Finite Group Databasebeta

← Group #72321920

Character table — Group #72321920

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111222222222222222222444444888888888888161616161616161616161616161616161616161616161616161616161616323232323232323232323232
order12222222224444444488888888882244444488882244444444888816161616161616161616161616161616444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
χ91111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ101111111111111111111111111111-1-11111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-111
χ121111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1
χ131111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ141111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1
χ151111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ161111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111
χ17222222222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000022-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-200000000-2-222220000000000000000000000000000
χ19222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2222200000000-2-2-2-2220000000000000000000000000000
χ20222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-20000000000000000000000000000
χ2122222-22-2-2-22-2-22-222-2-2-2-2-2222-22-20000000000000022-2-2000000000000000000002i2i−2i−2i00002i−2i000000
χ2222222-22-2-2-22-2-22-222-2-2-2-2-2222-22-20000000000000022-2-200000000000000000000−2i−2i2i2i0000−2i2i000000
χ2322222-22-2-2-22-2-22-222-2-2-2-2-2222-22-200000000000000-2-222000000000000000000002i2i−2i−2i0000−2i2i000000
χ2422222-22-2-2-22-2-22-222-2-2-2-2-2222-22-200000000000000-2-22200000000000000000000−2i−2i2i2i00002i−2i000000
χ252222-22-22-2-2-22-22-22-22-2-2-2-222-22-22000000000000220000-2-2000000000000002i2i−2i−2i00000000002i−2i0000
χ262222-22-22-2-2-22-22-22-22-2-2-2-222-22-22000000000000220000-2-200000000000000−2i−2i2i2i0000000000−2i2i0000
χ272222-22-22-2-2-22-22-22-22-2-2-2-222-22-22000000000000-2-2000022000000000000002i2i−2i−2i0000000000−2i2i0000
χ282222-22-22-2-2-22-22-22-22-2-2-2-222-22-22000000000000-2-200002200000000000000−2i−2i2i2i00000000002i−2i0000
χ292-2-2222-2-2-2222-2-222-2-222-2-22-2-2-222000000000000002i−2i2i−2i00000000000000002-22-2000000000000002i−2i
χ302-2-2222-2-2-2222-2-222-2-222-2-22-2-2-222000000000000002i−2i2i−2i0000000000000000-22-2200000000000000−2i2i
χ312-2-2222-2-2-2222-2-222-2-222-2-22-2-2-22200000000000000−2i2i−2i2i00000000000000002-22-200000000000000−2i2i
χ322-2-2222-2-2-2222-2-222-2-222-2-22-2-2-22200000000000000−2i2i−2i2i0000000000000000-22-22000000000000002i−2i
χ332-2-222-2-222-22-22-2-22-2222-2-2-222-2-220000000000002-200002-22i−2i002i−2i0000000000000000002i−2i00000000
χ342-2-222-2-222-22-22-2-22-2222-2-2-222-2-220000000000002-200002-2−2i2i00−2i2i000000000000000000−2i2i00000000
χ352-2-222-2-222-22-22-2-22-2222-2-2-222-2-22000000000000-220000-222i−2i002i−2i000000000000000000−2i2i00000000
χ362-2-222-2-222-22-22-2-22-2222-2-2-222-2-22000000000000-220000-22−2i2i00−2i2i0000000000000000002i−2i00000000
χ372-2-222-2-222-22-22-2-22-22-2-2222-2-222-2000000000000002i−2i−2i2i002i−2i00−2i2i00000000000000002-20000000000
χ382-2-222-2-222-22-22-2-22-22-2-2222-2-222-2000000000000002i−2i−2i2i00−2i2i002i−2i0000000000000000-220000000000
χ392-2-222-2-222-22-22-2-22-22-2-2222-2-222-200000000000000−2i2i2i−2i002i−2i00−2i2i0000000000000000-220000000000
χ402-2-222-2-222-22-22-2-22-22-2-2222-2-222-200000000000000−2i2i2i−2i00−2i2i002i−2i00000000000000002-20000000000
χ412-2-22-222-22-2-222-2-222-222-2-2-22-222-2002i2i−2i−2i00000000000000002i−2i0022-2-2000000002i−2i2i−2i000000000000
χ422-2-22-222-22-2-222-2-222-222-2-2-22-222-2002i2i−2i−2i00000000000000002i−2i00-2-22200000000−2i2i−2i2i000000000000
χ432-2-22-222-22-2-222-2-222-222-2-2-22-222-200−2i−2i2i2i0000000000000000−2i2i0022-2-200000000−2i2i−2i2i000000000000
χ442-2-22-222-22-2-222-2-222-222-2-2-22-222-200−2i−2i2i2i0000000000000000−2i2i00-2-222000000002i−2i2i−2i000000000000
