Finite Group Databasebeta

← Group #137152

Character table — Group #137152

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222222444444444488888888161616161616161616161616161616161616161616161616
order1222222222444422444488882488888822224444888888881616161616161616
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
χ911111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-111111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111-1-1-1-1111-1-1111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111-1-1-1-1111-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111-1-1-1-1111-1-1-1-11-111-1-1-1-11-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111-1-1-1-1111-1-1-1-11-111-1-1-1-11-111-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111-1-1-1-1111-1-1-1-11-111-1-1-1-11-111-1-111-1-11111-1-1−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
χ2322222-2-2-2-2222-2-2222-2-2-22222-22-2-2-2-222000000000000000000000000
χ2422222-2-2-2-2222-2-2-2-22-22222222-2-2-222-2-2000000000000000000000000
χ2522222-2-2-2-22-2-22222-22220000-2-200000000000000000000002−2−222−2−22
χ2622222-2-2-2-22-2-22222-22220000-2-20000000000000000000000−222−2−222−2
χ2722222-2-2-2-22-2-222-2-2-22-2-200002200000000000000000000002−2−22−222−2
χ2822222-2-2-2-22-2-222-2-2-22-2-20000220000000000000000000000−222−22−2−22
χ292222-222-2-2-2222200-2-20022-2-2002-200000000000000002-22-200000000
χ302222-222-2-2-2222200-2-20022-2-2002-20000000000000000-22-2200000000
χ312222-222-2-2-2222200-2-200-2-22200-220000000000002-22-2000000000000
χ322222-222-2-2-2222200-2-200-2-22200-22000000000000-22-22000000000000
χ332222-2-2-222-222-2-200-220022-2-200-220000000000002i−2i−2i2i000000000000
χ342222-2-2-222-222-2-200-220022-2-200-22000000000000−2i2i2i−2i000000000000
χ352222-2-2-222-222-2-200-2200-2-222002-200000000000000002i−2i−2i2i00000000
χ362222-2-2-222-222-2-200-2200-2-222002-20000000000000000−2i2i2i−2i00000000
χ374444-444-4-4-4-4-4-4-4004400000000000000000000000000000000000000
χ384444-4-4-444-4-4-444004-400000000000000000000000000000000000000
χ3944-4-440000-4000000004i−4i22−2222−2200002i2−2i200000000000000000000000000
χ4044-4-440000-4000000004i−4i−2222−22220000−2i22i200000000000000000000000000
χ4144-4-440000-400000000−4i4i22−2222−220000−2i22i200000000000000000000000000
χ4244-4-440000-400000000−4i4i−2222−222200002i2−2i200000000000000000000000000
χ4344-4-4-40000400004-4000022−22−222200000022−22000000000000000000000000
χ4444-4-4-40000400004-40000−222222−22000000−2222000000000000000000000000
χ4544-4-4-4000040000-44000022−22−2222000000−2222000000000000000000000000
χ4644-4-4-4000040000-440000−222222−2200000022−22000000000000000000000000
χ474-4-4404-40004-44-40000000000000000002-22-200000000000000000000
χ484-4-4404-40004-44-4000000000000000000-22-2200000000000000000000
χ494-4-4404-4000-44-4400000000000000000000002-22-20000000000000000
χ504-4-4404-4000-44-440000000000000000000000-22-220000000000000000
χ514-4-440-440004-4-440000000000000000002-2-2200000000000000000000
χ524-4-440-440004-4-44000000000000000000-222-200000000000000000000
χ534-4-440-44000-444-400000000000000000000002-2-220000000000000000
χ544-4-440-44000-444-40000000000000000000000-222-20000000000000000
χ558-88-80008-800000000000000000000000000000000000000000000000
χ568-88-8000-8800000000000000000000000000000000000000000000000

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