Finite Group Databasebeta

← Group #309488

Character table — Group #309488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-111-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-11-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-11-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11-111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1111-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11
χ17222222222-2-222-2-220000-22222-2000022220022-2-20000-2-20000000000000000000-200000
χ18222222222-2-222-2-220000-22222-20000-2-2-2-200-2-2-2-20000220000000000000000000200000
χ19222222222-2-222-2-220000-2-2-2-2-2-20000222200-2-2220000-2-20000000000000000000200000
χ20222222222-2-222-2-220000-2-2-2-2-2-20000-2-2-2-20022220000220000000000000000000-200000
χ2122222222-222-2-222-22222-20000-222220000220000-2-2-2-200000000000000000000-2000000
χ2222222222-222-2-222-22222-20000-2-2-2-2-20000-2-20000-2-222000000000000000000002000000
χ2322222222-222-2-222-2-2-2-2-2-20000-222220000-2-2000022-2-2000000000000000000002000000
χ2422222222-222-2-222-2-2-2-2-2-20000-2-2-2-2-20000220000222200000000000000000000-2000000
χ2522-22-2-2-22222-2-2-2-220000-22i2i−2i−2i20000000000002i−2i000000000022-2-200002i−2i00000000000
χ2622-22-2-2-22222-2-2-2-220000-22i2i−2i−2i20000000000002i−2i0000000000-2-2220000−2i2i00000000000
χ2722-22-2-2-22222-2-2-2-220000-2−2i−2i2i2i2000000000000−2i2i000000000022-2-20000−2i2i00000000000
χ2822-22-2-2-22222-2-2-2-220000-2−2i−2i2i2i2000000000000−2i2i0000000000-2-22200002i−2i00000000000
χ2922-22-2-2-222-2-2-2-22222i2i−2i−2i22i2i−2i−2i-2000000000000−2i2i2i−2i000000000000000000002-20000000
χ3022-22-2-2-222-2-2-2-22222i2i−2i−2i2−2i−2i2i2i-20000000000002i−2i2i−2i00000000000000000000-220000000
χ3122-22-2-2-222-2-2-2-2222−2i−2i2i2i22i2i−2i−2i-2000000000000−2i2i−2i2i00000000000000000000-220000000
χ3222-22-2-2-222-2-2-2-2222−2i−2i2i2i2−2i−2i2i2i-20000000000002i−2i−2i2i000000000000000000002-20000000
χ3322-22-2-2-22-2-2-22222-22i2i−2i−2i-20000200000000000000−2i2i000022-2-200000000002i−2i000000000
χ3422-22-2-2-22-2-2-22222-22i2i−2i−2i-20000200000000000000−2i2i0000-2-2220000000000−2i2i000000000
χ3522-22-2-2-22-2-2-22222-2−2i−2i2i2i-200002000000000000002i−2i000022-2-20000000000−2i2i000000000
χ3622-22-2-2-22-2-2-22222-2−2i−2i2i2i-200002000000000000002i−2i0000-2-22200000000002i−2i000000000
χ3722-2-2-222-202-2002-202i−2i2i−2i0000002i2i−2i−2ii2i2−i2−i22-200000000i2−i200002−22−222−2−20000000000i2−i20
χ3822-2-2-222-202-2002-202i−2i2i−2i0000002i2i−2i−2i−i2−i2i2i22-200000000−i2i20000−22−22−2−2220000000000−i2i20
χ3922-2-2-222-202-2002-202i−2i2i−2i000000−2i−2i2i2ii2i2−i2−i2-2200000000i2−i200002−22−2−2−2220000000000−i2i20
χ4022-2-2-222-202-2002-202i−2i2i−2i000000−2i−2i2i2i−i2−i2i2i2-2200000000−i2i20000−22−2222−2−20000000000i2−i20
χ4122-2-2-222-202-2002-20−2i2i−2i2i0000002i2i−2i−2ii2i2−i2−i2-2200000000i2−i20000−22−2222−2−20000000000−i2i20
χ4222-2-2-222-202-2002-20−2i2i−2i2i0000002i2i−2i−2i−i2−i2i2i2-2200000000−i2i200002−22−2−2−2220000000000i2−i20
χ4322-2-2-222-202-2002-20−2i2i−2i2i000000−2i−2i2i2ii2i2−i2−i22-200000000i2−i20000−22−22−2−2220000000000i2−i20
χ4422-2-2-222-202-2002-20−2i2i−2i2i000000−2i−2i2i2i−i2−i2i2i22-200000000−i2i200002−22−222−2−20000000000−i2i20
χ452-22-2-2-2222002-200-2000002-22-202−22−22i−2i2i−2i002i−2i00002−2002−22−20000i2−i2i2−i200000000i2−i2000
χ462-22-2-2-2222002-200-2000002-22-202−22−2−2i2i−2i2i00−2i2i00002−2002−22−20000−i2i2−i2i200000000−i2i2000
χ472-22-2-2-2222002-200-2000002-22-20−22−222i−2i2i−2i002i−2i0000−2200−22−220000−i2i2−i2i200000000−i2i2000
χ482-22-2-2-2222002-200-2000002-22-20−22−22−2i2i−2i2i00−2i2i0000−2200−22−220000i2−i2i2−i200000000i2−i2000
χ492-22-2-2-2222002-200-200000-22-2202−22−22i−2i2i−2i00−2i2i00002−200−22−220000i2−i2i2−i200000000−i2i2000
χ502-22-2-2-2222002-200-200000-22-2202−22−2−2i2i−2i2i002i−2i00002−200−22−220000−i2i2−i2i200000000i2−i2000
χ512-22-2-2-2222002-200-200000-22-220−22−222i−2i2i−2i00−2i2i0000−22002−22−20000−i2i2−i2i200000000i2−i2000
χ522-22-2-2-2222002-200-200000-22-220−22−22−2i2i−2i2i002i−2i0000−22002−22−20000i2−i2i2−i200000000−i2i2000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-404-400-440000000000000000000000000000000000022−22−222200000000000000000
χ55444-44-4-4-404-400-4400000000000000000000000000000000000−222222−2200000000000000000
χ56444-44-4-4-40-44004-404-4-44000000000000000000000000000000000000000000000000000
χ57444-44-4-4-40-44004-40-444-4000000000000000000000000000000000000000000000000000
χ5844-44-4-4-44-44444-4-4-4000040000-4000000000000000000000000000000000000000000000
χ5944-4-4-444-40-4400-440000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ6044-4-4-444-40-4400-44000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ614-44-4-4-444-400-44004000000000022−2222−22000000000000−2222000000000000000000000000000
χ624-44-4-4-444-400-440040000000000−2222−222200000000000022−22000000000000000000000000000
χ634-4-444-44-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ644-4-444-44-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ654-4-444-44-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ664-4-444-44-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ674-4-4-444-44400-4400-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ684-4-4-444-44400-4400-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ694-4-4-444-44-4004-400400000000000000000000000000000022−22−2222000000000000000000000
χ704-4-4-444-44-4004-4004000000000000000000000000000000−222222−22000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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