000-22000
χ392-22-22-22-22-2-2-2222-2-2−2i2i−2i2i200000000002i−2i0000000000000000002i−2i000000-22000
χ402-22-22-22-22-2-2-2222-2-2−2i2i−2i2i200000000002i−2i000000000000000000−2i2i0000002-2000
χ412-22-22-22-2-2222-2-2-22-20000200002i−2i000000−2i2i0000002-22-200000000002i−2i0000000
χ422-22-22-22-2-2222-2-2-22-20000200002i−2i000000−2i2i000000-22-220000000000−2i2i0000000
χ432-22-22-22-2-2222-2-2-22-2000020000−2i2i0000002i−2i0000002-22-20000000000−2i2i0000000
χ442-22-22-22-2-2222-2-2-22-2000020000−2i2i0000002i−2i000000-22-2200000000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-4-4-44404-400-400000000000000000000000000022−22−22220000000000000000000
χ47444-4-4-4-44404-400-4000000000000000000000000000−222222−220000000000000000000
χ48444-4-4-4-44-40-44004004i−4i−4i4i00000000000000000000000000000000000000000000
χ49444-4-4-4-44-40-4400400−4i4i4i−4i00000000000000000000000000000000000000000000
χ5044-44-4-44-404004-40-400000000000000000000000000000022−2222−22000000000000000
χ5144-44-4-44-404004-40-4000000000000000000000000000000−2222−2222000000000000000
χ5244-44-4-44-40-400-44040000004i−4i4i−4i000000000000000000000000000000000000000
χ5344-44-4-44-40-400-4404000000−4i4i−4i4i000000000000000000000000000000000000000
χ544-444-44-4-440-4400-400000002222−22−220000000000−2222000000000000000000000000000
χ554-444-44-4-440-4400-40000000−22−222222000000000022−22000000000000000000000000000
χ564-44-44-44-4-4-44444-4-440000-40000000000000000000000000000000000000000000
χ574-4-444-4-44000000000000002i2−2i2−2i22i20000000000000022−2200002i−2i−2i2i000000000000000
χ584-4-444-4-44000000000000002i2−2i2−2i22i200000000000000−22220000−2i2i2i−2i000000000000000
χ594-4-444-4-4400000000000000−2i22i22i2−2i20000000000000022−220000−2i2i2i−2i000000000000000
χ604-4-444-4-4400000000000000−2i22i22i2−2i200000000000000−222200002i−2i−2i2i000000000000000
χ614-4-4-4-44440400-440-400000000000000000000000000000000000000000000002i2−2i20
χ624-4-4-4-44440400-440-40000000000000000000000000000000000000000000000−2i22i20
χ634-4-4-4-44440-4004-404000000000000004-4000000000000000000000000000000000
χ644-4-4-4-44440-4004-40400000000000000-44000000000000000000000000000000000
χ6588-8-888-8-8000000000000000000000000000000000000000000000000000000000

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