Finite Group Databasebeta

← Group #310232

Character table — Group #310232

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1111-1-1-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-11-1-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-111-1-1-1-11
χ17222222222-2-22-2-22200002222-2-20000222200-2-2002200-2-2000000000000000-2000000000
χ18222222222-2-22-2-22200002222-2-20000-2-2-2-200-2-200-2-200220000000000000002000000000
χ19222222222-2-22-2-2220000-2-2-2-2-2-200002222002200-2-200-2-20000000000000002000000000
χ20222222222-2-22-2-2220000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000000-2000000000
χ2122222222-222-222-2-222220000-2-222220000-2-2002200-2-20000000000000000-20000000000
χ2222222222-222-222-2-222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000020000000000
χ2322222222-222-222-2-2-2-2-2-20000-2-2222200002200-2-200-2-2000000000000000020000000000
χ2422222222-222-222-2-2-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000-20000000000
χ2522-2-22-2-22222-2-2-22-22i2i−2i−2i2i2i−2i−2i-22000000002i−2i2i−2i000000000000000000000000002-200000
χ2622-2-22-2-22222-2-2-22-22i2i−2i−2i−2i−2i2i2i-22000000002i−2i−2i2i00000000000000000000000000-2200000
χ2722-2-22-2-22222-2-2-22-2−2i−2i2i2i2i2i−2i−2i-2200000000−2i2i2i−2i00000000000000000000000000-2200000
χ2822-2-22-2-22222-2-2-22-2−2i−2i2i2i−2i−2i2i2i-2200000000−2i2i−2i2i000000000000000000000000002-200000
χ2922-2-22-2-222-2-2-2222-200002i2i−2i−2i2-20000000000−2i2i00000000000022-2-2000000002i−2i0000000
χ3022-2-22-2-222-2-2-2222-200002i2i−2i−2i2-20000000000−2i2i000000000000-2-22200000000−2i2i0000000
χ3122-2-22-2-222-2-2-2222-20000−2i−2i2i2i2-200000000002i−2i00000000000022-2-200000000−2i2i0000000
χ3222-2-22-2-222-2-2-2222-20000−2i−2i2i2i2-200000000002i−2i000000000000-2-222000000002i−2i0000000
χ3322-2-22-2-22-2222-2-2-222i2i−2i−2i00002-200000000−2i2i00000000002i2i−2i−2i000000002-200000000000
χ3422-2-22-2-22-2222-2-2-222i2i−2i−2i00002-200000000−2i2i0000000000−2i−2i2i2i00000000-2200000000000
χ3522-2-22-2-22-2222-2-2-22−2i−2i2i2i00002-2000000002i−2i00000000002i2i−2i−2i00000000-2200000000000
χ3622-2-22-2-22-2222-2-2-22−2i−2i2i2i00002-2000000002i−2i0000000000−2i−2i2i2i000000002-200000000000
χ3722-2-2-222-202-202-2002i−2i2i−2i0000002i2i−2i−2ii2i2−i2−i200002-20000i2−i200002−22−222−2−20000000000i2−i20
χ3822-2-2-222-202-202-2002i−2i2i−2i0000002i2i−2i−2i−i2−i2i2i200002-20000−i2i20000−22−22−2−2220000000000−i2i20
χ3922-2-2-222-202-202-2002i−2i2i−2i000000−2i−2i2i2ii2i2−i2−i20000-220000i2−i200002−22−2−2−2220000000000−i2i20
χ4022-2-2-222-202-202-2002i−2i2i−2i000000−2i−2i2i2i−i2−i2i2i20000-220000−i2i20000−22−2222−2−20000000000i2−i20
χ4122-2-2-222-202-202-200−2i2i−2i2i0000002i2i−2i−2ii2i2−i2−i20000-220000i2−i20000−22−2222−2−20000000000−i2i20
χ4222-2-2-222-202-202-200−2i2i−2i2i0000002i2i−2i−2i−i2−i2i2i20000-220000−i2i200002−22−2−2−2220000000000i2−i20
χ4322-2-2-222-202-202-200−2i2i−2i2i000000−2i−2i2i2ii2i2−i2−i200002-20000i2−i20000−22−22−2−2220000000000i2−i20
χ4422-2-2-222-202-202-200−2i2i−2i2i000000−2i−2i2i2i−i2−i2i2i200002-20000−i2i200002−22−222−2−20000000000−i2i20
χ452-22-22-22-2-2002002-200002-22-200i2−i2i2−i22i−2i2i−2i0000002i−2ii2−i200i2−i2i2−i200002−22−2000000002−2000
χ462-22-22-22-2-2002002-200002-22-200i2−i2i2−i2−2i2i−2i2i000000−2i2ii2−i200i2−i2i2−i20000−22−2200000000−22000
χ472-22-22-22-2-2002002-200002-22-200−i2i2−i2i22i−2i2i−2i0000002i−2i−i2i200−i2i2−i2i20000−22−2200000000−22000
χ482-22-22-22-2-2002002-200002-22-200−i2i2−i2i2−2i2i−2i2i000000−2i2i−i2i200−i2i2−i2i200002−22−2000000002−2000
χ492-22-22-22-2-2002002-20000-22-2200i2−i2i2−i22i−2i2i−2i000000−2i2ii2−i200−i2i2−i2i200002−22−200000000−22000
χ502-22-22-22-2-2002002-20000-22-2200i2−i2i2−i2−2i2i−2i2i0000002i−2ii2−i200−i2i2−i2i20000−22−22000000002−2000
χ512-22-22-22-2-2002002-20000-22-2200−i2i2−i2i22i−2i2i−2i000000−2i2i−i2i200i2−i2i2−i20000−22−22000000002−2000
χ522-22-22-22-2-2002002-20000-22-2200−i2i2−i2i2−2i2i−2i2i0000002i−2i−i2i200i2−i2i2−i200002−22−200000000−22000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ544444-4-4-4-404-40-44004-4-44000000000000000000000000000000000000000000000000000
χ554444-4-4-4-404-40-4400-444-4000000000000000000000000000000000000000000000000000
χ564444-4-4-4-40-4404-400000000000000000000000000000000000022−22−222200000000000000000
χ574444-4-4-4-40-4404-4000000000000000000000000000000000000−222222−2200000000000000000
χ5844-4-44-4-44-4-4-4444-4400000000-44000000000000000000000000000000000000000000000
χ5944-4-4-444-40-440-4400000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ6044-4-4-444-40-440-440000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ614-44-44-44-4400-400-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ624-44-44-44-4400-400-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ634-4-4444-4-4400400-4-400000000000000000000000000000022−22−2222000000000000000000000
χ644-4-4444-4-4400400-4-4000000000000000000000000000000−222222−22000000000000000000000
χ654-4-4444-4-4-400-4004400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ664-4-4444-4-4-400-400440000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ674-4-44-4-44400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-44-4-44400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-44-4-444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-44-4-444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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