χ452-2-22-222-22-2-222-2-222-2-2-2222-22-2-22002i2i−2i−2i0000000000000000−2i2i00000022-2-22i−2i−2i2i0000000000000000
χ462-2-22-222-22-2-222-2-222-2-2-2222-22-2-22002i2i−2i−2i0000000000000000−2i2i000000-2-222−2i2i2i−2i0000000000000000
χ472-2-22-222-22-2-222-2-222-2-2-2222-22-2-2200−2i−2i2i2i00000000000000002i−2i00000022-2-2−2i2i2i−2i0000000000000000
χ482-2-22-222-22-2-222-2-222-2-2-2222-22-2-2200−2i−2i2i2i00000000000000002i−2i000000-2-2222i−2i−2i2i0000000000000000
χ492-2-22-2-222-22-2-2-2-22222-2-222-22-2-2220000000000002-20000-220000000000000000002-2-22000000002-200
χ502-2-22-2-222-22-2-2-2-22222-2-222-22-2-2220000000000002-20000-22000000000000000000-222-200000000-2200
χ512-2-22-2-222-22-2-2-2-22222-2-222-22-2-222000000000000-2200002-20000000000000000002-2-2200000000-2200
χ522-2-22-2-222-22-2-2-2-22222-2-222-22-2-222000000000000-2200002-2000000000000000000-222-2000000002-200
χ534444444444-4-4-4-4-4-4-4-40000000000440000-4-40000000000000000000000000000000000000000000000
χ544444444444-4-4-4-4-4-4-4-40000000000-4-40000440000000000000000000000000000000000000000000000
χ5544444-44-4-4-44-4-44-444-44444-4-4-44-44000000000000000000000000000000000000000000000000000000
χ5644444-44-4-4-4-444-44-4-4400000000000000000000000000000000000000002i2−2i22i2−2i200000000000000000000
χ5744444-44-4-4-4-444-44-4-440000000000000000000000000000000000000000−2i22i2−2i22i200000000000000000000
χ584444-44-44-4-44-44-44-44-40000000000000000000000000000000000002i2−2i22i2−2i2000000000000000000000000
χ594444-44-44-4-44-44-44-44-4000000000000000000000000000000000000−2i22i2−2i22i2000000000000000000000000
χ604444-44-44-4-4-44-44-44-444444-4-44-44-4000000000000000000000000000000000000000000000000000000
χ614444-4-4-4-44444-4-4-4-4440000000000004-44-4000000000000000000000000000000000000000000000000
χ624444-4-4-4-44444-4-4-4-444000000000000-44-44000000000000000000000000000000000000000000000000
χ634444-4-4-4-444-4-44444-4-4444444-4-4-4-4000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-444-4-44444-4-4-4-4-4-4-4-44444000000000000000000000000000000000000000000000000000000
χ654-4-4444-4-4-4444-4-444-4-4-4-444-4444-4-4000000000000000000000000000000000000000000000000000000
χ664-4-4444-4-4-44-4-444-4-4440000000000000000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ674-4-4444-4-4-44-4-444-4-444000000000000000000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ684-4-444-4-444-4-44-444-44-40000000000004i−4i−4i4i000000000000000000000000000000000000000000000000
χ694-4-444-4-444-4-44-444-44-4000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000
χ704-4-44-444-44-44-4-444-4-440000000000000000004i4i−4i−4i000000000000000000000000000000000000000000
χ714-4-44-444-44-44-4-444-4-44000000000000000000−4i−4i4i4i000000000000000000000000000000000000000000
χ724-4-44-4-444-444444-4-4-4-400000000000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ734-4-44-4-444-444444-4-4-4-40000000000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ744-4-44-4-444-44-4-4-4-4444444-4-44-444-4-4000000000000000000000000000000000000000000000000000000
χ7588-8-8000000000000004i2−4i24i2−4i20000000000004i−4i22−2222−22000000000000000000000000000000000000000000
χ7688-8-8000000000000004i2−4i24i2−4i2000000000000−4i4i−2222−2222000000000000000000000000000000000000000000
χ7788-8-800000000000000−4i24i2−4i24i20000000000004i−4i−2222−2222000000000000000000000000000000000000000000
χ7888-8-800000000000000−4i24i2−4i24i2000000000000−4i4i22−2222−22000000000000000000000000000000000000000000
χ798-88-8000000000000004i2−4i2−4i24i20000004-40000002i2−2i2−2i22i2000000000000000000000000000000000000000000
χ808-88-8000000000000004i2−4i2−4i24i2000000-44000000−2i22i22i2−2i2000000000000000000000000000000000000000000
χ818-88-800000000000000−4i24i24i2−4i20000004-4000000−2i22i22i2−2i2000000000000000000000000000000000000000000
χ828-88-800000000000000−4i24i24i2−4i2000000-440000002i2−2i2−2i22i2000000000000000000000000000000000000000000

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