Finite Group Databasebeta

← Group #238155

Character table — Group #238155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444224444448888888888888888224444444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-1-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111-1-1-1111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-111111111
χ91111111111111-1-1-1-1111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1111-11-1-1-1-11-111-1-111-1-1
χ101111111111111-1-1-1-1111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-111-11-11-1-11-11-1-111-1-111
χ111111111111111-1-1-1-1111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1111-1-1111-1-1-1-111
χ121111111111111-1-1-1-1111-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-11111-1-1
χ131111111111111-1-1-1-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-1111-1-11-1-11111-1-1
χ141111111111111-1-1-1-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-11111-111-1-1-1-111
χ151111111111111-1-1-1-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1111111-11-1-1-1-11-1-1-111-1-111
χ161111111111111-1-1-1-1111-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-11111-11-11-1-11-1111-1-111-1-1
χ1722222222222-2-22222-2-22-2-2-222-2-2-200000000000000000020000-220000-20000000000
χ1822222222222-2-22222-2-22-2-2-222-2-2-2000000000000000000-200002-2000020000000000
χ1922222222222-2-2-2-2-2-2-2-2222-2-2-222-200000000000000000020000-2-2000020000000000
χ2022222222222-2-2-2-2-2-2-2-2222-2-2-222-2000000000000000000-20000220000-20000000000
χ2122222222-2-2-222222222-222-2-2-2-2-2-200000000000000000000000002-2000-2200000000
χ2222222222-2-2-222222222-222-2-2-2-2-2-20000000000000000000000000-220002-200000000
χ2322222222-2-2-222-2-2-2-222-2-2-2-22222-2000000000000000000000000022000-2-200000000
χ2422222222-2-2-222-2-2-2-222-2-2-2-22222-20000000000000000000000000-2-20002200000000
χ2522222222-2-2-2-2-22222-2-2-2-2-22-2-22220000000000000000000002-200002-200000000000
χ2622222222-2-2-2-2-22222-2-2-2-2-22-2-2222000000000000000000000-220000-2200000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-220000000000000000000002-20000-2200000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-22000000000000000000000-2200002-200000000000
χ29222-22-2-2-222-22222-2-2-2-2-22-222-22-2-200000000000000002-202-20000000000000000000
χ30222-22-2-2-222-22222-2-2-2-2-22-222-22-2-20000000000000000-220-220000000000000000000
χ31222-22-2-2-222-222-2-222-2-2-2-222-22-22-200000000000000002-20-220000000000000000000
χ32222-22-2-2-222-222-2-222-2-2-2-222-22-22-20000000000000000-2202-20000000000000000000
χ33222-22-2-2-222-2-2-222-2-222-2-22-22-2-2220000000000000000000000000000000000002i−2i2i−2i
χ34222-22-2-2-222-2-2-222-2-222-2-22-22-2-222000000000000000000000000000000000000−2i2i−2i2i
χ35222-22-2-2-222-2-2-2-2-22222-22-2-2-222-220000000000000000000000000000000000002i−2i−2i2i
χ36222-22-2-2-222-2-2-2-2-22222-22-2-2-222-22000000000000000000000000000000000000−2i2i2i−2i
χ37222-22-2-2-2-2-222222-2-2-2-222-2-2-22-222000000000000000000000000000000002i−2i2i−2i0000
χ38222-22-2-2-2-2-222222-2-2-2-222-2-2-22-22200000000000000000000000000000000−2i2i−2i2i0000
χ39222-22-2-2-2-2-2222-2-222-2-22-22-22-22-22000000000000000000000000000000002i−2i−2i2i0000
χ40222-22-2-2-2-2-2222-2-222-2-22-22-22-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ41222-22-2-2-2-2-22-2-222-2-2222-222-222-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ42222-22-2-2-2-2-22-2-222-2-2222-222-222-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ43222-22-2-2-2-2-22-2-2-2-2222222-222-2-22-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000
χ44222-22-2-2-2-2-22-2-2-2-2222222-222-2-22-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000
χ4544-44-44-4-44-4400000000-4000000002222−22−222222−22−2200000000000000000000000000000000
χ4644-44-44-4-44-4400000000-400000000−22−222222−22−22222200000000000000000000000000000000
χ4744-44-44-4-4-44-400000000400000000000000002i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000000000
χ4844-44-44-4-4-44-40000000040000000000000000−2i2−2i22i22i2−2i2−2i22i22i2000000000000000000000000
χ4944-4-4-4-4444-4-400000000400000000000000002222−22−22−22−222222000000000000000000000000
χ5044-4-4-4-4444-4-40000000040000000000000000−22−2222222222−22−22000000000000000000000000
χ5144-4-4-4-444-44400000000-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000
χ5244-4-4-4-444-44400000000-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000
χ534-444-4-4-44000004i−4i4i−4i000000000002i−2i2i−2i2i−2i2i−2i2-22-22-22-2000000000000000000000000
χ544-444-4-4-44000004i−4i4i−4i00000000000−2i2i−2i2i−2i2i−2i2i-22-22-22-22000000000000000000000000
χ554-444-4-4-4400000−4i4i−4i4i000000000002i−2i2i−2i2i−2i2i−2i-22-22-22-22000000000000000000000000
χ564-444-4-4-4400000−4i4i−4i4i00000000000−2i2i−2i2i−2i2i−2i2i2-22-22-22-2000000000000000000000000
χ574-44-4-444-4000004i−4i−4i4i000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ584-44-4-444-4000004i−4i−4i4i00000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ594-44-4-444-400000−4i4i4i−4i000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ604-44-4-444-400000−4i4i4i−4i00000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ614-4-444-44-40004-400004-4000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000
χ624-4-444-44-40004-400004-400000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000
χ634-4-444-44-4000-440000-440000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ644-4-444-44-4000-440000-44000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ654-4-4-444-440004-40000-4400000000022−22−2222−222222−2200000000000000000000000000000000
χ664-4-4-444-440004-40000-44000000000−222222−2222−22−222200000000000000000000000000000000
χ674-4-4-444-44000-4400004-40000000000000000022−22−2222−222222−22000000000000000000000000
χ684-4-4-444-44000-4400004-400000000000000000−222222−2222−22−2222000000000000000000000000

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