Finite Group Databasebeta

← Group #137259

Character table — Group #137259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222224444444422444488884488888844444444888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111-1-1-1-111-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111-1-1-1-111-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111-1-1-1-111-1-1-1-11-111-1-1-1-11-111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111-1-1-1-111-1-1-1-11-111-1-1-1-11-111-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-200002-20000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222222222-2-2-2-222-2-2-2-200002-20000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ212222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ222222222222-2-2-2-2-2-2-2-2220000-220000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ23222222-2-2-2-222-2-2222-2-2-22222-22-2-2-2-222000000000000000000000000
χ24222222-2-2-2-222-2-2-2-22-22222222-2-2-222-2-2000000000000000000000000
χ25222222-2-2-2-2-2-22222-22220000-2-200000000000000000000002−2−222−2−22
χ26222222-2-2-2-2-2-22222-22220000-2-20000000000000000000000−222−2−222−2
χ27222222-2-2-2-2-2-222-2-2-22-2-200002200000000000000000000002−2−22−222−2
χ28222222-2-2-2-2-2-222-2-2-22-2-20000220000000000000000000000−222−22−2−22
χ292222-2-222-2-2222200-2-20022-2-2002-200000000000000002-22-200000000
χ302222-2-222-2-2222200-2-20022-2-2002-20000000000000000-22-2200000000
χ312222-2-222-2-2222200-2-200-2-22200-220000000000002-22-2000000000000
χ322222-2-222-2-2222200-2-200-2-22200-22000000000000-22-22000000000000
χ332222-2-2-2-22222-2-200-220022-2-200-220000000000002i−2i−2i2i000000000000
χ342222-2-2-2-22222-2-200-220022-2-200-22000000000000−2i2i2i−2i000000000000
χ352222-2-2-2-22222-2-200-2200-2-222002-200000000000000002i−2i−2i2i00000000
χ362222-2-2-2-22222-2-200-2200-2-222002-20000000000000000−2i2i2i−2i00000000
χ374444-4-444-4-4-4-4-4-4004400000000000000000000000000000000000000
χ384444-4-4-4-444-4-444004-400000000000000000000000000000000000000
χ394-44-4004i−4i004-44i−4i00000000000000000000002-22i−2i0000000000000000
χ404-44-4004i−4i004-44i−4i0000000000000000000000-22−2i2i0000000000000000
χ414-44-4004i−4i00-44−4i4i0000000000000000002-22i−2i00000000000000000000
χ424-44-4004i−4i00-44−4i4i000000000000000000-22−2i2i00000000000000000000
χ434-44-400−4i4i004-4−4i4i00000000000000000000002-2−2i2i0000000000000000
χ444-44-400−4i4i004-4−4i4i0000000000000000000000-222i−2i0000000000000000
χ454-44-400−4i4i00-444i−4i0000000000000000002-2−2i2i00000000000000000000
χ464-44-400−4i4i00-444i−4i000000000000000000-222i−2i00000000000000000000
χ474-4-444-40000000000004-42i2−2i22i2−2i200002i2−2i200000000000000000000000000
χ484-4-444-40000000000004-4−2i22i2−2i22i20000−2i22i200000000000000000000000000
χ494-4-444-4000000000000-442i2−2i22i2−2i20000−2i22i200000000000000000000000000
χ504-4-444-4000000000000-44−2i22i2−2i22i200002i2−2i200000000000000000000000000
χ514-4-44-44000000004-400002i2−2i2−2i22i20000002i2−2i2000000000000000000000000
χ524-4-44-44000000004-40000−2i22i22i2−2i2000000−2i22i2000000000000000000000000
χ534-4-44-4400000000-4400002i2−2i2−2i22i2000000−2i22i2000000000000000000000000
χ544-4-44-4400000000-440000−2i22i22i2−2i20000002i2−2i2000000000000000000000000
χ5588-8-800008-80000000000000000000000000000000000000000000000
χ5688-8-80000-880000000000000000000000000000000000000000000000

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