Finite Group Databasebeta

← Group #285194

Character table — Group #285194

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222224444444444444888888888888888881616161616161616161616161616163232
order12222244444444444888888884444488888888888822444888888888848
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1111111-1-1111111-1-1-111-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1111-1-1111-1-111-1-1-1-1-1
χ4111111111111111111111-1-1-1-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11111
χ511111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-11-1-11-1
χ611111111111111111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1111-1-1-1-1111-11
χ711111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11
χ811111111111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-11111111-1-1-1-1-11-1
χ9111111111111-1-111111111111-111-1-111111111-1-111-1-11-1-11-1-111-1-1-111-1-1
χ10111111111111-1-111111111111-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-111
χ11111111111111-1-11111111-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11-1-111
χ12111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-11111-1-1111-1-1
χ13111111111111-1-1111-1-1-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1111111-1-1-1-11
χ14111111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1111-1-1-1-111-1111-1
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11-1-1-111-1-1111111-1
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-11-1-111111-1-1-11
χ172222222-222-2200-2-2-22222000002200000022-2-2000000-200-200000000000
χ182222222-222-2200-2-2-2222200000-2-2000000-2-2-2-2000000200200000000000
χ192222222-222-2200-2-2-2-2-2-2-20000022000000-2-222000000-200200000000000
χ202222222-222-2200-2-2-2-2-2-2-200000-2-20000002222000000200-200000000000
χ21222222-22-2-22-2222-2-22i2i−2i−2i0000200-2-20000002i−2i000000000000002i−2i00000
χ22222222-22-2-22-2222-2-2−2i−2i2i2i0000200-2-2000000−2i2i00000000000000−2i2i00000
χ23222222-22-2-22-2-2-22-2-22i2i−2i−2i0000-200220000002i−2i00000000000000−2i2i00000
χ24222222-22-2-22-2-2-22-2-2−2i−2i2i2i0000-20022000000−2i2i000000000000002i−2i00000
χ25222222-2-2-2-2-2-200-2222i2i−2i−2i000000000000000−2i2i00002-200002i−2i000000000
χ26222222-2-2-2-2-2-200-2222i2i−2i−2i000000000000000−2i2i0000-220000−2i2i000000000
χ27222222-2-2-2-2-2-200-222−2i−2i2i2i0000000000000002i−2i00002-20000−2i2i000000000
χ28222222-2-2-2-2-2-200-222−2i−2i2i2i0000000000000002i−2i0000-2200002i−2i000000000
χ292222-2-222-2-22222-22-200002222-2002-20000000022-2-2000000000000-20000
χ302222-2-222-2-22222-22-20000-2-2-2-2-2002-200000000-2-22200000000000020000
χ312222-2-222-2-222-2-2-22-200002222200-2200000000-2-2-2-200000000000020000
χ322222-2-222-2-222-2-2-22-20000-2-2-2-2200-22000000002222000000000000-20000
χ332222-2-2-22222-222-2-2200000000-200-2222-2-2000000000002-2000000000000
χ342222-2-2-22222-222-2-2200000000-200-22-2-22200000000000-22000000000000
χ352222-2-2-22222-2-2-2-2-22000000002002-222-2-200000000000-22000000000000
χ362222-2-2-22222-2-2-2-2-22000000002002-2-2-222000000000002-2000000000000
χ3722-2-22-2-202-202000002i−2i2i−2ii2i2−i2−i202i−2i002−22−22-20000i2−i2000000002−2000i2−i200
χ3822-2-22-2-202-202000002i−2i2i−2ii2i2−i2−i20−2i2i002−22−2-220000i2−i200000000−22000−i2i200
χ3922-2-22-2-202-202000002i−2i2i−2i−i2−i2i2i202i−2i00−22−222-20000−i2i200000000−22000−i2i200
χ4022-2-22-2-202-202000002i−2i2i−2i−i2−i2i2i20−2i2i00−22−22-220000−i2i2000000002−2000i2−i200
χ4122-2-22-2-202-20200000−2i2i−2i2ii2i2−i2−i202i−2i00−22−22-220000i2−i2000000002−2000−i2i200
χ4222-2-22-2-202-20200000−2i2i−2i2ii2i2−i2−i20−2i2i00−22−222-20000i2−i200000000−22000i2−i200
χ4322-2-22-2-202-20200000−2i2i−2i2i−i2−i2i2i202i−2i002−22−2-220000−i2i200000000−22000i2−i200
χ4422-2-22-2-202-20200000−2i2i−2i2i−i2−i2i2i20−2i2i002−22−22-20000−i2i2000000002−2000−i2i200
χ454444-4-44-4-4-4-44004-44000000000000000000000000000000000000000000
χ464444-4-4-4-444-4-40044-4000000000000000000000000000000000000000000
χ4744-4-44-440-440-4000004-4-4400000000000000000000000000000000000000
χ4844-4-44-440-440-400000-444-400000000000000000000000000000000000000
χ4944-4-4-44404-40-400000000000000000022−22−22220000000000000000000000000
χ5044-4-4-44404-40-4000000000000000000−222222−220000000000000000000000000
χ5144-4-4-44-40-44040000000002i22i2−2i2−2i2000000000000000−2i22i200000000000000000
χ5244-4-4-44-40-4404000000000−2i2−2i22i22i20000000000000002i2−2i200000000000000000
χ534-4-44000400-404i−4i000000022−2222−2200000000000002i2−2i20000000000000000000
χ544-4-44000400-404i−4i0000000−2222−22220000000000000−2i22i20000000000000000000
χ554-4-44000400-40−4i4i000000022−2222−220000000000000−2i22i20000000000000000000
χ564-4-44000400-40−4i4i0000000−2222−222200000000000002i2−2i20000000000000000000
χ578-88-8000000000000000004i−4i−4i4i0000000000000000000000000000000000
χ588-88-800000000000000000−4i4i4i−4i0000000000000000000000000000000000
χ598-8-88000-8008000000000000000000000000000000000000000000000000

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