Finite Group Databasebeta

← Group #325539

Character table — Group #325539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444444448888224444888888888888888888248888884444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-111-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-11-11
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111-11-1
χ9111111111111111111-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111-1-1-1-111-111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-11-1-11
χ17222222222-2-222-2-22-2-22222000022-2-2-2-2000000000000000000-220000000000
χ18222222222-2-222-2-22-2-222220000-2-2-2-2220000000000000000002-20000000000
χ19222222222-2-222-2-22-2-2-2-2-2-200002222-2-20000000000000000002-20000000000
χ20222222222-2-222-2-22-2-2-2-2-2-20000-2-22222000000000000000000-220000000000
χ2122222222-222-2-222-2-2-222-2-22222002-20022-2-20000-2-200000000000000000000
χ2222222222-222-2-222-2-2-222-2-2-2-2-2-2002-200-2-22200002200000000000000000000
χ2322222222-222-2-222-2-2-2-2-222222200-2200-2-2220000-2-200000000000000000000
χ2422222222-222-2-222-2-2-2-2-222-2-2-2-200-220022-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000-220000000000002i2i−2i−2i000000002i−2i000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000-22000000000000−2i−2i2i2i00000000−2i2i000000
χ2722222222-2-2-2-2-2-2-2-222-2-2220000002-20000000000002i2i−2i−2i00000000−2i2i000000
χ2822222222-2-2-2-2-2-2-2-222-2-2220000002-2000000000000−2i−2i2i2i000000002i−2i000000
χ29222-22-2-2-22-2-2-2-22222-2000022-2-200000000002i2i−2i−2i2-200000000002i−2i00000000
χ30222-22-2-2-22-2-2-2-22222-2000022-2-20000000000−2i−2i2i2i2-20000000000−2i2i00000000
χ31222-22-2-2-22-2-2-2-22222-20000-2-22200000000002i2i−2i−2i-220000000000−2i2i00000000
χ32222-22-2-2-22-2-2-2-22222-20000-2-2220000000000−2i−2i2i2i-2200000000002i−2i00000000
χ33222-22-2-2-2-2-2-22222-2-22000022-2-200000000000000-2200002i2i−2i−2i0000002i−2i0000
χ34222-22-2-2-2-2-2-22222-2-22000022-2-200000000000000-220000−2i−2i2i2i000000−2i2i0000
χ35222-22-2-2-2-2-2-22222-2-220000-2-222000000000000002-200002i2i−2i−2i000000−2i2i0000
χ36222-22-2-2-2-2-2-22222-2-220000-2-222000000000000002-20000−2i−2i2i2i0000002i−2i0000
χ37444-44-4-4-4444-4-4-4-44-4400000000000000000000000000000000000000000000
χ38444-44-4-4-4-44444-4-4-44-400000000000000000000000000000000000000000000
χ3944-44-44-4-44004-400-400000000004-40000000000000000000000000000000000
χ4044-44-44-4-44004-400-40000000000-440000000000000000000000000000000000
χ4144-44-44-4-4-400-44004000000000000004i−4i000000000000000000000000000000
χ4244-44-44-4-4-400-4400400000000000000−4i4i000000000000000000000000000000
χ4344-4-4-4-444400-4400-4000000000000000000000000002i2−2i22i2−2i20000000000000000
χ4444-4-4-4-444400-4400-400000000000000000000000000−2i22i2−2i22i20000000000000000
χ4544-4-4-4-444-4004-40040000000000000000000000000022−22−22220000000000000000
χ4644-4-4-4-444-4004-400400000000000000000000000000−222222−220000000000000000
χ474-444-4-4-4400000000004i−4i0022−2222−220000002i2−2i20000000000000000000000000000
χ484-444-4-4-4400000000004i−4i00−2222−2222000000−2i22i20000000000000000000000000000
χ494-444-4-4-440000000000−4i4i0022−2222−22000000−2i22i20000000000000000000000000000
χ504-444-4-4-440000000000−4i4i00−2222−22220000002i2−2i20000000000000000000000000000
χ514-44-4-444-40000000000004i−4i22−22−2222000000002i2−2i200000000000000000000000000
χ524-44-4-444-40000000000004i−4i−222222−2200000000−2i22i200000000000000000000000000
χ534-44-4-444-4000000000000−4i4i22−22−222200000000−2i22i200000000000000000000000000
χ544-44-4-444-4000000000000−4i4i−222222−22000000002i2−2i200000000000000000000000000
χ554-4-444-44-404-4004-400000000000000000000000000000002i2−2i22i2−2i2000000000000
χ564-4-444-44-404-4004-40000000000000000000000000000000−2i22i2−2i22i2000000000000
χ574-4-444-44-40-4400-440000000000000000000002i2−2i22i2−2i20000000000000000000000
χ584-4-444-44-40-4400-44000000000000000000000−2i22i2−2i22i20000000000000000000000
χ594-4-4-444-4404-400-4400000000000000000000022−22−22220000000000000000000000
χ604-4-4-444-4404-400-44000000000000000000000−222222−220000000000000000000000
χ614-4-4-444-440-44004-4000000000000000000000000000000022−22−2222000000000000
χ624-4-4-444-440-44004-40000000000000000000000000000000−222222−22000000000000

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