Finite Group Databasebeta

← Group #312876

Character table — Group #312876

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822444444448888888888888888244444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111111-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1111-1
χ91111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-1-1-1-111
χ101111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-1-111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-111-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-111-1-11-1-111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11-1-111-111-1-11-1
χ17222222222-22-22-22-20000-2-22222-2-2-2-200220022000000000000000000-20000-2000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-200-2-2000000000000000000200002000000
χ19222222222-22-22-22-20000-2-2-2-2-2-22222002200-2-200000000000000000020000-2000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2222200-2-20022000000000000000000-200002000000
χ2122222222-22-22-22-222222-2-2000000002200-2-200-2-2-2-200002200000000000000000000
χ2222222222-22-22-22-222222-2-200000000-2-2002200-2-2220000-2-200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002200-2-20022220000-2-200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-200000000-2-200220022-2-200002200000000000000000000
χ2522-2-22-22-2020-20-20222-2-200i2i2−i2−i2i2i2−i2−i200002i−2i00002i−2ii2i2−i2−i20022−2−222−2−2000000000000
χ2622-2-22-22-2020-20-20222-2-200i2i2−i2−i2i2i2−i2−i20000−2i2i0000−2i2ii2i2−i2−i200−2−222−2−222000000000000
χ2722-2-22-22-2020-20-20222-2-200−i2−i2i2i2−i2−i2i2i200002i−2i00002i−2i−i2−i2i2i200−2−222−2−222000000000000
χ2822-2-22-22-2020-20-20222-2-200−i2−i2i2i2−i2−i2i2i20000−2i2i0000−2i2i−i2−i2i2i20022−2−222−2−2000000000000
χ2922-2-22-22-2020-20-202-2-22200i2i2−i2−i2i2i2−i2−i200002i−2i0000−2i2i−i2−i2i2i20022−2−2−2−222000000000000
χ3022-2-22-22-2020-20-202-2-22200i2i2−i2−i2i2i2−i2−i20000−2i2i00002i−2i−i2−i2i2i200−2−22222−2−2000000000000
χ3122-2-22-22-2020-20-202-2-22200−i2−i2i2i2−i2−i2i2i200002i−2i0000−2i2ii2i2−i2−i200−2−22222−2−2000000000000
χ3222-2-22-22-2020-20-202-2-22200−i2−i2i2i2−i2−i2i2i20000−2i2i00002i−2ii2i2−i2−i20022−2−2−2−222000000000000
χ332-22-2-2-22202020-20-22i−2i2i−2i002−22−22−22−22-20000000000i2−i2i2−i22i−2i2−22−2i2−i2i2−i2000000000000
χ342-22-2-2-22202020-20-22i−2i2i−2i002−22−22−22−2-220000000000i2−i2i2−i2−2i2i−22−22−i2i2−i2i2000000000000
χ352-22-2-2-22202020-20-22i−2i2i−2i00−22−22−22−222-20000000000−i2i2−i2i22i−2i−22−22−i2i2−i2i2000000000000
χ362-22-2-2-22202020-20-22i−2i2i−2i00−22−22−22−22-220000000000−i2i2−i2i2−2i2i2−22−2i2−i2i2−i2000000000000
χ372-22-2-2-22202020-20-2−2i2i−2i2i002−22−22−22−22-20000000000−i2i2−i2i2−2i2i2−22−2−i2i2−i2i2000000000000
χ382-22-2-2-22202020-20-2−2i2i−2i2i002−22−22−22−2-220000000000−i2i2−i2i22i−2i−22−22i2−i2i2−i2000000000000
χ392-22-2-2-22202020-20-2−2i2i−2i2i00−22−22−22−222-20000000000i2−i2i2−i2−2i2i−22−22i2−i2i2−i2000000000000
χ402-22-2-2-22202020-20-2−2i2i−2i2i00−22−22−22−22-220000000000i2−i2i2−i22i−2i2−22−2−i2i2−i2i2000000000000
χ412-2-22-222-222-2-222-2-22i−2i−2i2i-222i−2i−2i2i2i−2i−2i2i000000002i−2i00-222-20000000000000000000000
χ422-2-22-222-222-2-222-2-22i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i000000002i−2i002-2-220000000000000000000000
χ432-2-22-222-222-2-222-2-2−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i00000000−2i2i002-2-220000000000000000000000
χ442-2-22-222-222-2-222-2-2−2i2i2i−2i-22−2i2i2i−2i−2i2i2i−2i00000000−2i2i00-222-20000000000000000000000
χ452-2-22-222-22-2-222-2-2200002-22i−2i−2i2i−2i2i2i−2i0000000000000000000000000002i−2i2-20000000
χ462-2-22-222-22-2-222-2-2200002-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000−2i2i-220000000
χ472-2-22-222-22-2-222-2-2200002-2−2i2i2i−2i2i−2i−2i2i0000000000000000000000000002i−2i-220000000
χ482-2-22-222-22-2-222-2-2200002-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000−2i2i2-20000000
χ492-2-22-222-2-222-2-222-22i−2i−2i2i2-20000000000000000−2i2i000000002-2-222i−2i−2i2i000000000000
χ502-2-22-222-2-222-2-222-22i−2i−2i2i2-20000000000000000−2i2i00000000-222-2−2i2i2i−2i000000000000
χ512-2-22-222-2-222-2-222-2−2i2i2i−2i2-200000000000000002i−2i000000002-2-22−2i2i2i−2i000000000000
χ522-2-22-222-2-222-2-222-2−2i2i2i−2i2-200000000000000002i−2i00000000-222-22i−2i−2i2i000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ5444-44-4-4-4440-40-40400000000000000000000000000000000000000000000000002i2−2i200
χ5544-44-4-4-4440-40-4040000000000000000000000000000000000000000000000000−2i22i200
χ5644-44-4-4-44-404040-4000000000000000004i−4i0000000000000000000000000000000000
χ5744-44-4-4-44-404040-400000000000000000−4i4i0000000000000000000000000000000000
χ5844-4-44-44-40-404040-40000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5944-4-44-44-40-404040-4000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ604-4444-4-4-44040-40-40000000000000000000000000000000000000000000000022−220000
χ614-4444-4-4-44040-40-400000000000000000000000000000000000000000000000−22220000
χ624-4444-4-4-4-40-404040000000000000000000004i−4i000000000000000000000000000000
χ634-4444-4-4-4-40-40404000000000000000000000−4i4i000000000000000000000000000000
χ644-44-4-4-4440-40-4040400000022−2222−22−2222−222200000000000000000000000000000000000000
χ654-44-4-4-4440-40-40404000000−2222−222222−2222−2200000000000000000000000000000000000000
χ664-4-44-444-4-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ67888-8-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-888-88000000000000000000000000000000000000000000000000000000000000

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