Finite Group Databasebeta

← Group #306923

Character table — Group #306923

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-11-111-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-111111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-111-1-111111111-1-1-1-1111111-11-1-1-1-1-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111111-1-1-11111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-11111-1-111-1
χ17222222222-22-22-22-2-20000-22222002200-2-2-2-2-2-2000000000000020000000000000
χ18222222222-22-22-22-2-20000-2222200-2-2002222-2-20000000000000-20000000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-2002200-2-222220000000000000-20000000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-20022-2-222000000000000020000000000000
χ2122222222-22-22-22-22-22222-20000-2-20022000000-2-20000220000-200000000000000
χ2222222222-22-22-22-22-22222-20000-2-200-2-2000000220000-2-20000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220022000000220000-2-20000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200002200-2-2000000-2-20000220000200000000000000
χ252-222-22-2-22-2-222-2-22-222-2-2200002-200000000000000000000000000002i−2i002i−2i000
χ262-222-22-2-22-2-222-2-22-222-2-2200002-20000000000000000000000000000−2i2i00−2i2i000
χ272-222-22-2-22-2-222-2-22-2-2-22220000-2200000000000000000000000000002i−2i00−2i2i000
χ282-222-22-2-22-2-222-2-22-2-2-22220000-220000000000000000000000000000−2i2i002i−2i000
χ292-222-22-2-2-222-2-222-2-2000020000002i−2i002i−2i00000022-2-200000000002i−2i000000000
χ302-222-22-2-2-222-2-222-2-2000020000002i−2i002i−2i000000-2-2220000000000−2i2i000000000
χ312-222-22-2-2-222-2-222-2-200002000000−2i2i00−2i2i00000022-2-20000000000−2i2i000000000
χ322-222-22-2-2-222-2-222-2-200002000000−2i2i00−2i2i000000-2-22200000000002i−2i000000000
χ332-222-22-2-2-2-222-2-222222-2-2-20000-222i−2i00−2i2i0000000000000000002i−2i00000000000
χ342-222-22-2-2-2-222-2-222222-2-2-20000-22−2i2i002i−2i000000000000000000−2i2i00000000000
χ352-222-22-2-2-2-222-2-2222-2-222-200002-22i−2i00−2i2i000000000000000000−2i2i00000000000
χ362-222-22-2-2-2-222-2-2222-2-222-200002-2−2i2i002i−2i0000000000000000002i−2i00000000000
χ372-2-2-2222-202020-20-202i−2i2i−2i022−2−200002-200002−200i2−i2i2−i22i−2ii2i2−i2−i2000000002−200000
χ382-2-2-2222-202020-20-202i−2i2i−2i022−2−20000-2200002−200i2−i2i2−i2−2i2i−i2−i2i2i200000000−2200000
χ392-2-2-2222-202020-20-202i−2i2i−2i0−2−22200002-20000−2200−i2i2−i2i22i−2i−i2−i2i2i200000000−2200000
χ402-2-2-2222-202020-20-202i−2i2i−2i0−2−2220000-220000−2200−i2i2−i2i2−2i2ii2i2−i2−i2000000002−200000
χ412-2-2-2222-202020-20-20−2i2i−2i2i022−2−200002-200002−200−i2i2−i2i2−2i2i−i2−i2i2i2000000002−200000
χ422-2-2-2222-202020-20-20−2i2i−2i2i022−2−20000-2200002−200−i2i2−i2i22i−2ii2i2−i2−i200000000−2200000
χ432-2-2-2222-202020-20-20−2i2i−2i2i0−2−22200002-20000−2200i2−i2i2−i2−2i2ii2i2−i2−i200000000−2200000
χ442-2-2-2222-202020-20-20−2i2i−2i2i0−2−2220000-220000−2200i2−i2i2−i22i−2i−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-44-4-4-440-40-40400000004-44-4000000000000000000000000000000000000000
χ47444-44-4-4-440-40-4040000000-44-44000000000000000000000000000000000000000
χ48444-44-4-4-4-404040-4000000000000000000000000000000022−2222−22000000000000000
χ49444-44-4-4-4-404040-40000000000000000000000000000000−2222−2222000000000000000
χ5044-4-4-44-44040-40-4040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5144-4-4-44-44040-40-404000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5244-4-4-44-440-404040-404i−4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-4-44-440-404040-40−4i4i4i−4i00000000000000000000000000000000000000000000
χ544-444-44-4-444-4-444-4-440000-40000000000000000000000000000000000000000000
χ554-44-4-4-4444040-40-4000000000000000000000000000000000000000000000002i2−2i20
χ564-44-4-4-4444040-40-400000000000000000000000000000000000000000000000−2i22i20
χ574-44-4-4-444-40-4040400000000000000000004-400000000000000000000000000000
χ584-44-4-4-444-40-404040000000000000000000-4400000000000000000000000000000
χ594-4-444-4-440000000000000022−22−22220000000000002i2−2i20000002i−2i−2i2i000000000000000
χ604-4-444-4-440000000000000022−22−2222000000000000−2i22i2000000−2i2i2i−2i000000000000000
χ614-4-444-4-4400000000000000−222222−220000000000002i2−2i2000000−2i2i2i−2i000000000000000
χ624-4-444-4-4400000000000000−222222−22000000000000−2i22i20000002i−2i−2i2i000000000000000
χ634-4-4-4444-40-40-404040000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-4444-40-40-40404000000−22−222222000000000022−22000000000000000000000000000
χ6588-88-8-88-8000000000000000000000000000000000000000000000000000000000

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