Finite Group Databasebeta

← Group #352572

Character table — Group #352572

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444442222444444444488888888444444888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-111-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-11-11-1
χ91111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ101111111111111111-1-1-1-111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ121111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111-1-11-1-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-111-1-1-1-1111-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111-1-1-1-1-1-11111-1-1-11-11
χ172222222222-2-22-2-222222-2-2-2-2-2-222-2-2000000002-222-2-2000000000000000000000000
χ182222222222-2-22-2-222222-2-2-2-2-2-2-2-22200000000-22-2-222000000000000000000000000
χ192222222222-2-22-2-22-2-2-2-2-2-2222222-2-2000000002-2-2-222000000000000000000000000
χ202222222222-2-22-2-22-2-2-2-2-2-22222-2-22200000000-2222-2-2000000000000000000000000
χ2122222222-2-222-222-20000-2-20000222222222222-2-20000-2-2-2-200000000000000000000
χ2222222222-2-222-222-20000-2-200002222-2-2-2-2-2-2-2-2-2-20000222200000000000000000000
χ2322222222-2-222-222-20000-2-20000-2-2-2-22222-2-2-2-2220000-2-22200000000000000000000
χ2422222222-2-222-222-20000-2-20000-2-2-2-2-2-2-2-2222222000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000022000022-2-200000000-22000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2000022000022-2-200000000-2200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-20000220000-2-222000000002-2000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-20000220000-2-222000000002-200000000−2i−2i2i2i2i2i−2i−2i000000000000
χ29222-22-2-2-2222-2-22-2-222-2-22-222-2-20000000022-2-2000000002-200002-22-2000000000000
χ30222-22-2-2-2222-2-22-2-222-2-22-222-2-200000000-2-22200000000-220000-22-22000000000000
χ31222-22-2-2-2222-2-22-2-2-2-2222-2-2-2220000000022-2-2000000002-20000-22-22000000000000
χ32222-22-2-2-2222-2-22-2-2-2-2222-2-2-22200000000-2-22200000000-2200002-22-2000000000000
χ33222-22-2-2-222-22-2-22-222-2-2-22-2-222000022-2-200000000002-2002-22-20000000000000000
χ34222-22-2-2-222-22-2-22-222-2-2-22-2-2220000-2-2220000000000-2200-22-220000000000000000
χ35222-22-2-2-222-22-2-22-2-2-222-2222-2-2000022-2-200000000002-200-22-220000000000000000
χ36222-22-2-2-222-22-2-22-2-2-222-2222-2-20000-2-2220000000000-22002-22-20000000000000000
χ37222-22-2-2-2-2-22-222-220000-2200000000000022-2-2002i−2i2i−2i00-222i−2i−2i2i0000000000000000
χ38222-22-2-2-2-2-22-222-220000-2200000000000022-2-200−2i2i−2i2i00-22−2i2i2i−2i0000000000000000
χ39222-22-2-2-2-2-22-222-220000-22000000000000-2-222002i−2i2i−2i002-2−2i2i2i−2i0000000000000000
χ40222-22-2-2-2-2-22-222-220000-22000000000000-2-22200−2i2i−2i2i002-22i−2i−2i2i0000000000000000
χ41222-22-2-2-2-2-2-222-22200002-20000000022-2-20000002i−2i−2i2i-22000000−2i2i2i−2i000000000000
χ42222-22-2-2-2-2-2-222-22200002-20000000022-2-2000000−2i2i2i−2i-220000002i−2i−2i2i000000000000
χ43222-22-2-2-2-2-2-222-22200002-200000000-2-2220000002i−2i−2i2i2-20000002i−2i−2i2i000000000000
χ44222-22-2-2-2-2-2-222-22200002-200000000-2-222000000−2i2i2i−2i2-2000000−2i2i2i−2i000000000000
χ4544-44-4-44-44-400400-44-44-4000000000000000000000000000000000000000000000000
χ4644-44-4-44-44-400400-4-44-44000000000000000000000000000000000000000000000000
χ4744-44-4-44-4-4400-40040000004i−4i4i−4i000000000000000000000000000000000000000000
χ4844-44-4-44-4-4400-4004000000−4i4i−4i4i000000000000000000000000000000000000000000
χ4944-4-4-44-444-400-40044-4-44000000000000000000000000000000000000000000000000
χ5044-4-4-44-444-400-4004-444-4000000000000000000000000000000000000000000000000
χ5144-4-4-44-44-4400400-40000004i−4i−4i4i000000000000000000000000000000000000000000
χ5244-4-4-44-44-4400400-4000000−4i4i4i−4i000000000000000000000000000000000000000000
χ534-444-4-4-44000000000000000000004-42i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000000000000000
χ544-444-4-4-44000000000000000000004-4−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000000000000000
χ554-444-4-4-4400000000000000000000-442i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ564-444-4-4-4400000000000000000000-44−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ574-44-4-444-40000000000000000004-4002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ584-44-4-444-40000000000000000004-400−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ594-44-4-444-4000000000000000000-44002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000
χ604-44-4-444-4000000000000000000-4400−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000
χ614-4-4444-4-400440-4-4000000000000000000000000000000000000000000022−2200000000
χ624-4-4444-4-400440-4-40000000000000000000000000000000000000000000−222200000000
χ634-4-4444-4-400-4-4044000000000000000000000000000000000000000002i2−2i20000000000
χ644-4-4444-4-400-4-404400000000000000000000000000000000000000000−2i22i20000000000
χ654-4-4-44-444004-40-4400000000000000000000000000000000000000000000022−22000000
χ664-4-4-44-444004-40-44000000000000000000000000000000000000000000000−2222000000
χ674-4-4-44-44400-4404-40000000000000000000000000000000000000000000000022−220000
χ684-4-4-44-44400-4404-400000000000000000000000000000000000000000000000−22220000

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