Finite Group Databasebeta

← Group #306342

Character table — Group #306342

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-111-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111111-1-11-1-1-1-1-1-11
χ17222222222-22-22-22-200002222-2-2000022220022-2-200000000-2-20000000000000-20000000
χ18222222222-22-22-22-200002222-2-20000-2-2-2-200-2-2-2-20000000022000000000000020000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20000222200-2-22200000000-2-2000000000000020000000
χ20222222222-22-22-22-20000-2-2-2-2-2-20000-2-2-2-200222200000000220000000000000-20000000
χ2122222222-22-22-22-2222220000-2-222220000220000-2-20000-2-20000000000-2000000000000
χ2222222222-22-22-22-2222220000-2-2-2-2-2-20000-2-20000-2-200002200000000002000000000000
χ2322222222-22-22-22-22-2-2-2-20000-2-222220000-2-20000220000-2-200000000002000000000000
χ2422222222-22-22-22-22-2-2-2-20000-2-2-2-2-2-20000220000220000220000000000-2000000000000
χ252-222-2-2-222-2-222-2-2222-2-20000-22000000000000002-22i2i−2i−2i0000000000000002i−2i00000000
χ262-222-2-2-222-2-222-2-2222-2-20000-22000000000000002-2−2i−2i2i2i000000000000000−2i2i00000000
χ272-222-2-2-222-2-222-2-22-2-2220000-2200000000000000-222i2i−2i−2i000000000000000−2i2i00000000
χ282-222-2-2-222-2-222-2-22-2-2220000-2200000000000000-22−2i−2i2i2i0000000000000002i−2i00000000
χ292-222-2-2-22-222-2-222-200002i2i−2i−2i-220000000000002i−2i000000000022-2-200000000002i−2i00000
χ302-222-2-2-22-222-2-222-200002i2i−2i−2i-220000000000002i−2i0000000000-2-2220000000000−2i2i00000
χ312-222-2-2-22-222-2-222-20000−2i−2i2i2i-22000000000000−2i2i000000000022-2-20000000000−2i2i00000
χ322-222-2-2-22-222-2-222-20000−2i−2i2i2i-22000000000000−2i2i0000000000-2-22200000000002i−2i00000
χ332-222-2-2-22-2-222-2-22222-2-22i2i−2i−2i2-2000000000000−2i2i-22000000000000000002i−2i0000000000
χ342-222-2-2-22-2-222-2-22222-2-2−2i−2i2i2i2-20000000000002i−2i-2200000000000000000−2i2i0000000000
χ352-222-2-2-22-2-222-2-222-2-2222i2i−2i−2i2-2000000000000−2i2i2-200000000000000000−2i2i0000000000
χ362-222-2-2-22-2-222-2-222-2-222−2i−2i2i2i2-20000000000002i−2i2-2000000000000000002i−2i0000000000
χ372-22-222-2-20-202020-22-22-200000022-2-2i2i2−i2−i22-2000000000000i2−i2i2−i2i2−i2i2i2−i2−i200000000i2−i2000
χ382-22-222-2-20-202020-22-22-200000022-2-2−i2−i2i2i22-2000000000000−i2i2−i2i2−i2i2−i2−i2i2i200000000−i2i2000
χ392-22-222-2-20-202020-22-22-2000000-2-222i2i2−i2−i2-22000000000000i2−i2i2−i2i2−i2−i2−i2i2i200000000−i2i2000
χ402-22-222-2-20-202020-22-22-2000000-2-222−i2−i2i2i2-22000000000000−i2i2−i2i2−i2i2i2i2−i2−i200000000i2−i2000
χ412-22-222-2-20-202020-2-22-2200000022-2-2i2i2−i2−i2-22000000000000i2−i2−i2i2−i2i2i2i2−i2−i200000000−i2i2000
χ422-22-222-2-20-202020-2-22-2200000022-2-2−i2−i2i2i2-22000000000000−i2i2i2−i2i2−i2−i2−i2i2i200000000i2−i2000
χ432-22-222-2-20-202020-2-22-22000000-2-222i2i2−i2−i22-2000000000000i2−i2−i2i2−i2i2−i2−i2i2i200000000i2−i2000
χ442-22-222-2-20-202020-2-22-22000000-2-222−i2−i2i2i22-2000000000000−i2i2i2−i2i2−i2i2i2−i2−i200000000−i2i2000
χ452-2-222-22-220-20-202000002-22-200i2−i2i2−i22i−2i2i−2i002i−2i0000i2−i2i2−i2i2−i20000002−22−200000000002−20
χ462-2-222-22-220-20-202000002-22-200i2−i2i2−i2−2i2i−2i2i00−2i2i0000i2−i2i2−i2i2−i2000000−22−220000000000−220
χ472-2-222-22-220-20-202000002-22-200−i2i2−i2i22i−2i2i−2i002i−2i0000−i2i2−i2i2−i2i2000000−22−220000000000−220
χ482-2-222-22-220-20-202000002-22-200−i2i2−i2i2−2i2i−2i2i00−2i2i0000−i2i2−i2i2−i2i20000002−22−200000000002−20
χ492-2-222-22-220-20-20200000-22-2200i2−i2i2−i22i−2i2i−2i00−2i2i0000−i2i2−i2i2i2−i20000002−22−20000000000−220
χ502-2-222-22-220-20-20200000-22-2200i2−i2i2−i2−2i2i−2i2i002i−2i0000−i2i2−i2i2i2−i2000000−22−2200000000002−20
χ512-2-222-22-220-20-20200000-22-2200−i2i2−i2i22i−2i2i−2i00−2i2i0000i2−i2i2−i2−i2i2000000−22−2200000000002−20
χ522-2-222-22-220-20-20200000-22-2200−i2i2−i2i2−2i2i−2i2i002i−2i0000i2−i2i2−i2−i2i20000002−22−20000000000−220
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-404040-40-44-4-44000000000000000000000000000000000000000000000000000
χ55444-4-4-44-404040-40-4-444-4000000000000000000000000000000000000000000000000000
χ56444-4-4-44-40-40-4040400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ57444-4-4-44-40-40-404040000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5844-44-44-4-44040-40-400000000000000000000000000022−22−22220000000000000000000000000
χ5944-44-44-4-44040-40-4000000000000000000000000000−222222−220000000000000000000000000
χ6044-44-44-4-4-40-40404000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ6144-44-44-4-4-40-4040400000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6244-4-44-4-440000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ6344-4-44-4-440000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ6444-4-44-4-44000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ6544-4-44-4-44000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ664-444-4-4-4444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ674-44-444-4-4040-40-404000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ684-44-444-4-4040-40-40400000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ694-4-444-44-4-404040-4000000000002i2−2i22i2−2i20000000000000000−2i22i200000000000000000000000
χ704-4-444-44-4-404040-400000000000−2i22i2−2i22i200000000000000002i2−2i200000000000000000000000
χ718-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000

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