Finite Group Databasebeta

← Group #309529

Character table — Group #309529

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ511111111111111111111-1-1-1-11111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-111-1-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-111-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-222-2-22-200002222-2-222220000220000-2-2-2-200000000000000-2000000000000
χ18222222222-222-2-22-200002222-2-2-2-2-2-20000-2-20000-2-222000000000000002000000000000
χ19222222222-222-2-22-20000-2-2-2-2-2-222220000-2-2000022-2-2000000000000002000000000000
χ20222222222-222-2-22-20000-2-2-2-2-2-2-2-2-2-20000220000222200000000000000-2000000000000
χ2122222222-22-2-222-2222220000-2-2000022220022-2-20000-2-200000000000000000-20000000
χ2222222222-22-2-222-2222220000-2-20000-2-2-2-200-2-2-2-20000220000000000000000020000000
χ2322222222-22-2-222-22-2-2-2-20000-2-20000222200-2-2220000-2-20000000000000000020000000
χ2422222222-22-2-222-22-2-2-2-20000-2-20000-2-2-2-200222200002200000000000000000-20000000
χ2522-22-22-2-2-202-20020000022-2-2002i2i−2i−2i22−2−22i−2i000000002−2000022−2−2i2i2−i2−i20000000000i2−i20
χ2622-22-22-2-2-202-20020000022-2-2002i2i−2i−2i−2−2222i−2i00000000−220000−2−222−i2−i2i2i20000000000−i2i20
χ2722-22-22-2-2-202-20020000022-2-200−2i−2i2i2i22−2−2−2i2i000000002−2000022−2−2−i2−i2i2i20000000000−i2i20
χ2822-22-22-2-2-202-20020000022-2-200−2i−2i2i2i−2−222−2i2i00000000−220000−2−222i2i2−i2−i20000000000i2−i20
χ2922-22-22-2-2-202-200200000-2-222002i2i−2i−2i22−2−2−2i2i000000002−20000−2−222i2i2−i2−i20000000000−i2i20
χ3022-22-22-2-2-202-200200000-2-222002i2i−2i−2i−2−222−2i2i00000000−22000022−2−2−i2−i2i2i20000000000i2−i20
χ3122-22-22-2-2-202-200200000-2-22200−2i−2i2i2i22−2−22i−2i000000002−20000−2−222−i2−i2i2i20000000000i2−i20
χ3222-22-22-2-2-202-200200000-2-22200−2i−2i2i2i−2−2222i−2i00000000−22000022−2−2i2i2−i2−i20000000000−i2i20
χ3322-2-22-22-222-2-2-2-2222i2i−2i−2i2i−2i2i−2i2-20000000000002i−2i2i−2i00000000000000000002-200000000
χ3422-2-22-22-222-2-2-2-2222i2i−2i−2i−2i2i−2i2i2-20000000000002i−2i−2i2i0000000000000000000-2200000000
χ3522-2-22-22-222-2-2-2-222−2i−2i2i2i2i−2i2i−2i2-2000000000000−2i2i2i−2i0000000000000000000-2200000000
χ3622-2-22-22-222-2-2-2-222−2i−2i2i2i−2i2i−2i2i2-2000000000000−2i2i−2i2i00000000000000000002-200000000
χ3722-2-22-22-22-2-2-2222-200002i−2i2i−2i-2200000000000000−2i2i000022-2-20000000002i−2i0000000000
χ3822-2-22-22-22-2-2-2222-200002i−2i2i−2i-2200000000000000−2i2i0000-2-222000000000−2i2i0000000000
χ3922-2-22-22-22-2-2-2222-20000−2i2i−2i2i-22000000000000002i−2i000022-2-2000000000−2i2i0000000000
χ4022-2-22-22-22-2-2-2222-20000−2i2i−2i2i-22000000000000002i−2i0000-2-2220000000002i−2i0000000000
χ4122-2-22-22-2-2222-2-2-222i2i−2i−2i0000-22000000000000−2i2i00000000002-22-200000000002i−2i00000
χ4222-2-22-22-2-2222-2-2-222i2i−2i−2i0000-22000000000000−2i2i0000000000-22-220000000000−2i2i00000
χ4322-2-22-22-2-2222-2-2-22−2i−2i2i2i0000-220000000000002i−2i00000000002-22-20000000000−2i2i00000
χ4422-2-22-22-2-2222-2-2-22−2i−2i2i2i0000-220000000000002i−2i0000000000-22-2200000000002i−2i00000
χ452-2-2-222-2202002-20-22i−2i2i−2i0000002−22−22i−2i2i−2i002-200002−200i2−i2i2−i20000i2−i2i2−i2000000002−2000
χ462-2-2-222-2202002-20-22i−2i2i−2i0000002−22−2−2i2i−2i2i00-2200002−200i2−i2i2−i20000−i2i2−i2i200000000−22000
χ472-2-2-222-2202002-20-22i−2i2i−2i000000−22−222i−2i2i−2i002-20000−2200−i2i2−i2i20000−i2i2−i2i200000000−22000
χ482-2-2-222-2202002-20-22i−2i2i−2i000000−22−22−2i2i−2i2i00-220000−2200−i2i2−i2i20000i2−i2i2−i2000000002−2000
χ492-2-2-222-2202002-20-2−2i2i−2i2i0000002−22−22i−2i2i−2i00-2200002−200−i2i2−i2i20000i2−i2i2−i200000000−22000
χ502-2-2-222-2202002-20-2−2i2i−2i2i0000002−22−2−2i2i−2i2i002-200002−200−i2i2−i2i20000−i2i2−i2i2000000002−2000
χ512-2-2-222-2202002-20-2−2i2i−2i2i000000−22−222i−2i2i−2i00-220000−2200i2−i2i2−i20000−i2i2−i2i2000000002−2000
χ522-2-2-222-2202002-20-2−2i2i−2i2i000000−22−22−2i2i−2i2i002-20000−2200i2−i2i2−i20000i2−i2i2−i200000000−22000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-44404-400-40000000000000000000000000000000000022−22−222200000000000000000
χ55444-4-4-4-44404-400-400000000000000000000000000000000000−222222−2200000000000000000
χ56444-4-4-4-44-40-44004000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ57444-4-4-4-44-40-4400400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ5844-44-44-4-440-4400-40000000000000002222−22−220000000000−22220000000000000000000000000
χ5944-44-44-4-440-4400-4000000000000000−22−222222000000000022−220000000000000000000000000
χ6044-4-44-44-4-4-44444-4-4000000004-4000000000000000000000000000000000000000000000
χ614-4444-4-4-40400-440-44-4-44000000000000000000000000000000000000000000000000000
χ624-4444-4-4-40400-440-4-444-4000000000000000000000000000000000000000000000000000
χ634-4444-4-4-40-4004-4040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ644-4444-4-4-40-4004-404000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ654-44-4-444-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ664-44-4-444-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ674-44-4-444-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ684-44-4-444-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ694-4-4-444-440-400-4404000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-444-440-400-44040000000000−2222−222200000000000022−22000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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