Finite Group Databasebeta

← Group #351521

Character table — Group #351521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442244444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ511111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ91111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111111111-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ111111111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1111-1-11
χ121111111111111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-111-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-111-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222-2-2-2-2222-2-22222-2-2-2-2-2-2000000002-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-22222-2-2000000002-2-2-222000000000000000000000000
χ1922222222222-2-2-2-22-2-2-2-22222-2-2-2-22200000000-22-2-222000000000000000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-2-2-222222200000000-2222-2-2000000000000000000000000
χ2122222222-2-2-22222-222-2-2000000002222222222-2-20000-2-2-2-200000000000000000000
χ2222222222-2-2-22222-222-2-20000000022-2-2-2-2-2-2-2-2-2-20000222200000000000000000000
χ2322222222-2-2-22222-2-2-2-2-200000000-2-22222-2-2-2-2220000-2-22200000000000000000000
χ2422222222-2-2-22222-2-2-2-2-200000000-2-2-2-2-2-2222222000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222200000000-2-200000000-22000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2222200000000-2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2220000000022000000002-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2220000000022000000002-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ292-222-2-2-222-2-222-2-22002-2000000000000002i2i−2i−2i002i−2i2i−2i002i−2i2-22-20000000000000000
χ302-222-2-2-222-2-222-2-22002-2000000000000002i2i−2i−2i00−2i2i−2i2i002i−2i-22-220000000000000000
χ312-222-2-2-222-2-222-2-22002-200000000000000−2i−2i2i2i002i−2i2i−2i00−2i2i-22-220000000000000000
χ322-222-2-2-222-2-222-2-22002-200000000000000−2i−2i2i2i00−2i2i−2i2i00−2i2i2-22-20000000000000000
χ332-222-2-2-222-2-2-2-222200-22000000000022-2-20000002i−2i−2i2i2-20000002i−2i2i−2i000000000000
χ342-222-2-2-222-2-2-2-222200-22000000000022-2-2000000−2i2i2i−2i2-2000000−2i2i−2i2i000000000000
χ352-222-2-2-222-2-2-2-222200-220000000000-2-2220000002i−2i−2i2i-22000000−2i2i−2i2i000000000000
χ362-222-2-2-222-2-2-2-222200-220000000000-2-222000000−2i2i2i−2i-220000002i−2i2i−2i000000000000
χ372-222-2-2-22-22222-2-2-200-222i2i−2i−2i2i2i−2i−2i0000002i2i−2i−2i00000000−2i2i00002-2-22000000000000
χ382-222-2-2-22-22222-2-2-200-222i2i−2i−2i2i2i−2i−2i000000−2i−2i2i2i000000002i−2i0000-222-2000000000000
χ392-222-2-2-22-22222-2-2-200-22−2i−2i2i2i−2i−2i2i2i0000002i2i−2i−2i00000000−2i2i0000-222-2000000000000
χ402-222-2-2-22-22222-2-2-200-22−2i−2i2i2i−2i−2i2i2i000000−2i−2i2i2i000000002i−2i00002-2-22000000000000
χ412-222-2-2-22-222-2-222-2002-22i2i−2i−2i−2i−2i2i2i0022-2-20000000000-22002i−2i−2i2i0000000000000000
χ422-222-2-2-22-222-2-222-2002-22i2i−2i−2i−2i−2i2i2i00-2-22200000000002-200−2i2i2i−2i0000000000000000
χ432-222-2-2-22-222-2-222-2002-2−2i−2i2i2i2i2i−2i−2i0022-2-20000000000-2200−2i2i2i−2i0000000000000000
χ442-222-2-2-22-222-2-222-2002-2−2i−2i2i2i2i2i−2i−2i00-2-22200000000002-2002i−2i−2i2i0000000000000000
χ45444-44-4-4-4000000004-400000000000022−2222−2222−2222−22000000000000000000000000000000
χ46444-44-4-4-4000000004-4000000000000−2222−2222−2222−2222000000000000000000000000000000
χ47444-44-4-4-400000000-4400000000000022−2222−22−2222−2222000000000000000000000000000000
χ48444-44-4-4-400000000-44000000000000−2222−222222−2222−22000000000000000000000000000000
χ4944-44-4-44-444-40000-4000000004-44-40000000000000000000000000000000000000000
χ5044-44-4-44-444-40000-400000000-44-440000000000000000000000000000000000000000
χ5144-44-4-44-4-4-440000400004i−4i4i−4i00000000000000000000000000000000000000000000
χ5244-44-4-44-4-4-44000040000−4i4i−4i4i00000000000000000000000000000000000000000000
χ5344-4-4-44-440004-44-40000000000000000000000000000000000000000000002i2−2i2000000
χ5444-4-4-44-440004-44-4000000000000000000000000000000000000000000000−2i22i2000000
χ5544-4-4-44-44000-44-44000000000000000000000000000000000000000002i2−2i20000000000
χ5644-4-4-44-44000-44-4400000000000000000000000000000000000000000−2i22i20000000000
χ574-44-4-444-4000000000000000000004i−4i22−22−22222i2−2i2−2i22i2000000000000000000000000000000
χ584-44-4-444-4000000000000000000004i−4i−222222−22−2i22i22i2−2i2000000000000000000000000000000
χ594-44-4-444-400000000000000000000−4i4i22−22−2222−2i22i22i2−2i2000000000000000000000000000000
χ604-44-4-444-400000000000000000000−4i4i−222222−222i2−2i2−2i22i2000000000000000000000000000000
χ614-4-4444-4-44-440000-400004-4-4400000000000000000000000000000000000000000000
χ624-4-4444-4-44-440000-40000-444-400000000000000000000000000000000000000000000
χ634-4-4444-4-4-44-400004000000004i−4i−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-4-44-40000400000000−4i4i4i−4i0000000000000000000000000000000000000000
χ654-4-4-44-4440004-4-44000000000000000000000000000000000000000000022−2200000000
χ664-4-4-44-4440004-4-440000000000000000000000000000000000000000000−222200000000
χ674-4-4-44-444000-444-40000000000000000000000000000000000000000000000022−220000
χ684-4-4-44-444000-444-400000000000000000000000000000000000000000000000−22220000

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