Finite Group Databasebeta

← Group #285206

Character table — Group #285206

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888884444488888888888824444888888888828
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111111111-1-11111-1-1-1111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-111-1-1-1-111-1-1-1-111111-1111-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-11-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1111-1-11-1-1-111-1-11-1
χ611111111111111111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-11111-1-111-11
χ711111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111-1-11-1
χ9111111111111-1-111111111111-111-1-11111-1-1111111-1-11-1-1-1-1-11-1-11111-1-1
χ10111111111111-1-111111111111-1-1-1-1-11111-1-111-1-111-1-1-111-1-1-1-111-1-1-1-111
χ11111111111111-1-11111111-1-1-1-1-111-1-1-1-11111-1-111-1-1111-1-1-1-111-1-1-1-1-1-111
χ12111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-11-1111111-1-1
χ13111111111111-1-1111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-11111-1-1-11
χ14111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-11-1-1-1-1111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-11-1-1111-111-1-1111-1
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1111111-1-111-1-1-11
χ172222222-2-2-2-22222-2-22i2i−2i−2i0000200-2-2002i−2i00000000000002i−2i0000000000
χ182222222-2-2-2-22222-2-2−2i−2i2i2i0000200-2-200−2i2i0000000000000−2i2i0000000000
χ192222222-2-2-2-22-2-22-2-22i2i−2i−2i0000-20022002i−2i0000000000000−2i2i0000000000
χ202222222-2-2-2-22-2-22-2-2−2i−2i2i2i0000-2002200−2i2i00000000000002i−2i0000000000
χ21222222-22222-200-2-2-2222200000220000-2-20000220000-200000-200000000
χ22222222-22222-200-2-2-2222200000-2-20000-2-20000-2-20000200000200000000
χ23222222-22222-200-2-2-2-2-2-2-200000220000220000-2-20000-200000200000000
χ24222222-22222-200-2-2-2-2-2-2-200000-2-20000220000220000200000-200000000
χ25222222-2-2-2-2-2-200-2222i2i−2i−2i00000000000−2i2i000000000002-200002i−2i000000
χ26222222-2-2-2-2-2-200-2222i2i−2i−2i00000000000−2i2i00000000000-220000−2i2i000000
χ27222222-2-2-2-2-2-200-222−2i−2i2i2i000000000002i−2i000000000002-20000−2i2i000000
χ28222222-2-2-2-2-2-200-222−2i−2i2i2i000000000002i−2i00000000000-2200002i−2i000000
χ292222-2-2222-2-2222-22-200002222-2002-20000220000-2-20000000-2000000000
χ302222-2-2222-2-2222-22-20000-2-2-2-2-2002-20000-2-200002200000002000000000
χ312222-2-2222-2-22-2-2-22-200002222200-220000-2-20000-2-200000002000000000
χ322222-2-2222-2-22-2-2-22-20000-2-2-2-2200-220000220000220000000-2000000000
χ332222-2-22-2-222222-2-2200000000-200-22220000-2-20000-22000000000000000
χ342222-2-22-2-222222-2-2200000000-200-22-2-200002200002-2000000000000000
χ352222-2-22-2-2222-2-2-2-22000000002002-2220000-2-200002-2000000000000000
χ362222-2-22-2-2222-2-2-2-22000000002002-2-2-20000220000-22000000000000000
χ3722-2-22-202-22-20000002-22-2i2i2−i2−i202-200i2−i20000i2−i22-2i2−i200000000000i2−i2i2−i200
χ3822-2-22-202-22-20000002-22-2i2i2−i2−i20-2200i2−i20000i2−i2-22i2−i200000000000−i2i2−i2i200
χ3922-2-22-202-22-20000002-22-2−i2−i2i2i202-200−i2i20000−i2i22-2−i2i200000000000−i2i2−i2i200
χ4022-2-22-202-22-20000002-22-2−i2−i2i2i20-2200−i2i20000−i2i2-22−i2i200000000000i2−i2i2−i200
χ4122-2-22-202-22-2000000-22-22i2i2−i2−i202-200−i2i20000−i2i2-22i2−i200000000000i2−i2−i2i200
χ4222-2-22-202-22-2000000-22-22i2i2−i2−i20-2200−i2i20000−i2i22-2i2−i200000000000−i2i2i2−i200
χ4322-2-22-202-22-2000000-22-22−i2−i2i2i202-200i2−i20000i2−i2-22−i2i200000000000−i2i2i2−i200
χ4422-2-22-202-22-2000000-22-22−i2−i2i2i20-2200i2−i20000i2−i22-2−i2i200000000000i2−i2−i2i200
χ454444-4-4-444-4-4-4004-44000000000000000000000000000000000000000000
χ464444-4-4-4-4-444-40044-4000000000000000000000000000000000000000000
χ4744-4-44-40-44-440000004i−4i−4i4i00000000000000000000000000000000000000
χ4844-4-44-40-44-44000000−4i4i4i−4i00000000000000000000000000000000000000
χ4944-4-4-4404-4-4400000000002i22i2−2i2−2i2000000000000000−2i22i200000000000000000
χ5044-4-4-4404-4-440000000000−2i2−2i22i22i20000000000000002i2−2i200000000000000000
χ5144-4-4-440-444-400000000000000000002i2−2i20000−2i22i2000000000000000000000
χ5244-4-4-440-444-40000000000000000000−2i22i200002i2−2i2000000000000000000000
χ534-4-440040000-44i−4i000000022−2222−220000000002i2−2i200000000000000000000000
χ544-4-440040000-44i−4i0000000−2222−2222000000000−2i22i200000000000000000000000
χ554-4-440040000-4−4i4i000000022−2222−22000000000−2i22i200000000000000000000000
χ564-4-440040000-4−4i4i0000000−2222−22220000000002i2−2i200000000000000000000000
χ578-88-8000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ588-88-800000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ598-8-8800-80000800000000000000000000000000000000000000000000000

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