Finite Group Databasebeta

← Group #351246

Character table — Group #351246

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444888888888888888888161616161616161632323232
order12222222444444444444444444444488888888224444888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ511111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-11-1
χ9111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ10111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ11111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11-1-11
χ12111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-11-11
χ17222222222-2-222-2-22-2-22222-2-2-2-222-2-20000000022-2-22-2000000000000000000000000
χ18222222222-2-222-2-22-2-22222-2-2-2-2-2-22200000000-2-222-22000000000000000000000000
χ19222222222-2-222-2-22-2-2-2-2-2-2222222-2-200000000-2-2222-2000000000000000000000000
χ20222222222-2-222-2-22-2-2-2-2-2-22222-2-2220000000022-2-2-22000000000000000000000000
χ2122222222-222-2-222-2-2-2000000002222222222220000-2-2-2-20000-2-20000000000000000
χ2222222222-222-2-222-2-2-2000000002222-2-2-2-2-2-2-2-20000-2-2220000220000000000000000
χ2322222222-222-2-222-2-2-200000000-2-2-2-22222-2-2-2-2000022-2-20000220000000000000000
χ2422222222-222-2-222-2-2-200000000-2-2-2-2-2-2-2-22222000022220000-2-20000000000000000
χ2522222222-2-2-2-2-2-2-2-2220000000022-2-2000000000000-22002i2i−2i−2i002i2i−2i−2i000000000000
χ2622222222-2-2-2-2-2-2-2-2220000000022-2-2000000000000-2200−2i−2i2i2i00−2i−2i2i2i000000000000
χ2722222222-2-2-2-2-2-2-2-22200000000-2-2220000000000002-2002i2i−2i−2i00−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22200000000-2-2220000000000002-200−2i−2i2i2i002i2i−2i−2i000000000000
χ29222-2-22-2-222-2-2-22-222-200000000000000002i2i−2i−2i2-22-200002i−2i2i−2i2i−2i0000000000000000
χ30222-2-22-2-222-2-2-22-222-200000000000000002i2i−2i−2i-22-220000−2i2i−2i2i2i−2i0000000000000000
χ31222-2-22-2-222-2-2-22-222-20000000000000000−2i−2i2i2i2-22-20000−2i2i−2i2i−2i2i0000000000000000
χ32222-2-22-2-222-2-2-22-222-20000000000000000−2i−2i2i2i-22-2200002i−2i2i−2i−2i2i0000000000000000
χ33222-2-22-2-22-22-2-2-222-220000000000002i2i−2i−2i00002-2-22002i−2i0000002i−2i2i−2i000000000000
χ34222-2-22-2-22-22-2-2-222-220000000000002i2i−2i−2i0000-222-2002i−2i000000−2i2i−2i2i000000000000
χ35222-2-22-2-22-22-2-2-222-22000000000000−2i−2i2i2i00002-2-2200−2i2i000000−2i2i−2i2i000000000000
χ36222-2-22-2-22-22-2-2-222-22000000000000−2i−2i2i2i0000-222-200−2i2i0000002i−2i2i−2i000000000000
χ37222-2-22-2-2-22-2222-2-2-222i2i−2i−2i2i2i−2i−2i000000002i2i−2i−2i000000000000−2i2i2-2-22000000000000
χ38222-2-22-2-2-22-2222-2-2-222i2i−2i−2i2i2i−2i−2i00000000−2i−2i2i2i0000000000002i−2i-222-2000000000000
χ39222-2-22-2-2-22-2222-2-2-22−2i−2i2i2i−2i−2i2i2i000000002i2i−2i−2i000000000000−2i2i-222-2000000000000
χ40222-2-22-2-2-22-2222-2-2-22−2i−2i2i2i−2i−2i2i2i00000000−2i−2i2i2i0000000000002i−2i2-2-22000000000000
χ41222-2-22-2-2-2-2222-22-22-22i2i−2i−2i−2i−2i2i2i00002i2i−2i−2i0000000000−2i2i-222-2000000000000000000
χ42222-2-22-2-2-2-2222-22-22-22i2i−2i−2i−2i−2i2i2i0000−2i−2i2i2i00000000002i−2i2-2-22000000000000000000
χ43222-2-22-2-2-2-2222-22-22-2−2i−2i2i2i2i2i−2i−2i00002i2i−2i−2i0000000000−2i2i2-2-22000000000000000000
χ44222-2-22-2-2-2-2222-22-22-2−2i−2i2i2i2i2i−2i−2i0000−2i−2i2i2i00000000002i−2i-222-2000000000000000000
χ4544-44-4-44-4000000000000000000004i−4i2i2−2i22i2−2i222−2222−22000000000000000000000000000000
χ4644-44-4-44-4000000000000000000004i−4i−2i22i2−2i22i2−2222−2222000000000000000000000000000000
χ4744-44-4-44-400000000000000000000−4i4i2i2−2i22i2−2i2−2222−2222000000000000000000000000000000
χ4844-44-4-44-400000000000000000000−4i4i−2i22i2−2i22i222−2222−22000000000000000000000000000000
χ4944-4-44-4-440000000000000000004i−4i0022−22−22222i2−2i2−2i22i2000000000000000000000000000000
χ5044-4-44-4-440000000000000000004i−4i00−222222−22−2i22i22i2−2i2000000000000000000000000000000
χ5144-4-44-4-44000000000000000000−4i4i0022−22−2222−2i22i22i2−2i2000000000000000000000000000000
χ5244-4-44-4-44000000000000000000−4i4i00−222222−222i2−2i2−2i22i2000000000000000000000000000000
χ534-4444-4-4-404-400-4400000000000000000000000000000000000000000002i2−2i200000000
χ544-4444-4-4-404-400-440000000000000000000000000000000000000000000−2i22i200000000
χ554-4444-4-4-40-44004-4000000000000000000000000000000000000000002i2−2i20000000000
χ564-4444-4-4-40-44004-400000000000000000000000000000000000000000−2i22i20000000000
χ574-44-4-4-44404400-4-40000000000000000000000000000000000000000000002i2−2i2000000
χ584-44-4-4-44404400-4-4000000000000000000000000000000000000000000000−2i22i2000000
χ594-44-4-4-4440-4-400440000000000000000000000000000000000000000000000022−220000
χ604-44-4-4-4440-4-4004400000000000000000000000000000000000000000000000−22220000
χ614-4-44-44-444004-400-40000004i−4i4i−4i000000000000000000000000000000000000000000
χ624-4-44-44-444004-400-4000000−4i4i−4i4i000000000000000000000000000000000000000000
χ634-4-44-44-44-400-44004004-44-40000000000000000000000000000000000000000000000
χ644-4-44-44-44-400-4400400-44-440000000000000000000000000000000000000000000000
χ654-4-4-4444-4400-4400-4004i−4i−4i4i0000000000000000000000000000000000000000000000
χ664-4-4-4444-4400-4400-400−4i4i4i−4i0000000000000000000000000000000000000000000000
χ674-4-4-4444-4-4004-40040000004-4-44000000000000000000000000000000000000000000
χ684-4-4-4444-4-4004-4004000000-444-4000000000000000000000000000000000000000000

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