Finite Group Databasebeta

← Group #309103

Character table — Group #309103

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-1-111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-11-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-1111-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1-1-1111-1
χ172222222222-2-22-2-22-22222-200000000-2-22200-2-2002200000000-2-20000000000000000
χ182222222222-2-22-2-22-22222-200000000-2-2-2-2002200-2-200000000220000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-200000000222200-2-200-2-200000000220000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-20000000022-2-20022002200000000-2-20000000000000000
χ2122222222-2-222-222-2-20000-22222-2-2-2-20000220022000000000000000000-200-2000000
χ2222222222-2-222-222-2-20000-22222-2-2-2-20000-2-200-2-20000000000000000002002000000
χ2322222222-2-222-222-2-20000-2-2-2-2-2222200002200-2-2000000000000000000200-2000000
χ2422222222-2-222-222-2-20000-2-2-2-2-222220000-2-20022000000000000000000-2002000000
χ2522-2-22-22-22-200-200202i2i−2i−2i022−2−222−2−2002-20000002i−2ii2i2−i2−i222−2−200i2i2−i2−i2000000000000
χ2622-2-22-22-22-200-200202i2i−2i−2i022−2−222−2−200-22000000−2i2ii2i2−i2−i2−2−22200−i2−i2i2i2000000000000
χ2722-2-22-22-22-200-200202i2i−2i−2i0−2−222−2−222002-20000002i−2i−i2−i2i2i2−2−22200−i2−i2i2i2000000000000
χ2822-2-22-22-22-200-200202i2i−2i−2i0−2−222−2−22200-22000000−2i2i−i2−i2i2i222−2−200i2i2−i2−i2000000000000
χ2922-2-22-22-22-200-20020−2i−2i2i2i022−2−222−2−2002-2000000−2i2i−i2−i2i2i222−2−200−i2−i2i2i2000000000000
χ3022-2-22-22-22-200-20020−2i−2i2i2i022−2−222−2−200-220000002i−2i−i2−i2i2i2−2−22200i2i2−i2−i2000000000000
χ3122-2-22-22-22-200-20020−2i−2i2i2i0−2−222−2−222002-2000000−2i2ii2i2−i2−i2−2−22200i2i2−i2−i2000000000000
χ3222-2-22-22-22-200-20020−2i−2i2i2i0−2−222−2−22200-220000002i−2ii2i2−i2−i222−2−200−i2−i2i2i2000000000000
χ332-222-2-22-22222-2-2-2-220000-22-22-22-22-2000000000000000000000000002-202-20000000
χ342-222-2-22-22222-2-2-2-220000-22-22-22-22-200000000000000000000000000-220-220000000
χ352-222-2-22-22222-2-2-2-220000-2-22-22-22-22000000000000000000000000002-20-220000000
χ362-222-2-22-22222-2-2-2-220000-2-22-22-22-2200000000000000000000000000-2202-20000000
χ372-222-2-22-2-2-2222-2-22-22i−2i2i−2i22-22-2-22-222i−2i00000000002i−2i2i−2i0000000000000000000000
χ382-222-2-22-2-2-2222-2-22-22i−2i2i−2i2-22-222-22-22i−2i0000000000−2i2i−2i2i0000000000000000000000
χ392-222-2-22-2-2-2222-2-22-2−2i2i−2i2i22-22-2-22-22−2i2i0000000000−2i2i−2i2i0000000000000000000000
χ402-222-2-22-2-2-2222-2-22-2−2i2i−2i2i2-22-222-22-2−2i2i00000000002i−2i2i−2i0000000000000000000000
χ412-222-2-22-2-2-2-2-2222222i−2i2i−2i-200000000−2i2i000000000000002-22-2002i−2i2i−2i000000000000
χ422-222-2-22-2-2-2-2-2222222i−2i2i−2i-200000000−2i2i00000000000000-22-2200−2i2i−2i2i000000000000
χ432-222-2-22-2-2-2-2-222222−2i2i−2i2i-2000000002i−2i000000000000002-22-200−2i2i−2i2i000000000000
χ442-222-2-22-2-2-2-2-222222−2i2i−2i2i-2000000002i−2i00000000000000-22-22002i−2i2i−2i000000000000
χ452-2-2-2-2222-2200-200202-2-2202−2−22−222−20000002-200002−2−222−2−222-22−2−22000000000000
χ462-2-2-2-2222-2200-200202-2-2202−2−22−222−2000000-2200002−2−22−222−2-22−222−2000000000000
χ472-2-2-2-2222-2200-200202-2-220−222−22−2−220000002-20000−222−2−222−22-2−222−2000000000000
χ482-2-2-2-2222-2200-200202-2-220−222−22−2−22000000-220000−222−22−2−22-222−2−22000000000000
χ492-2-2-2-2222-2200-20020-222-202−2−22−222−20000002-20000−222−22−2−22-22−222−2000000000000
χ502-2-2-2-2222-2200-20020-222-202−2−22−222−2000000-220000−222−2−222−22-22−2−22000000000000
χ512-2-2-2-2222-2200-20020-222-20−222−22−2−220000002-200002−2−22−222−2-222−2−22000000000000
χ522-2-2-2-2222-2200-20020-222-20−222−22−2−22000000-2200002−2−222−2−222-2−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-44-4-4004-404-40000000000000000000000000000000000000000000000022−220000
χ55444-4-44-4-4004-404-400000000000000000000000000000000000000000000000−22220000
χ56444-4-44-4-400-440-4400000000000000000004-400000000000000000000000000000000
χ57444-4-44-4-400-440-440000000000000000000-4400000000000000000000000000000000
χ5844-4-44-44-4-4400400-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-4-44-44-4-4400400-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-444-4-44-444-4-4-444-4-4000040000000000000000000000000000000000000000000000
χ614-44-44-4-44004-40-44000000000000000000000000000000000000000000000000022−2200
χ624-44-44-4-44004-40-440000000000000000000000000000000000000000000000000−222200
χ634-44-44-4-4400-4404-4000000000000000000000004-40000000000000000000000000000
χ644-44-44-4-4400-4404-400000000000000000000000-440000000000000000000000000000
χ654-4-4-4-44444-400400-400000022−22−222222−22−222200000000000000000000000000000000000000
χ664-4-4-4-44444-400400-4000000−222222−22−222222−2200000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8888-8-8000000000000000000000000000000000000000000000000000000000000

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