Finite Group Databasebeta

← Group #312901

Character table — Group #312901

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888222444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-11-1-1-1-111-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-111-1-11-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11111-1-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-111-1-111-11
χ91111111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-1-111111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1111-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111111-1-1-1-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-1-11
χ17222222222-22-22-22-20000-2-22222-2-2-2-20022-2-200000000000000000000002-200000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-2220000000000000000000000-2200000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222220022220000000000000000000000-2-200000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2222200-2-2-2-200000000000000000000002200000000
χ2122222222-22-22-22-222222-2-200000000-2-2000022-2-2220000-2-200000000000000000000
χ2222222222-22-22-22-222222-2-200000000-2-20000-2-222-2-200002200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000022000022-2-2-2-200002200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000220000-2-222220000-2-200000000000000000000
χ2522-2-2-22-2222-2-222-2-22i2i−2i−2i-222i2i−2i−2i2i2i−2i−2i2i−2i000000000022-2-20000000000000000000000
χ2622-2-2-22-2222-2-222-2-22i2i−2i−2i-22−2i−2i2i2i−2i−2i2i2i2i−2i0000000000-2-2220000000000000000000000
χ2722-2-2-22-2222-2-222-2-2−2i−2i2i2i-222i2i−2i−2i2i2i−2i−2i−2i2i0000000000-2-2220000000000000000000000
χ2822-2-2-22-2222-2-222-2-2−2i−2i2i2i-22−2i−2i2i2i−2i−2i2i2i−2i2i000000000022-2-20000000000000000000000
χ2922-2-2-22-222-2-222-2-2200002-22i2i−2i−2i−2i−2i2i2i000000000000000000000000002-2002i−2i000000
χ3022-2-2-22-222-2-222-2-2200002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000-2200−2i2i000000
χ3122-2-2-22-222-2-222-2-2200002-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000002-200−2i2i000000
χ3222-2-2-22-222-2-222-2-2200002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000-22002i−2i000000
χ3322-2-2-22-22-222-2-222-22i2i−2i−2i2-200000000−2i2i000000000000000022-2-22i2i−2i−2i000000000000
χ3422-2-2-22-22-222-2-222-22i2i−2i−2i2-200000000−2i2i0000000000000000-2-222−2i−2i2i2i000000000000
χ3522-2-2-22-22-222-2-222-2−2i−2i2i2i2-2000000002i−2i000000000000000022-2-2−2i−2i2i2i000000000000
χ3622-2-2-22-22-222-2-222-2−2i−2i2i2i2-2000000002i−2i0000000000000000-2-2222i2i−2i−2i000000000000
χ372-222-22-2-2020-20-2022i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20000002-2002i−2i2−22−200i2−i2i2−i22−22−2000000000000
χ382-222-22-2-2020-20-2022i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2000000-2200−2i2i2−22−200−i2i2−i2i2−22−22000000000000
χ392-222-22-2-2020-20-2022i−2i2i−2i00−i2i2−i2i2−i2i2−i2i20000002-2002i−2i−22−2200−i2i2−i2i2−22−22000000000000
χ402-222-22-2-2020-20-2022i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000000-2200−2i2i−22−2200i2−i2i2−i22−22−2000000000000
χ412-222-22-2-2020-20-202−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i20000002-200−2i2i−22−2200i2−i2i2−i2−22−22000000000000
χ422-222-22-2-2020-20-202−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000000-22002i−2i−22−2200−i2i2−i2i22−22−2000000000000
χ432-222-22-2-2020-20-202−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20000002-200−2i2i2−22−200−i2i2−i2i22−22−2000000000000
χ442-222-22-2-2020-20-202−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000000-22002i−2i2−22−200i2−i2i2−i2−22−22000000000000
χ452-2-2-2222-202020-20-22-2-22002−2−222−2−22000000002i−2i002−2−222i−2ii2−i2−i2i2−i2i2i2−i2000000000000
χ462-2-2-2222-202020-20-22-2-22002−2−222−2−2200000000−2i2i002−2−22−2i2i−i2i2i2−i2i2−i2−i2i2000000000000
χ472-2-2-2222-202020-20-22-2-2200−222−2−222−2000000002i−2i00−222−22i−2i−i2i2i2−i2i2−i2−i2i2000000000000
χ482-2-2-2222-202020-20-22-2-2200−222−2−222−200000000−2i2i00−222−2−2i2ii2−i2−i2i2−i2i2i2−i2000000000000
χ492-2-2-2222-202020-20-2-222-2002−2−222−2−22000000002i−2i00−222−2−2i2ii2−i2−i2i2i2−i2−i2i2000000000000
χ502-2-2-2222-202020-20-2-222-2002−2−222−2−2200000000−2i2i00−222−22i−2i−i2i2i2−i2−i2i2i2−i2000000000000
χ512-2-2-2222-202020-20-2-222-200−222−2−222−2000000002i−2i002−2−22−2i2i−i2i2i2−i2−i2i2i2−i2000000000000
χ522-2-2-2222-202020-20-2-222-200−222−2−222−200000000−2i2i002−2−222i−2ii2−i2−i2i2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-44040-40-4000000000000000004-40000000000000000000000000000000000
χ55444-44-4-4-44040-40-400000000000000000-440000000000000000000000000000000000
χ56444-44-4-4-4-40-4040400000000000000000000000000000000000000000000000002i2−2i200
χ57444-44-4-4-4-40-404040000000000000000000000000000000000000000000000000−2i22i200
χ5844-44-4-44-440-40-40400000000000000000004i−4i00000000000000000000000000000000
χ5944-44-4-44-440-40-4040000000000000000000−4i4i00000000000000000000000000000000
χ6044-44-4-44-4-404040-4000000000000000000000000000000000000000000000002i2−2i20000
χ6144-44-4-44-4-404040-400000000000000000000000000000000000000000000000−2i22i20000
χ6244-4-4-44-44-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ634-444-44-4-40-404040-40000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ644-444-44-4-40-404040-4000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4444-40-40-4040400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4444-40-40-40404000000−222222−2222−22−222200000000000000000000000000000000000000
χ678-88-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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