Finite Group Databasebeta

← Group #306550

Character table — Group #306550

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-11-1-1-1-111-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111111-1-1-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1111111111111-1-11-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-11111-1-11111-1-1-1-1-1-11
χ17222222222-22-22-22-22222-20000-222220000220000-2-20000-2-2000000000000000-20000000
χ18222222222-22-22-22-22222-20000-2-2-2-2-20000-2-20000-2-200002200000000000000020000000
χ19222222222-22-22-22-2-2-2-2-2-20000-222220000-2-20000220000-2-200000000000000020000000
χ20222222222-22-22-22-2-2-2-2-2-20000-2-2-2-2-2000022000022000022000000000000000-20000000
χ2122222222-22-22-22-220000-22222-20000222200-2-222000000000000-2-2000000-20000000000
χ2222222222-22-22-22-220000-22222-20000-2-2-2-200-2-2-2-20000000000002200000020000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-2000022220022-2-2000000000000-2-200000020000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-200222200000000000022000000-20000000000
χ2522-22-22-2-20-20-202020000022-2-2022−2−22i2i−2i−2i00002i−2i0000002−222−2−200i2i2−i2−i200000000i2−i2000
χ2622-22-22-2-20-20-202020000022-2-2022−2−2−2i−2i2i2i0000−2i2i0000002−222−2−200−i2−i2i2i200000000−i2i2000
χ2722-22-22-2-20-20-202020000022-2-20−2−2222i2i−2i−2i00002i−2i000000−22−2−22200−i2−i2i2i200000000−i2i2000
χ2822-22-22-2-20-20-202020000022-2-20−2−222−2i−2i2i2i0000−2i2i000000−22−2−22200i2i2−i2−i200000000i2−i2000
χ2922-22-22-2-20-20-2020200000-2-222022−2−22i2i−2i−2i0000−2i2i0000002−2−2−22200i2i2−i2−i200000000−i2i2000
χ3022-22-22-2-20-20-2020200000-2-222022−2−2−2i−2i2i2i00002i−2i0000002−2−2−22200−i2−i2i2i200000000i2−i2000
χ3122-22-22-2-20-20-2020200000-2-2220−2−2222i2i−2i−2i0000−2i2i000000−2222−2−200−i2−i2i2i200000000i2−i2000
χ3222-22-22-2-20-20-2020200000-2-2220−2−222−2i−2i2i2i00002i−2i000000−2222−2−200i2i2−i2−i200000000−i2i2000
χ332-222-2-2-222020-20-202i2i−2i−2i0000002-22-22−22−22i−2i000000i2i2−i2−i20000002−22−22−20000000000i2−i20
χ342-222-2-2-222020-20-202i2i−2i−2i0000002-22-2−22−222i−2i000000−i2−i2i2i2000000−22−22−220000000000−i2i20
χ352-222-2-2-222020-20-202i2i−2i−2i000000-22-222−22−2−2i2i000000i2i2−i2−i20000002−2−22−220000000000−i2i20
χ362-222-2-2-222020-20-202i2i−2i−2i000000-22-22−22−22−2i2i000000−i2−i2i2i2000000−222−22−20000000000i2−i20
χ372-222-2-2-222020-20-20−2i−2i2i2i0000002-22-22−22−2−2i2i000000−i2−i2i2i20000002−22−22−20000000000−i2i20
χ382-222-2-2-222020-20-20−2i−2i2i2i0000002-22-2−22−22−2i2i000000i2i2−i2−i2000000−22−22−220000000000i2−i20
χ392-222-2-2-222020-20-20−2i−2i2i2i000000-22-222−22−22i−2i000000−i2−i2i2i20000002−2−22−220000000000i2−i20
χ402-222-2-2-222020-20-20−2i−2i2i2i000000-22-22−22−222i−2i000000i2i2−i2−i2000000−222−22−20000000000−i2i20
χ412-22-2-222-22-2-222-2-220000-22-22-2200000000002-200002i−2i2i−2i0000000000002i−2i00000000000
χ422-22-2-222-22-2-222-2-220000-22-22-2200000000002-20000−2i2i−2i2i000000000000−2i2i00000000000
χ432-22-2-222-22-2-222-2-220000-2-22-2220000000000-2200002i−2i2i−2i000000000000−2i2i00000000000
χ442-22-2-222-22-2-222-2-220000-2-22-2220000000000-220000−2i2i−2i2i0000000000002i−2i00000000000
χ452-22-2-222-2-222-2-222-22i−2i2i−2i-200002000000000000002i−2i0000002-22-20000000000002i−2i00000
χ462-22-2-222-2-222-2-222-22i−2i2i−2i-200002000000000000002i−2i000000-22-22000000000000−2i2i00000
χ472-22-2-222-2-222-2-222-2−2i2i−2i2i-20000200000000000000−2i2i0000002-22-2000000000000−2i2i00000
χ482-22-2-222-2-222-2-222-2−2i2i−2i2i-20000200000000000000−2i2i000000-22-220000000000002i−2i00000
χ492-22-2-222-2-2-222-2-2222i−2i2i−2i22-22-2-20000000000-2200−2i2i00000000000000000002i−2i00000000
χ502-22-2-222-2-2-222-2-2222i−2i2i−2i2-22-22-200000000002-200−2i2i0000000000000000000−2i2i00000000
χ512-22-2-222-2-2-222-2-222−2i2i−2i2i22-22-2-20000000000-22002i−2i0000000000000000000−2i2i00000000
χ522-22-2-222-2-2-222-2-222−2i2i−2i2i2-22-22-200000000002-2002i−2i00000000000000000002i−2i00000000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ54444-44-4-4-440-40-40400000000000000000000000000022−22−22220000000000000000000000000
χ55444-44-4-4-440-40-404000000000000000000000000000−222222−220000000000000000000000000
χ56444-44-4-4-4-404040-404-4-44000000000000000000000000000000000000000000000000000
χ57444-44-4-4-4-404040-40-444-4000000000000000000000000000000000000000000000000000
χ5844-44-44-4-404040-40-400000000002222−22−220000000000000000−222200000000000000000000000
χ5944-44-44-4-404040-40-40000000000−22−222222000000000000000022−2200000000000000000000000
χ604-444-4-4-44-40-4040400000000000000022−2222−22000000000000000000−222200000000000000000
χ614-444-4-4-44-40-40404000000000000000−2222−222200000000000000000022−2200000000000000000
χ624-44-4-444-444-4-444-4-4000040000-4000000000000000000000000000000000000000000000
χ634-4-444-44-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ644-4-444-44-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ654-4-444-44-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ664-4-444-44-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ674-4-4-444-44040-40-404000004-4-440000000000000000000000000000000000000000000000
χ684-4-4-444-44040-40-40400000-444-40000000000000000000000000000000000000000000000
χ694-4-4-444-440-404040-40000000000000000000000000000000022−22−22220000000000000000000
χ704-4-4-444-440-404040-400000000000000000000000000000000−222222−220000000000000000000
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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