Finite Group Databasebeta

← Group #264262

Character table — Group #264262

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822222244448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111111-1-1-1-1-1111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-111111-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ172222222222-2-2-2-222-20000-22222-2-2-2-200220022000000000000000000-20000-2000000
χ182222222222-2-2-2-222-20000-22222-2-2-2-200-2-200-2-2000000000000000000200002000000
χ192222222222-2-2-2-222-20000-2-2-2-2-22222002200-2-2000000000000000000-200002000000
χ202222222222-2-2-2-222-20000-2-2-2-2-2222200-2-2002200000000000000000020000-2000000
χ2122222222-2-22222-2-2-22222-200000000-2-2002200-2-222-2-2000000000000000000000000
χ2222222222-2-22222-2-2-22222-200000000-2-200-2-20022-2-222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000000022002200-2-2-2-222000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2000000002200-2-2002222-2-2000000000000000000000000
χ2522-2-22-22-2002-22-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i002-222−2−222−2−2i2i2−i2−i2000000000000
χ2622-2-22-22-2002-22-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i00-2222−2−2−2−222−i2−i2i2i2000000000000
χ2722-2-22-22-2002-22-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i002-2−2−222−2−222−i2−i2i2i2000000000000
χ2822-2-22-22-2002-22-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i00-22−2−22222−2−2i2i2−i2−i2000000000000
χ2922-2-22-22-2002-22-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i00-22−2−22222−2−2−i2−i2i2i2000000000000
χ3022-2-22-22-2002-22-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i002-2−2−222−2−222i2i2−i2−i2000000000000
χ3122-2-22-22-2002-22-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i00-2222−2−2−2−222i2i2−i2−i2000000000000
χ3222-2-22-22-2002-22-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i002-222−2−222−2−2−i2−i2i2i2000000000000
χ332-22-2-222-2002-2-220002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i200002-200002i−2i002−22−2i2−i2i2−i22−22−2000000000000
χ342-22-2-222-2002-2-220002i−2i2i−2i0i2−i2i2−i2i2−i2i2−i20000-220000−2i2i002−22−2−i2i2−i2i2−22−22000000000000
χ352-22-2-222-2002-2-220002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i200002-200002i−2i00−22−22−i2i2−i2i2−22−22000000000000
χ362-22-2-222-2002-2-220002i−2i2i−2i0−i2i2−i2i2−i2i2−i2i20000-220000−2i2i00−22−22i2−i2i2−i22−22−2000000000000
χ372-22-2-222-2002-2-22000−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i200002-20000−2i2i00−22−22i2−i2i2−i2−22−22000000000000
χ382-22-2-222-2002-2-22000−2i2i−2i2i0i2−i2i2−i2i2−i2i2−i20000-2200002i−2i00−22−22−i2i2−i2i22−22−2000000000000
χ392-22-2-222-2002-2-22000−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i200002-20000−2i2i002−22−2−i2i2−i2i22−22−2000000000000
χ402-22-2-222-2002-2-22000−2i2i−2i2i0−i2i2−i2i2−i2i2−i2i20000-2200002i−2i002−22−2i2−i2i2−i2−22−22000000000000
χ412-2-22-2-2222222-2-2-2-222-2-22-2000000002-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ422-2-22-2-2222222-2-2-2-222-2-22-2000000002-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ432-2-22-2-2222222-2-2-2-22-222-2-200000000-2200000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ442-2-22-2-2222222-2-2-2-22-222-2-200000000-220000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ452-2-22-2-222-2-222-2-222-22-2-2222-2-222-2-22-220000000000002-2-2200000000000000000000
χ462-2-22-2-222-2-222-2-222-22-2-222-222-2-222-2-22000000000000-222-200000000000000000000
χ472-2-22-2-222-2-222-2-222-2-222-222-2-222-2-222-2000000000000-222-200000000000000000000
χ482-2-22-2-222-2-222-2-222-2-222-22-222-2-222-22-20000000000002-2-2200000000000000000000
χ492-2-22-2-222-2-2-2-2222220000-22-2-22-222-20000000000000000000000000002-22-20000000
χ502-2-22-2-222-2-2-2-2222220000-22-2-22-222-2000000000000000000000000000-22-220000000
χ512-2-22-2-222-2-2-2-2222220000-2-222-22-2-220000000000000000000000000002-2-220000000
χ522-2-22-2-222-2-2-2-2222220000-2-222-22-2-22000000000000000000000000000-222-20000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-444-400004-40000000000000000000000000000000000000000000000002i2−2i200
χ55444-4-4-4-444-400004-4000000000000000000000000000000000000000000000000−2i22i200
χ56444-4-4-4-44-440000-44000000000000000000004i−4i000000000000000000000000000000
χ57444-4-4-4-44-440000-4400000000000000000000−4i4i000000000000000000000000000000
χ5844-4-44-44-400-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-4-44-44-400-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-44-4-444-400-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ614-44-4-444-400-444-400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ624-4-44-4-44444-4-444-4-4-4000040000000000000000000000000000000000000000000000
χ634-4-4-444-444-40000-4400000000000000004-40000000000000000000000000000000000
χ644-4-4-444-444-40000-440000000000000000-440000000000000000000000000000000000
χ654-4-4-444-44-4400004-4000000000000000000000000000000000000000000000022−220000
χ664-4-4-444-44-4400004-40000000000000000000000000000000000000000000000−22220000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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