Finite Group Databasebeta

← Group #282713

Character table — Group #282713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ5111111111111111111111-1-1-1-1111111111-1-11111-1-111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1111111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ172222222222-22-2-2-222222-20000-2000022220022-2-20000-2-2000000000000000-2000000000
χ182222222222-22-2-2-222222-20000-20000-2-2-2-200-2-2-2-20000220000000000000002000000000
χ192222222222-22-2-2-22-2-2-2-2-20000-20000222200-2-2220000-2-20000000000000002000000000
χ202222222222-22-2-2-22-2-2-2-2-20000-20000-2-2-2-2002222000022000000000000000-2000000000
χ2122222222-2-22-2222-20000-22222-222220000-2-2000022-2-200000000000000-2000000000000
χ2222222222-2-22-2222-20000-22222-2-2-2-2-20000-2-20000-2-222000000000000002000000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-222220000220000-2-2-2-2000000000000002000000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-2-2-2-2-20000220000222200000000000000-2000000000000
χ2522-2-22-22-22-20-200022i2i−2i−2i00000022−2−222-2-2002i−2i00002−200i2i2−i2−i2000022−2−200000000i2−i2000
χ2622-2-22-22-22-20-200022i2i−2i−2i00000022−2−2-2-22200−2i2i00002−200i2i2−i2−i20000−2−22200000000−i2i2000
χ2722-2-22-22-22-20-200022i2i−2i−2i000000−2−22222-2-2002i−2i0000−2200−i2−i2i2i20000−2−22200000000−i2i2000
χ2822-2-22-22-22-20-200022i2i−2i−2i000000−2−222-2-22200−2i2i0000−2200−i2−i2i2i2000022−2−200000000i2−i2000
χ2922-2-22-22-22-20-20002−2i−2i2i2i00000022−2−222-2-200−2i2i00002−200−i2−i2i2i2000022−2−200000000−i2i2000
χ3022-2-22-22-22-20-20002−2i−2i2i2i00000022−2−2-2-222002i−2i00002−200−i2−i2i2i20000−2−22200000000i2−i2000
χ3122-2-22-22-22-20-20002−2i−2i2i2i000000−2−22222-2-200−2i2i0000−2200i2i2−i2−i20000−2−22200000000i2−i2000
χ3222-2-22-22-22-20-20002−2i−2i2i2i000000−2−222-2-222002i−2i0000−2200i2i2−i2−i2000022−2−200000000−i2i2000
χ3322-2-2-22-2200202-2-20000002i2i−2i−2i02-22-22−22−20000002i−2i002−20000i2i2−i2−i22−22−20000000000i2−i20
χ3422-2-2-22-2200202-2-20000002i2i−2i−2i02-22-2−22−220000002i−2i00−220000−i2−i2i2i2−22−220000000000−i2i20
χ3522-2-2-22-2200202-2-20000002i2i−2i−2i0-22-222−22−2000000−2i2i002−20000i2i2−i2−i2−22−220000000000−i2i20
χ3622-2-2-22-2200202-2-20000002i2i−2i−2i0-22-22−22−22000000−2i2i00−220000−i2−i2i2i22−22−20000000000i2−i20
χ3722-2-2-22-2200202-2-2000000−2i−2i2i2i02-22-22−22−2000000−2i2i002−20000−i2−i2i2i22−22−20000000000−i2i20
χ3822-2-2-22-2200202-2-2000000−2i−2i2i2i02-22-2−22−22000000−2i2i00−220000i2i2−i2−i2−22−220000000000i2−i20
χ3922-2-2-22-2200202-2-2000000−2i−2i2i2i0-22-222−22−20000002i−2i002−20000−i2−i2i2i2−22−220000000000i2−i20
χ4022-2-2-22-2200202-2-2000000−2i−2i2i2i0-22-22−22−220000002i−2i00−220000i2i2−i2−i22−22−20000000000−i2i20
χ412-2-22-2-222222-2-2-22-22i−2i2i−2i22-22-2-2000000002-2002i−2i00000000000000000002i−2i0000000000
χ422-2-22-2-222222-2-2-22-22i−2i2i−2i2-22-22-200000000-22002i−2i0000000000000000000−2i2i0000000000
χ432-2-22-2-222222-2-2-22-2−2i2i−2i2i22-22-2-2000000002-200−2i2i0000000000000000000−2i2i0000000000
χ442-2-22-2-222222-2-2-22-2−2i2i−2i2i2-22-22-200000000-2200−2i2i00000000000000000002i−2i0000000000
χ452-2-22-2-22222-2-222-2-22i−2i2i−2i-200002000000000000−2i2i00000000002i−2i2i−2i00000000002-200000
χ462-2-22-2-22222-2-222-2-22i−2i2i−2i-200002000000000000−2i2i0000000000−2i2i−2i2i0000000000-2200000
χ472-2-22-2-22222-2-222-2-2−2i2i−2i2i-2000020000000000002i−2i00000000002i−2i2i−2i0000000000-2200000
χ482-2-22-2-22222-2-222-2-2−2i2i−2i2i-2000020000000000002i−2i0000000000−2i2i−2i2i00000000002-200000
χ492-2-22-2-222-2-222-2-2220000-22-22-2200000000-2200000000002-22-20000000000002-20000000
χ502-2-22-2-222-2-222-2-2220000-22-22-2200000000-220000000000-22-22000000000000-220000000
χ512-2-22-2-222-2-222-2-2220000-2-22-222000000002-200000000002-22-2000000000000-220000000
χ522-2-22-2-222-2-222-2-2220000-2-22-222000000002-20000000000-22-220000000000002-20000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ554444-4-4-4-400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ564444-4-4-4-4000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ574444-4-4-4-4000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ5844-4-44-44-4-4404000-400000000002222−22−22000000000000−2222000000000000000000000000000
χ5944-4-44-44-4-4404000-40000000000−22−22222200000000000022−22000000000000000000000000000
χ6044-4-4-44-4400-40-44400000000000000022−2222−220000000000−22220000000000000000000000000
χ6144-4-4-44-4400-40-444000000000000000−2222−2222000000000022−220000000000000000000000000
χ624-44-44-4-440040-44-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ634-44-44-4-440040-44-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-44-44-4-4400-404-440000000000000000000000000000000000022−22−222200000000000000000
χ654-44-44-4-4400-404-4400000000000000000000000000000000000−222222−2200000000000000000
χ664-44-4-444-44-404000-44-4-44000000000000000000000000000000000000000000000000000
χ674-44-4-444-44-404000-4-444-4000000000000000000000000000000000000000000000000000
χ684-44-4-444-4-440-400040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ694-44-4-444-4-440-40004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ704-4-44-4-444-4-4-4444-44000040000-4000000000000000000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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