Finite Group Databasebeta

← Group #309999

Character table — Group #309999

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-11111-1-1-1-111111111-11-1-1-1-1-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-111-1-111-1-111-1
χ911111111111111111-1-1-1-11111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ1111111111111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1111-1-11111-1-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-1-111111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ172222222222-2-22-2-22-200002222-20000222200-2-2002200-2-2000000000000-2000000000000
χ182222222222-2-22-2-22-200002222-20000-2-2-2-200-2-200-2-200220000000000002000000000000
χ192222222222-2-22-2-22-20000-2-2-2-2-200002222002200-2-200-2-20000000000002000000000000
χ202222222222-2-22-2-22-20000-2-2-2-2-20000-2-2-2-2002200220022000000000000-2000000000000
χ2122222222-2-222-222-2-222220000-222220000-2-2002200-2-2000000000000000-200000000000
χ2222222222-2-222-222-2-222220000-2-2-2-2-20000-2-200-2-20022000000000000000200000000000
χ2322222222-2-222-222-2-2-2-2-2-20000-2222200002200-2-200-2-2000000000000000200000000000
χ2422222222-2-222-222-2-2-2-2-2-20000-2-2-2-2-200002200220022000000000000000-200000000000
χ2522-22-2-2-22002-202-2002i2i−2i−2i0000022-2-2i2i2−i2−i200002i−2i0000i2−i2000022−2−2i2i2−i2−i200000000002−20
χ2622-22-2-2-22002-202-2002i2i−2i−2i0000022-2-2−i2−i2i2i200002i−2i0000−i2i20000−2−222−i2−i2i2i20000000000−220
χ2722-22-2-2-22002-202-2002i2i−2i−2i00000-2-222i2i2−i2−i20000−2i2i0000i2−i2000022−2−2−i2−i2i2i20000000000−220
χ2822-22-2-2-22002-202-2002i2i−2i−2i00000-2-222−i2−i2i2i20000−2i2i0000−i2i20000−2−222i2i2−i2−i200000000002−20
χ2922-22-2-2-22002-202-200−2i−2i2i2i0000022-2-2i2i2−i2−i20000−2i2i0000i2−i20000−2−222i2i2−i2−i20000000000−220
χ3022-22-2-2-22002-202-200−2i−2i2i2i0000022-2-2−i2−i2i2i20000−2i2i0000−i2i2000022−2−2−i2−i2i2i200000000002−20
χ3122-22-2-2-22002-202-200−2i−2i2i2i00000-2-222i2i2−i2−i200002i−2i0000i2−i20000−2−222−i2−i2i2i200000000002−20
χ3222-22-2-2-22002-202-200−2i−2i2i2i00000-2-222−i2−i2i2i200002i−2i0000−i2i2000022−2−2i2i2−i2−i20000000000−220
χ332-222-22-2-2-2-2002002000002i2i−2i−2i02−22−22-22-20000002i−2i2−200i2i2−i2−i200002−22−200000000i2−i2000
χ342-222-22-2-2-2-2002002000002i2i−2i−2i02−22−2-22-22000000−2i2i2−200i2i2−i2−i20000−22−2200000000−i2i2000
χ352-222-22-2-2-2-2002002000002i2i−2i−2i0−22−222-22-20000002i−2i−2200−i2−i2i2i20000−22−2200000000−i2i2000
χ362-222-22-2-2-2-2002002000002i2i−2i−2i0−22−22-22-22000000−2i2i−2200−i2−i2i2i200002−22−200000000i2−i2000
χ372-222-22-2-2-2-200200200000−2i−2i2i2i02−22−22-22-2000000−2i2i2−200−i2−i2i2i200002−22−200000000−i2i2000
χ382-222-22-2-2-2-200200200000−2i−2i2i2i02−22−2-22-220000002i−2i2−200−i2−i2i2i20000−22−2200000000i2−i2000
χ392-222-22-2-2-2-200200200000−2i−2i2i2i0−22−222-22-2000000−2i2i−2200i2i2−i2−i20000−22−2200000000i2−i2000
χ402-222-22-2-2-2-200200200000−2i−2i2i2i0−22−22-22-220000002i−2i−2200i2i2−i2−i200002−22−200000000−i2i2000
χ412-22-22-2-222-2222-2-2-2-22i−2i2i−2i2i−2i2i−2i2000000002i−2i2i−2i0000000000000000000000002-20000000
χ422-22-22-2-222-2222-2-2-2-22i−2i2i−2i−2i2i−2i2i2000000002i−2i−2i2i000000000000000000000000-220000000
χ432-22-22-2-222-2222-2-2-2-2−2i2i−2i2i2i−2i2i−2i200000000−2i2i2i−2i000000000000000000000000-220000000
χ442-22-22-2-222-2222-2-2-2-2−2i2i−2i2i−2i2i−2i2i200000000−2i2i−2i2i0000000000000000000000002-20000000
χ452-22-22-2-222-2-2-2222-2200002i−2i2i−2i-20000000000−2i2i0000000000002-22-20000002i−2i000000000
χ462-22-22-2-222-2-2-2222-2200002i−2i2i−2i-20000000000−2i2i000000000000-22-22000000−2i2i000000000
χ472-22-22-2-222-2-2-2222-220000−2i2i−2i2i-200000000002i−2i0000000000002-22-2000000−2i2i000000000
χ482-22-22-2-222-2-2-2222-220000−2i2i−2i2i-200000000002i−2i000000000000-22-220000002i−2i000000000
χ492-22-22-2-22-2222-2-2-2222i−2i2i−2i0000-200000000−2i2i00000000002i−2i2i−2i000000000000002-200000
χ502-22-22-2-22-2222-2-2-2222i−2i2i−2i0000-200000000−2i2i0000000000−2i2i−2i2i00000000000000-2200000
χ512-22-22-2-22-2222-2-2-222−2i2i−2i2i0000-2000000002i−2i00000000002i−2i2i−2i00000000000000-2200000
χ522-22-22-2-22-2222-2-2-222−2i2i−2i2i0000-2000000002i−2i0000000000−2i2i−2i2i000000000000002-200000
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-44-44-400-400400000000000000000000000000000022−22−2222000000000000000000000
χ55444-4-4-44-44-400-4004000000000000000000000000000000−222222−22000000000000000000000
χ56444-4-4-44-4-4400400-4000004-4-440000000000000000000000000000000000000000000000
χ57444-4-4-44-4-4400400-400000-444-40000000000000000000000000000000000000000000000
χ5844-44-4-4-4400-440-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ5944-44-4-4-4400-440-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ604-444-44-4-44400-400-4000000000022−2222−22000000000000−2222000000000000000000000000000
χ614-444-44-4-44400-400-40000000000−2222−222200000000000022−22000000000000000000000000000
χ624-44-44-4-44-44-4-4-4444-4000000004000000000000000000000000000000000000000000000
χ634-4-444-44-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ644-4-444-44-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ654-4-444-44-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ664-4-444-44-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ674-4-4-4-4444004-40-44004-4-4400000000000000000000000000000000000000000000000000
χ684-4-4-4-4444004-40-4400-444-400000000000000000000000000000000000000000000000000
χ694-4-4-4-444400-4404-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-4-444400-4404-400000000000000000000000000000000000−222222−2200000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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