Finite Group Databasebeta

← Group #337231

Character table — Group #337231

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882222444488888888888888444444888888244
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1-1-11
χ51111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-111-1-1-1-1111111-1-1-1-1111111-1-1-111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11-1111-111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111-111
χ11111111111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-11-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1111-1-1
χ13111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111-1111-1-1-111-1-11-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-111-1-1111-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-11111-11-1
χ1722222222222-2-2-2-22-2-2222200220000-2-2000000000000-2-20002000000000
χ1822222222222-2-2-2-22-2-2222200-2-20000-2-200000000000022000-2000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20022000022000000000000-22000-2000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-200-2-20000220000000000002-20002000000000
χ2122222222-2-2-22222-2-2-200002200-2-2220022-2-20000000000-2000000000000
χ2222222222-2-2-22222-2-2-200002200-2-2-2-200-2-22200000000002000000000000
χ2322222222-2-2-22222-2-2-20000-2-200222200-2-2220000000000-2000000000000
χ2422222222-2-2-22222-2-2-20000-2-20022-2-20022-2-200000000002000000000000
χ2522-22-2-22-20002-22-2000i2i2−i2−i200002i−2i2-2i2−i2002i−2i22−2−222−2−20000000000i2−i2000
χ2622-22-2-22-20002-22-2000i2i2−i2−i200002i−2i-22i2−i200−2i2i22−2−2−2−2220000000000−i2i2000
χ2722-22-2-22-20002-22-2000i2i2−i2−i20000−2i2i2-2i2−i200−2i2i−2−222−2−2220000000000i2−i2000
χ2822-22-2-22-20002-22-2000i2i2−i2−i20000−2i2i-22i2−i2002i−2i−2−22222−2−20000000000−i2i2000
χ2922-22-2-22-20002-22-2000−i2−i2i2i200002i−2i2-2−i2i2002i−2i−2−222−2−2220000000000−i2i2000
χ3022-22-2-22-20002-22-2000−i2−i2i2i200002i−2i-22−i2i200−2i2i−2−22222−2−20000000000i2−i2000
χ3122-22-2-22-20002-22-2000−i2−i2i2i20000−2i2i2-2−i2i200−2i2i22−2−222−2−20000000000−i2i2000
χ3222-22-2-22-20002-22-2000−i2−i2i2i20000−2i2i-22−i2i2002i−2i22−2−2−2−2220000000000i2−i2000
χ332-2222-2-2-2-2-2222-2-222-20000000000000000002-22-200000002i−2i0002i−2i00000
χ342-2222-2-2-2-2-2222-2-222-20000000000000000002-22-20000000−2i2i000−2i2i00000
χ352-2222-2-2-2-2-2222-2-222-2000000000000000000-22-2200000002i−2i000−2i2i00000
χ362-2222-2-2-2-2-2222-2-222-2000000000000000000-22-220000000−2i2i0002i−2i00000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ3844-44-4-44-4000-44-440002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ3944-44-4-44-4000-44-44000−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ4044-4-44-4-444-440000-400000000000000000000000000000000002i2−2i20000000
χ4144-4-44-4-444-440000-40000000000000000000000000000000000−2i22i20000000
χ4244-4-44-4-44-44-400004000000004-4000000000000000000000000000000000
χ4344-4-44-4-44-44-40000400000000-44000000000000000000000000000000000
χ444-4444-4-4-444-444-4-4-4-4400000000000000000000000000000000000000000
χ454-4444-4-4-444-4-4-444-44-400000000000000000000000000000000000000000
χ464-4444-4-4-4-4-44-4-4444-4400000000000000000000000000000000000000000
χ474-44-4-4-444000000000022−2222−22000000000022−220000002-22-2000000000000000
χ484-44-4-4-444000000000022−2222−220000000000−2222000000-22-22000000000000000
χ494-44-4-4-4440000000000−2222−2222000000000022−22000000-22-22000000000000000
χ504-44-4-4-4440000000000−2222−22220000000000−22220000002-22-2000000000000000
χ514-4-44-44-440004-4-4400000000000000000000022−22−22220000000000000000000
χ524-4-44-44-440004-4-44000000000000000000000−222222−220000000000000000000
χ534-4-44-44-44000-444-400000004-400000000000000000000000000000000000
χ544-4-44-44-44000-444-40000000-4400000000000000000000000000000000000
χ554-4-4-4444-44-4-40000400000000000000000000000022−22−2222000000000000000
χ564-4-4-4444-44-4-400004000000000000000000000000−222222−22000000000000000
χ574-4-4-4444-4-4440000-4004i−4i−4i4i0000000000000000000000000000000000000
χ584-4-4-4444-4-4440000-400−4i4i4i−4i0000000000000000000000000000000000000
χ59888-8-88-8-8000000000000000000000000000000000000000000000000000

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