Finite Group Databasebeta

← Group #311307

Character table — Group #311307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-111-1-1111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-111-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111-1-111-1-1-111-11
χ911111111111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-11-1-1-1-111
χ1011111111111111111-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-11111-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-111111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1-11
χ172222222222-2-22-2-22-22222-2000000000000-2-222-2-22200000000-2-20000000000000000
χ182222222222-2-22-2-22-22222-2000000000000-2-2-2-222-2-200000000220000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-20000000000002222-2-2-2-200000000220000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-200000000000022-2-2222200000000-2-20000000000000000
χ2122222222-2-222-222-2-20000-22222-2-2-2-222220000000000000000000000-20000-2000000
χ2222222222-2-222-222-2-20000-22222-2-2-2-2-2-2-2-20000000000000000000000200002000000
χ2322222222-2-222-222-2-20000-2-2-2-2-2222222-2-2000000000000000000000020000-2000000
χ2422222222-2-222-222-2-20000-2-2-2-2-22222-2-2220000000000000000000000-200002000000
χ2522-2-22-22-2-2-200200202i2i−2i−2i022−2−222−2−20000002-2002i−2ii2i2−i2−i222−2−200i2i2−i2−i2000000000000
χ2622-2-22-22-2-2-200200202i2i−2i−2i022−2−222−2−2000000-2200−2i2ii2i2−i2−i2−2−22200−i2−i2i2i2000000000000
χ2722-2-22-22-2-2-200200202i2i−2i−2i0−2−222−2−2220000002-2002i−2i−i2−i2i2i2−2−22200−i2−i2i2i2000000000000
χ2822-2-22-22-2-2-200200202i2i−2i−2i0−2−222−2−222000000-2200−2i2i−i2−i2i2i222−2−200i2i2−i2−i2000000000000
χ2922-2-22-22-2-2-20020020−2i−2i2i2i022−2−222−2−20000002-200−2i2i−i2−i2i2i222−2−200−i2−i2i2i2000000000000
χ3022-2-22-22-2-2-20020020−2i−2i2i2i022−2−222−2−2000000-22002i−2i−i2−i2i2i2−2−22200i2i2−i2−i2000000000000
χ3122-2-22-22-2-2-20020020−2i−2i2i2i0−2−222−2−2220000002-200−2i2ii2i2−i2−i2−2−22200i2i2−i2−i2000000000000
χ3222-2-22-22-2-2-20020020−2i−2i2i2i0−2−222−2−222000000-22002i−2ii2i2−i2−i222−2−200−i2−i2i2i2000000000000
χ332-22-22-2-222-200-200202-22-20i2−i2i2−i2i2−i2i2−i2000000002-200i2−i2i2−i2i2−i2i2−i22-2i2−i2i2−i2000000000000
χ342-22-22-2-222-200-200202-22-20i2−i2i2−i2i2−i2i2−i200000000-2200i2−i2i2−i2−i2i2−i2i2-22−i2i2−i2i2000000000000
χ352-22-22-2-222-200-200202-22-20−i2i2−i2i2−i2i2−i2i2000000002-200−i2i2−i2i2−i2i2−i2i22-2−i2i2−i2i2000000000000
χ362-22-22-2-222-200-200202-22-20−i2i2−i2i2−i2i2−i2i200000000-2200−i2i2−i2i2i2−i2i2−i2-22i2−i2i2−i2000000000000
χ372-22-22-2-222-200-20020-22-220i2−i2i2−i2i2−i2i2−i2000000002-200−i2i2−i2i2i2−i2i2−i2-22−i2i2−i2i2000000000000
χ382-22-22-2-222-200-20020-22-220i2−i2i2−i2i2−i2i2−i200000000-2200−i2i2−i2i2−i2i2−i2i22-2i2−i2i2−i2000000000000
χ392-22-22-2-222-200-20020-22-220−i2i2−i2i2−i2i2−i2i2000000002-200i2−i2i2−i2−i2i2−i2i2-22i2−i2i2−i2000000000000
χ402-22-22-2-222-200-20020-22-220−i2i2−i2i2−i2i2−i2i200000000-2200i2−i2i2−i2i2−i2i2−i22-2−i2i2−i2i2000000000000
χ412-2-2222-2-22-2-2-2222-2-2000022i−2i−2i2i−2i2i2i−2i0000000000000000000000000002-22i−2i0000000
χ422-2-2222-2-22-2-2-2222-2-2000022i−2i−2i2i−2i2i2i−2i000000000000000000000000000-22−2i2i0000000
χ432-2-2222-2-22-2-2-2222-2-200002−2i2i2i−2i2i−2i−2i2i0000000000000000000000000002-2−2i2i0000000
χ442-2-2222-2-22-2-2-2222-2-200002−2i2i2i−2i2i−2i−2i2i000000000000000000000000000-222i−2i0000000
χ452-2-2222-2-2-2222-2-2-22-22i−2i−2i2i20000000000002i−2i00000000002i−2i−2i2i00-222-2000000000000
χ462-2-2222-2-2-2222-2-2-22-22i−2i−2i2i20000000000002i−2i0000000000−2i2i2i−2i002-2-22000000000000
χ472-2-2222-2-2-2222-2-2-22-2−2i2i2i−2i2000000000000−2i2i00000000002i−2i−2i2i002-2-22000000000000
χ482-2-2222-2-2-2222-2-2-22-2−2i2i2i−2i2000000000000−2i2i0000000000−2i2i2i−2i00-222-2000000000000
χ492-2-2222-2-2-22-2-2-222222i−2i−2i2i-22i−2i−2i2i2i−2i−2i2i0000−2i2i000000-222-20000000000000000000000
χ502-2-2222-2-2-22-2-2-222222i−2i−2i2i-2−2i2i2i−2i−2i2i2i−2i0000−2i2i0000002-2-220000000000000000000000
χ512-2-2222-2-2-22-2-2-22222−2i2i2i−2i-22i−2i−2i2i2i−2i−2i2i00002i−2i0000002-2-220000000000000000000000
χ522-2-2222-2-2-22-2-2-22222−2i2i2i−2i-2−2i2i2i−2i−2i2i2i−2i00002i−2i000000-222-20000000000000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-44-4-4004-404-40000000000000004-4000000000000000000000000000000000000
χ55444-4-44-4-4004-404-4000000000000000-44000000000000000000000000000000000000
χ56444-4-44-4-400-440-44000000000000000000000000000000000000000000000000022−2200
χ57444-4-44-4-400-440-440000000000000000000000000000000000000000000000000−222200
χ5844-4-44-44-44400-400-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-4-44-44-44400-400-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-44-44-4-44-4400400-40000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-44-44-4-44-4400400-4000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-4444-4-44-4444-4-4-440000-40000000000000000000000000000000000000000000000
χ634-4-4-4-4444004-40-440000000000000000000000000000000000000000000000022−220000
χ644-4-4-4-4444004-40-4400000000000000000000000000000000000000000000000−22220000
χ654-4-4-4-444400-4404-4000000000000000004-40000000000000000000000000000000000
χ664-4-4-4-444400-4404-400000000000000000-440000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-8-88-8000000000000000000000000000000000000000000000000000000000000

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