Finite Group Databasebeta

← Group #100925

Character table — Group #100925

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244442222444444444422444488888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ172222222222222222-2-2-2-22222222222-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000000000
χ19222222222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2-2-222222-22-200000000-2-2002-2000000000022-2-222-2-20000000000000000
χ2222222222-2-2-2-222222-22-200000000-2-2002-20000000000-2-222-2-2220000000000000000
χ2322222222-2-2-2-22222-22-2200000000-2-200-220022-2-222-2-2000000000000000000000000
χ2422222222-2-2-2-22222-22-2200000000-2-200-2200-2-222-2-222000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22-22-2000000002200-22002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22-22-2000000002200-2200−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-22-220000000022002-200000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-22-220000000022002-20000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-22-2-2-222-2-2000022-2-2000022-2-2002-200002−22−22−22−22−22−22−22−20000000000000000
χ30222-22-2-2-222-2-2000022-2-2000022-2-2002-20000−22−22−22−22−22−22−22−220000000000000000
χ31222-22-2-2-222-2-2000022-2-20000-2-22200-2200002−22−22−22−2−22−22−22−220000000000000000
χ32222-22-2-2-222-2-2000022-2-20000-2-22200-220000−22−22−22−222−22−22−22−20000000000000000
χ33222-22-2-2-222-2-20000-2-222000022-2-200-220000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ34222-22-2-2-222-2-20000-2-222000022-2-200-220000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ35222-22-2-2-222-2-20000-2-2220000-2-222002-20000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i20000000000000000
χ36222-22-2-2-222-2-20000-2-2220000-2-222002-20000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i20000000000000000
χ37222-22-2-2-2-2-22200002-2-222i2i−2i−2i00000000002i−2ii2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ38222-22-2-2-2-2-22200002-2-222i2i−2i−2i00000000002i−2i−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ39222-22-2-2-2-2-22200002-2-22−2i−2i2i2i0000000000−2i2ii2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ40222-22-2-2-2-2-22200002-2-22−2i−2i2i2i0000000000−2i2i−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ41222-22-2-2-2-2-2220000-222-22i2i−2i−2i0000000000−2i2i2−2−222−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ42222-22-2-2-2-2-2220000-222-22i2i−2i−2i0000000000−2i2i−222−2−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ43222-22-2-2-2-2-2220000-222-2−2i−2i2i2i00000000002i−2i2−2−222−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ44222-22-2-2-2-2-2220000-222-2−2i−2i2i2i00000000002i−2i−222−2−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ452-2-222-22-22-22-22i2i−2i−2i00002i−2i2i−2i2-22-22i−2i0000000000000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i
χ462-2-222-22-22-22-22i2i−2i−2i00002i−2i2i−2i2-22-22i−2i000000000000000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i
χ472-2-222-22-22-22-22i2i−2i−2i0000−2i2i−2i2i-22-222i−2i0000000000000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i
χ482-2-222-22-22-22-22i2i−2i−2i0000−2i2i−2i2i-22-222i−2i000000000000000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i
χ492-2-222-22-22-22-2−2i−2i2i2i00002i−2i2i−2i-22-22−2i2i0000000000000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i
χ502-2-222-22-22-22-2−2i−2i2i2i00002i−2i2i−2i-22-22−2i2i000000000000000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i
χ512-2-222-22-22-22-2−2i−2i2i2i0000−2i2i−2i2i2-22-2−2i2i0000000000000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i
χ522-2-222-22-22-22-2−2i−2i2i2i0000−2i2i−2i2i2-22-2−2i2i000000000000000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i
χ5344-4-4-444-400004i−4i4i−4i00000000000000000000000000000000000000002-22i−2i00000000
χ5444-4-4-444-400004i−4i4i−4i0000000000000000000000000000000000000000-22−2i2i00000000
χ5544-4-4-444-40000−4i4i−4i4i00000000000000000000000000000000000000002-2−2i2i00000000
χ5644-4-4-444-40000−4i4i−4i4i0000000000000000000000000000000000000000-222i−2i00000000
χ574-44-4-4-44400004-4-440000000000000000000000000000000000002-22-2000000000000
χ584-44-4-4-44400004-4-44000000000000000000000000000000000000-22-22000000000000
χ594-44-4-4-4440000-444-40000000000000000000000000000000000002-2-22000000000000
χ604-44-4-4-4440000-444-4000000000000000000000000000000000000-222-2000000000000
χ614-4-444-44-4-44-444i4i−4i−4i000000000000−4i4i00000000000000000000000000000000000000
χ624-4-444-44-4-44-44−4i−4i4i4i0000000000004i−4i00000000000000000000000000000000000000
χ634-4-4-444-444-4-440000000000004-4-440000000000000000000000000000000000000000
χ644-4-4-444-444-4-44000000000000-444-40000000000000000000000000000000000000000
χ654-4-4-444-44-444-4000000004-4-4400000000000000000000000000000000000000000000
χ664-4-4-444-44-444-400000000-444-400000000000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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