Finite Group Databasebeta

← Group #312912

Character table — Group #312912

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-1-1-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-11-11111-1-11-1
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
χ101111111111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1
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
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1111-1-1-1-1-1111-1
χ17222222222-22-22-22-20000-2-22222-2-2-2-2002200-2-2000000000000000000002-200000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200-2-2002200000000000000000000-2200000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222220022002200000000000000000000-2-200000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2222200-2-200-2-2000000000000000000002200000000
χ2122222222-22-22-22-222222-2-200000000-2-2002200-2-2-2-200002200000000000000000000
χ2222222222-22-22-22-222222-2-200000000-2-200-2-20022220000-2-200000000000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000022002200-2-2220000-2-200000000000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000002200-2-20022-2-200002200000000000000000000
χ25222-2-2-22-20-20-202022i2i−2i−2i0022−2−222−2−2000000002-22i−2ii2i2−i2−i20022−2−2i2i2−i2−i2000000000000
χ26222-2-2-22-20-20-202022i2i−2i−2i0022−2−222−2−200000000-22−2i2ii2i2−i2−i200−2−222−i2−i2i2i2000000000000
χ27222-2-2-22-20-20-202022i2i−2i−2i00−2−222−2−222000000002-22i−2i−i2−i2i2i200−2−222−i2−i2i2i2000000000000
χ28222-2-2-22-20-20-202022i2i−2i−2i00−2−222−2−22200000000-22−2i2i−i2−i2i2i20022−2−2i2i2−i2−i2000000000000
χ29222-2-2-22-20-20-20202−2i−2i2i2i0022−2−222−2−2000000002-2−2i2i−i2−i2i2i20022−2−2−i2−i2i2i2000000000000
χ30222-2-2-22-20-20-20202−2i−2i2i2i0022−2−222−2−200000000-222i−2i−i2−i2i2i200−2−222i2i2−i2−i2000000000000
χ31222-2-2-22-20-20-20202−2i−2i2i2i00−2−222−2−222000000002-2−2i2ii2i2−i2−i200−2−222i2i2−i2−i2000000000000
χ32222-2-2-22-20-20-20202−2i−2i2i2i00−2−222−2−22200000000-222i−2ii2i2−i2−i20022−2−2−i2−i2i2i2000000000000
χ332-2-22-222-20-202020-22-22-200i2−i2i2−i2i2−i2i2−i200002i−2i000000i2−i2i2−i22i−2i2−22−22−22−2000000000000
χ342-2-22-222-20-202020-22-22-200i2−i2i2−i2i2−i2i2−i20000−2i2i000000i2−i2i2−i2−2i2i−22−22−22−22000000000000
χ352-2-22-222-20-202020-22-22-200−i2i2−i2i2−i2i2−i2i200002i−2i000000−i2i2−i2i22i−2i−22−22−22−22000000000000
χ362-2-22-222-20-202020-22-22-200−i2i2−i2i2−i2i2−i2i20000−2i2i000000−i2i2−i2i2−2i2i2−22−22−22−2000000000000
χ372-2-22-222-20-202020-2-22-2200i2−i2i2−i2i2−i2i2−i200002i−2i000000−i2i2−i2i2−2i2i2−22−2−22−22000000000000
χ382-2-22-222-20-202020-2-22-2200i2−i2i2−i2i2−i2i2−i20000−2i2i000000−i2i2−i2i22i−2i−22−222−22−2000000000000
χ392-2-22-222-20-202020-2-22-2200−i2i2−i2i2−i2i2−i2i200002i−2i000000i2−i2i2−i2−2i2i−22−222−22−2000000000000
χ402-2-22-222-20-202020-2-22-2200−i2i2−i2i2−i2i2−i2i20000−2i2i000000i2−i2i2−i22i−2i2−22−2−22−22000000000000
χ412-2-2-22-22222-2-222-2-22i−2i−2i2i-222i−2i−2i2i2i−2i−2i2i2i−2i0000000000-222-20000000000000000000000
χ422-2-2-22-22222-2-222-2-22i−2i−2i2i-22−2i2i2i−2i−2i2i2i−2i2i−2i00000000002-2-220000000000000000000000
χ432-2-2-22-22222-2-222-2-2−2i2i2i−2i-222i−2i−2i2i2i−2i−2i2i−2i2i00000000002-2-220000000000000000000000
χ442-2-2-22-22222-2-222-2-2−2i2i2i−2i-22−2i2i2i−2i−2i2i2i−2i−2i2i0000000000-222-20000000000000000000000
χ452-2-2-22-2222-2-222-2-2200002-22i−2i−2i2i−2i2i2i−2i000000000000000000000000002i−2i002-2000000
χ462-2-2-22-2222-2-222-2-2200002-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000−2i2i00-22000000
χ472-2-2-22-2222-2-222-2-2200002-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000002i−2i00-22000000
χ482-2-2-22-2222-2-222-2-2200002-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000−2i2i002-2000000
χ492-2-2-22-222-222-2-222-22i−2i−2i2i2-200000000−2i2i00000000000000002-2-222i−2i−2i2i000000000000
χ502-2-2-22-222-222-2-222-22i−2i−2i2i2-200000000−2i2i0000000000000000-222-2−2i2i2i−2i000000000000
χ512-2-2-22-222-222-2-222-2−2i2i2i−2i2-2000000002i−2i00000000000000002-2-22−2i2i2i−2i000000000000
χ522-2-2-22-222-222-2-222-2−2i2i2i−2i2-2000000002i−2i0000000000000000-222-22i−2i−2i2i000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-4-4-44-404040-40-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ55444-4-4-44-404040-40-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-44-4-4-444040-40-4000000000000000000000000000000000000000000000000022−2200
χ5744-44-4-4-444040-40-40000000000000000000000000000000000000000000000000−222200
χ5844-44-4-4-44-40-404040000000000000000000004i−4i000000000000000000000000000000
χ5944-44-4-4-44-40-40404000000000000000000000−4i4i000000000000000000000000000000
χ604-44-4-44-4440-40-404000000000000000000000000000000000000000000000002i2−2i20000
χ614-44-4-44-4440-40-40400000000000000000000000000000000000000000000000−2i22i20000
χ624-44-4-44-44-404040-4000000000000000004i−4i0000000000000000000000000000000000
χ634-44-4-44-44-404040-400000000000000000−4i4i0000000000000000000000000000000000
χ644-4-44-444-4040-40-4040000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ654-4-44-444-4040-40-404000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ664-4-4-44-444-4-444-4-4440000-440000000000000000000000000000000000000000000000
χ6788-8-888-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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