Finite Group Databasebeta

← Group #337302

Character table — Group #337302

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888444444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1111-1-1-1-1-1-111-1
χ311111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-1-1-11
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-11111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-1-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-1-1-111111-11
χ11111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-1-111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-11-1-111-1-111-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-11111-1-1-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-111-1-111111-1-1
χ172222222222-2-2-2-222-2-22222000022000000-2-200000000000-22-2000000000
χ182222222222-2-2-2-222-2-222220000-2-2000000-2-2000000000002-22000000000
χ192222222222-2-2-2-222-2-2-2-2-2-20000220000002200000000000-2-22000000000
χ202222222222-2-2-2-222-2-2-2-2-2-20000-2-2000000220000000000022-2000000000
χ2122222222-2-22222-2-2-2-2000022-2-2002222-2-20000000000-200000000000000
χ2222222222-2-22222-2-2-2-2000022-2-200-2-2-2-2220000000000200000000000000
χ2322222222-2-22222-2-2-2-20000-2-2220022-2-2220000000000-200000000000000
χ2422222222-2-22222-2-2-2-20000-2-22200-2-222-2-20000000000200000000000000
χ2522-2-22-22-2-2-222-2-2222-200000000000000000022-2-2000002i−2i000002i−2i00000
χ2622-2-22-22-2-2-222-2-2222-200000000000000000022-2-200000−2i2i00000−2i2i00000
χ2722-2-22-22-2-2-222-2-2222-2000000000000000000-2-222000002i−2i00000−2i2i00000
χ2822-2-22-22-2-2-222-2-2222-2000000000000000000-2-22200000−2i2i000002i−2i00000
χ2922-2-2-22-22002-22-20000i2i2−i2−i2002i−2i002-2002i−2ii2−i22−22−222−2−20000000000i2−i2000
χ3022-2-2-22-22002-22-20000i2i2−i2−i2002i−2i00-2200−2i2ii2−i22−22−2−2−2220000000000−i2i2000
χ3122-2-2-22-22002-22-20000i2i2−i2−i200−2i2i002-200−2i2ii2−i2−22−22−2−2220000000000i2−i2000
χ3222-2-2-22-22002-22-20000i2i2−i2−i200−2i2i00-22002i−2ii2−i2−22−2222−2−20000000000−i2i2000
χ3322-2-2-22-22002-22-20000−i2−i2i2i2002i−2i002-2002i−2i−i2i2−22−22−2−2220000000000−i2i2000
χ3422-2-2-22-22002-22-20000−i2−i2i2i2002i−2i00-2200−2i2i−i2i2−22−2222−2−20000000000i2−i2000
χ3522-2-2-22-22002-22-20000−i2−i2i2i200−2i2i002-200−2i2i−i2i22−22−222−2−20000000000−i2i2000
χ3622-2-2-22-22002-22-20000−i2−i2i2i200−2i2i00-22002i−2i−i2i22−22−2−2−2220000000000i2−i2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ384444-4-4-4-4004-4-44000000000000000000000022−22−22220000000000000000000
χ394444-4-4-4-4004-4-440000000000000000000000−222222−220000000000000000000
χ404444-4-4-4-400-444-4000000004-400000000000000000000000000000000000
χ414444-4-4-4-400-444-400000000-4400000000000000000000000000000000000
χ4244-4-44-44-44444-4-4-4-4-4400000000000000000000000000000000000000000
χ4344-4-44-44-444-4-444-4-44-400000000000000000000000000000000000000000
χ4444-4-44-44-4-4-4-4-44444-4400000000000000000000000000000000000000000
χ4544-4-4-44-4400-44-4400002i22i2−2i2−2i2000000000000−2i22i200000000000000000000000
χ4644-4-4-44-4400-44-440000−2i2−2i22i22i20000000000002i2−2i200000000000000000000000
χ474-44-44-4-444-400004-400000000004i−4i0000000000000000000000000000000
χ484-44-44-4-444-400004-40000000000−4i4i0000000000000000000000000000000
χ494-44-44-4-44-440000-4400000000000000000000000000000000002i2−2i20000000
χ504-44-44-4-44-440000-440000000000000000000000000000000000−2i22i20000000
χ514-44-4-444-4000000000022−2222−22000000002i2−2i2000000002i−2i2i−2i000000000000000
χ524-44-4-444-4000000000022−2222−2200000000−2i22i200000000−2i2i−2i2i000000000000000
χ534-44-4-444-40000000000−2222−2222000000002i2−2i200000000−2i2i−2i2i000000000000000
χ544-44-4-444-40000000000−2222−222200000000−2i22i2000000002i−2i2i−2i000000000000000
χ554-4-4444-4-44-40000-44004i−4i−4i4i0000000000000000000000000000000000000
χ564-4-4444-4-44-40000-4400−4i4i4i−4i0000000000000000000000000000000000000
χ574-4-4444-4-4-4400004-40000000000000000000000002i2−2i2−2i22i2000000000000000
χ584-4-4444-4-4-4400004-4000000000000000000000000−2i22i22i2−2i2000000000000000
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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