Finite Group Databasebeta

← Group #338953

Character table — Group #338953

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488884444444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1111111111111111-1-1-1-1-111-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1
χ4111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111111-11
χ51111111111111111111111-1-111111111-1-11111-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-11-11
χ61111111111111111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-11-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1111111-1111-1-1-1-11111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-11
χ10111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-111-1-111-1
χ11111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-111-1-11-1-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111-111-1-1-1-1-1-111-111
χ13111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-111
χ14111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-11-1-1-1-111-1-11111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-11
χ172222222222-2-22-2-22-2-200002222-2-20000220000-2-20000-200000000000000
χ182222222222-2-22-2-22-2-2000022-2-2220000-2-20000220000-200000000000000
χ192222222222-2-22-2-22-2-20000-2-222-2-20000-2-20000220000200000000000000
χ202222222222-2-22-2-22-2-20000-2-2-2-2220000220000-2-20000200000000000000
χ2122222222-2-222-222-2-2-2222200000022-2-20000000000000-22-200000000000
χ2222222222-2-222-222-2-2-22222000000-2-2-2-200000000000002-2200000000000
χ2322222222-2-222-222-2-2-2-2-2-2-200000022220000000000000-2-2200000000000
χ2422222222-2-222-222-2-2-2-2-2-2-2000000-2-222000000000000022-200000000000
χ25222-2-22-2-2-22-2-2-2222-22000000000000000022-2-200000000002i−2i002i−2i00000
χ26222-2-22-2-2-22-2-2-2222-22000000000000000022-2-20000000000−2i2i00−2i2i00000
χ27222-2-22-2-2-22-2-2-2222-220000000000000000-2-22200000000002i−2i00−2i2i00000
χ28222-2-22-2-2-22-2-2-2222-220000000000000000-2-2220000000000−2i2i002i−2i00000
χ2922-2-22-22-22-200-200200i2i2−i2−i22i−2i2-20000i2−i22i−2ii2−i2i2−i20022−2−20000002−20000000
χ3022-2-22-22-22-200-200200i2i2−i2−i22i−2i-220000i2−i2−2i2i−i2i2−i2i200−2−2220000002−20000000
χ3122-2-22-22-22-200-200200i2i2−i2−i2−2i2i2-20000i2−i2−2i2ii2−i2i2−i200−2−222000000−220000000
χ3222-2-22-22-22-200-200200i2i2−i2−i2−2i2i-220000i2−i22i−2i−i2i2−i2i20022−2−2000000−220000000
χ3322-2-22-22-22-200-200200−i2−i2i2i22i−2i2-20000−i2i22i−2i−i2i2−i2i200−2−222000000−220000000
χ3422-2-22-22-22-200-200200−i2−i2i2i22i−2i-220000−i2i2−2i2ii2−i2i2−i20022−2−2000000−220000000
χ3522-2-22-22-22-200-200200−i2−i2i2i2−2i2i2-20000−i2i2−2i2i−i2i2−i2i20022−2−20000002−20000000
χ3622-2-22-22-22-200-200200−i2−i2i2i2−2i2i-220000−i2i22i−2ii2−i2i2−i200−2−2220000002−20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-44-4-44-4444-4-4-4-4400000000000000000000000000000000000000000
χ39444-4-44-4-44-4-4-4444-44-400000000000000000000000000000000000000000
χ40444-4-44-4-4-4444-4-4-444-400000000000000000000000000000000000000000
χ4144-44-4-4-444400-400-400000000004-40000000000000000000000000000000
χ4244-44-4-4-444400-400-40000000000-440000000000000000000000000000000
χ4344-44-4-4-44-4-40040040000000000000000002i2−2i2−2i22i2000000000000000000000
χ4444-44-4-4-44-4-4004004000000000000000000−2i22i22i2−2i2000000000000000000000
χ4544-4-44-44-4-4400400-4002i22i2−2i2−2i200000000−2i22i2000000000000000000000000000
χ4644-4-44-44-4-4400400-400−2i2−2i22i22i2000000002i2−2i2000000000000000000000000000
χ474-44-44-4-44000000000022−2222−2200000000000000002i2−2i22i−2i2i−2i000000000000000
χ484-44-44-4-44000000000022−2222−220000000000000000−2i22i2−2i2i−2i2i000000000000000
χ494-44-44-4-440000000000−2222−222200000000000000002i2−2i2−2i2i−2i2i000000000000000
χ504-44-44-4-440000000000−2222−22220000000000000000−2i22i22i−2i2i−2i000000000000000
χ514-4-4444-4-4004-404-400000000000000000000000002i2−2i2−2i22i2000000000000000
χ524-4-4444-4-4004-404-40000000000000000000000000−2i22i22i2−2i2000000000000000
χ534-4-4444-4-400-440-440004i−4i−4i4i0000000000000000000000000000000000000
χ544-4-4444-4-400-440-44000−4i4i4i−4i0000000000000000000000000000000000000
χ554-4-4-4-4444004-40-4400000000000000000000000000000000000000022−22000
χ564-4-4-4-4444004-40-44000000000000000000000000000000000000000−2222000
χ574-4-4-4-444400-4404-400000000000004-400000000000000000000000000000
χ584-4-4-4-444400-4404-40000000000000-4400000000000000000000000000000
χ598-888-8-88-8000000000000000000000000000000000000000000000000000

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