Finite Group Databasebeta

← Group #312113

Character table — Group #312113

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111111111-1-1-1-1111111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111111-1-111-1-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111-11111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-111-111-1-111111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-11111-1-1111-1-11-1-1-1-11
χ17222222222-22-22-22-22222-20000-200002222-2-2000022-2-20000000000000000-20000000000
χ18222222222-22-22-22-22222-20000-20000-2-2-2-2-2-20000-2-222000000000000000020000000000
χ19222222222-22-22-22-2-2-2-2-2-20000-200002222220000-2-2-2-2000000000000000020000000000
χ20222222222-22-22-22-2-2-2-2-2-20000-20000-2-2-2-222000022220000000000000000-20000000000
χ2122222222-22-22-22-220000-22222-22222000000-2-222000000000000-2-200000000000-200000
χ2222222222-22-22-22-220000-22222-2-2-2-2-2000000-2-2-2-20000000000002200000000000200000
χ2322222222-22-22-22-220000-2-2-2-2-2-2222200000022-2-2000000000000-2-200000000000200000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-2-2-200000022220000000000002200000000000-200000
χ2522-2-222-2-22-2-222-2-220000-22i2i−2i−2i200000000002i−2i0000002i2i−2i−2i0000000000000002-2000000
χ2622-2-222-2-22-2-222-2-220000-22i2i−2i−2i200000000002i−2i000000−2i−2i2i2i000000000000000-22000000
χ2722-2-222-2-22-2-222-2-220000-2−2i−2i2i2i20000000000−2i2i0000002i2i−2i−2i000000000000000-22000000
χ2822-2-222-2-22-2-222-2-220000-2−2i−2i2i2i20000000000−2i2i000000−2i−2i2i2i0000000000000002-2000000
χ2922-2-222-2-2-222-2-222-22i2i−2i−2i-200002000000002i−2i0000000000002i2i−2i−2i0000002-200000000000
χ3022-2-222-2-2-222-2-222-22i2i−2i−2i-200002000000002i−2i000000000000−2i−2i2i2i000000-2200000000000
χ3122-2-222-2-2-222-2-222-2−2i−2i2i2i-20000200000000−2i2i0000000000002i2i−2i−2i000000-2200000000000
χ3222-2-222-2-2-222-2-222-2−2i−2i2i2i-20000200000000−2i2i000000000000−2i−2i2i2i0000002-200000000000
χ3322-2-222-2-2-2-222-2-2222i2i−2i−2i22i2i−2i−2i-200000000−2i2i−2i2i000000000000000000000002-200000000
χ3422-2-222-2-2-2-222-2-2222i2i−2i−2i2−2i−2i2i2i-200000000−2i2i2i−2i00000000000000000000000-2200000000
χ3522-2-222-2-2-2-222-2-222−2i−2i2i2i22i2i−2i−2i-2000000002i−2i−2i2i00000000000000000000000-2200000000
χ3622-2-222-2-2-2-222-2-222−2i−2i2i2i2−2i−2i2i2i-2000000002i−2i2i−2i000000000000000000000002-200000000
χ3722-2-2-2-2222020-20-202i−2i2i−2i00000022−2−22i2i−2i−2i0000002-200i2−i2i2−i200002−2i2i2−i2−i2000000002−2000
χ3822-2-2-2-2222020-20-202i−2i2i−2i00000022−2−2−2i−2i2i2i000000-2200i2−i2i2−i200002−2−i2−i2i2i200000000−22000
χ3922-2-2-2-2222020-20-202i−2i2i−2i000000−2−2222i2i−2i−2i0000002-200−i2i2−i2i20000−22−i2−i2i2i200000000−22000
χ4022-2-2-2-2222020-20-202i−2i2i−2i000000−2−222−2i−2i2i2i000000-2200−i2i2−i2i20000−22i2i2−i2−i2000000002−2000
χ4122-2-2-2-2222020-20-20−2i2i−2i2i00000022−2−22i2i−2i−2i000000-2200−i2i2−i2i200002−2i2i2−i2−i200000000−22000
χ4222-2-2-2-2222020-20-20−2i2i−2i2i00000022−2−2−2i−2i2i2i0000002-200−i2i2−i2i200002−2−i2−i2i2i2000000002−2000
χ4322-2-2-2-2222020-20-20−2i2i−2i2i000000−2−2222i2i−2i−2i000000-2200i2−i2i2−i20000−22−i2−i2i2i2000000002−2000
χ4422-2-2-2-2222020-20-20−2i2i−2i2i000000−2−222−2i−2i2i2i0000002-200i2−i2i2−i20000−22i2i2−i2−i200000000−22000
χ452-22-22-22-2020-20-202000002i−2i2i−2i02i−2i2i−2ii2−i2i2−i200002-200i2−i200002−22−2002−22−20000000000i2−i20
χ462-22-22-22-2020-20-202000002i−2i2i−2i02i−2i2i−2i−i2i2−i2i200002-200−i2i20000−22−2200−22−220000000000−i2i20
χ472-22-22-22-2020-20-202000002i−2i2i−2i0−2i2i−2i2ii2−i2i2−i20000-2200i2−i200002−22−200−22−220000000000−i2i20
χ482-22-22-22-2020-20-202000002i−2i2i−2i0−2i2i−2i2i−i2i2−i2i20000-2200−i2i20000−22−22002−22−20000000000i2−i20
χ492-22-22-22-2020-20-20200000−2i2i−2i2i02i−2i2i−2ii2−i2i2−i20000-2200i2−i20000−22−22002−22−20000000000−i2i20
χ502-22-22-22-2020-20-20200000−2i2i−2i2i02i−2i2i−2i−i2i2−i2i20000-2200−i2i200002−22−200−22−220000000000i2−i20
χ512-22-22-22-2020-20-20200000−2i2i−2i2i0−2i2i−2i2ii2−i2i2−i200002-200i2−i20000−22−2200−22−220000000000i2−i20
χ522-22-22-22-2020-20-20200000−2i2i−2i2i0−2i2i−2i2i−i2i2−i2i200002-200−i2i200002−22−2002−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-440-40-4040000000000000000000000000000022−22−222200000000000000000000000
χ554444-4-4-4-440-40-40400000000000000000000000000000−222222−2200000000000000000000000
χ564444-4-4-4-4-404040-404-4-44000000000000000000000000000000000000000000000000000
χ574444-4-4-4-4-404040-40-444-4000000000000000000000000000000000000000000000000000
χ5844-4-444-4-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ5944-4-4-4-444-40-40404000000000002222−22−220000000000000000000000−222200000000000000000
χ6044-4-4-4-444-40-4040400000000000−22−222222000000000000000000000022−2200000000000000000
χ614-44-44-44-40-404040-4000000000000002i2−2i22i2−2i200000000−2i22i2000000000000000000000000000
χ624-44-44-44-40-404040-400000000000000−2i22i2−2i22i2000000002i2−2i2000000000000000000000000000
χ634-4-444-4-4404040-40-4000000000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ644-4-444-4-4404040-40-400000000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ654-4-444-4-440-40-40404000004-4-440000000000000000000000000000000000000000000000
χ664-4-444-4-440-40-4040400000-444-40000000000000000000000000000000000000000000000
χ674-4-44-444-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ684-4-44-444-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ694-4-44-444-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ704-4-44-444-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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