Finite Group Databasebeta

← Group #104792

Character table — Group #104792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444444488888888888888888161616161616161616161616161616163232
order12222222222244444444444444444444488888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ92222222222222222-2-2-222-2-2-2-2000000000000000022-2-200000000000000
χ102222222222222222-2-2-222-2-2-2-20000000000000000-2-22200000000000000
χ11222222222222-2-2-2-2222-2-2-2-22-22222-2-2-2-200000000000000000000000000
χ12222222222222-2-2-2-2222-2-2-2-22-2-2-2-2-2222200000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2-2-222-220000000000000000000022-2-20000000000
χ14222222222222-2-2-2-2-2-2-2-2-222-2200000000000000000000-2-2220000000000
χ1522222222-2-2-2-2222222-2-2-222-2-200000000000000000000000000002i2i−2i−2i00
χ1622222222-2-2-2-2222222-2-2-222-2-20000000000000000000000000000−2i−2i2i2i00
χ1722222222-2-2-2-22222-2-22-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ1822222222-2-2-2-22222-2-22-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ1922222222-2-2-2-2-2-2-2-222-222-2-2-22000000000000000000000000000000002-2
χ2022222222-2-2-2-2-2-2-2-222-222-2-2-2200000000000000000000000000000000-22
χ2122222222-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000002i2i−2i−2i000000
χ2222222222-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000−2i−2i2i2i000000
χ23222-22-2-2-222-2-200002-220000-2022-2-2000022−2−222−2−2000000002−22−2000000
χ24222-22-2-2-222-2-200002-220000-2022-2-20000−2−222−2−22200000000−22−22000000
χ25222-22-2-2-222-2-200002-220000-20-2-222000022−2−222−2−200000000−22−22000000
χ26222-22-2-2-222-2-200002-220000-20-2-2220000−2−222−2−222000000002−22−2000000
χ27222-22-2-2-2-2-2220000-2220000-20000022-2-2i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i2000000
χ28222-22-2-2-2-2-2220000-2220000-20000022-2-2−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i2000000
χ29222-22-2-2-2-2-2220000-2220000-200000-2-222i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i2000000
χ30222-22-2-2-2-2-2220000-2220000-200000-2-222−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i2000000
χ3122-2-2-2-2222-22-2-2-2220002-2000000000000i2−i2i2−i2i2−i2i2−i22-20000000000i2−i2i2−i200
χ3222-2-2-2-2222-22-2-2-2220002-2000000000000i2−i2i2−i2i2−i2i2−i2-220000000000−i2i2−i2i200
χ3322-2-2-2-2222-22-2-2-2220002-2000000000000−i2i2−i2i2−i2i2−i2i22-20000000000−i2i2−i2i200
χ3422-2-2-2-2222-22-2-2-2220002-2000000000000−i2i2−i2i2−i2i2−i2i2-220000000000i2−i2i2−i200
χ3522-2-2-2-222-22-22-2-222000-220000000000002−22−2−22−22002-2000000002−2−2200
χ3622-2-2-2-222-22-22-2-222000-220000000000002−22−2−22−2200-2200000000−222−200
χ3722-2-2-2-222-22-22-2-222000-22000000000000−22−222−22−2002-200000000−222−200
χ3822-2-2-2-222-22-22-2-222000-22000000000000−22−222−22−200-22000000002−2−2200
χ39444-44-4-4-444-4-40000-44-40000400000000000000000000000000000000000
χ40444-44-4-4-4-4-44400004-4-40000400000000000000000000000000000000000
χ4144-44-44-4-44-4-440000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4244-44-44-4-44-4-44000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4344-44-44-4-4-444-40000000000000000000002-2-22-222-2000000000000000000
χ4444-44-44-4-4-444-4000000000000000000000-222-22-2-22000000000000000000
χ4544-4-4-4-4444-44-444-4-4000-4400000000000000000000000000000000000000
χ4644-4-4-4-444-44-4444-4-40004-400000000000000000000000000000000000000
χ474-444-4-4-4400000000000004i−4i002i−2i2i−2i2-22-200000000000000000000000000
χ484-444-4-4-4400000000000004i−4i00−2i2i−2i2i-22-2200000000000000000000000000
χ494-444-4-4-440000000000000−4i4i002i−2i2i−2i-22-2200000000000000000000000000
χ504-444-4-4-440000000000000−4i4i00−2i2i−2i2i2-22-200000000000000000000000000
χ514-44-4-444-400004i−4i4i−4i0000000002i−2i−2i2i2-2-2200000000000000000000000000
χ524-44-4-444-400004i−4i4i−4i000000000−2i2i2i−2i-222-200000000000000000000000000
χ534-44-4-444-40000−4i4i−4i4i0000000002i−2i−2i2i-222-200000000000000000000000000
χ544-44-4-444-40000−4i4i−4i4i000000000−2i2i2i−2i2-2-2200000000000000000000000000
χ554-4-444-44-400004i−4i−4i4i000000000000000000000000000002-22i−2i0000000000
χ564-4-444-44-400004i−4i−4i4i00000000000000000000000000000-22−2i2i0000000000
χ574-4-444-44-40000−4i4i4i−4i000000000000000000000000000002-2−2i2i0000000000
χ584-4-444-44-40000−4i4i4i−4i00000000000000000000000000000-222i−2i0000000000
χ598-8-8-888-88000000000000000000000000000000000000000000000000000

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