Finite Group Databasebeta

← Group #285329

Character table — Group #285329

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444224448888888888882244488888888888848
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-11-1-111-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1111-1-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-11
χ51111111111111111111-1-111111-1-1111111-111-1-1111-1-1-11-1-11-1-1-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11111
χ71111111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-11
χ81111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-111-1-11-1-1111-1111-1-11-1
χ91111111111111-1-111-1-111-111111111-1-1-1-1111-1-1-1-1-11-1-11-1-1-1-1-111
χ101111111111111-1-111-1-111-1111111-1-111111-1-1-1-11-1-11-1-1-111111-1-1
χ111111111111111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1111-1111-1-11111-1
χ121111111111111-1-111-1-111-1-1-1-1-1-1-1-1-11111111-1-1-111-111-111-1-1-1-11
χ131111111111111-1-111-1-1-1-1-11111-1-111-1-1-1-1-11111-1-1-1-111111-111-1-1
χ141111111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-111-1-1-11-1-111
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-1-11111-1-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-11111-11111-1111-1-1-1-1-1-1111-1
χ1722222222-2-2-2-2222-2-2-2-20022i2i−2i−2i000000000000002i−2i00000000000
χ1822222222-2-2-2-2222-2-2-2-2002−2i−2i2i2i00000000000000−2i2i00000000000
χ1922222222-2-2-2-22-2-2-2-22200-22i2i−2i−2i00000000000000−2i2i00000000000
χ2022222222-2-2-2-22-2-2-2-22200-2−2i−2i2i2i000000000000002i−2i00000000000
χ21222222-2-22222-200-2-2002202-22-222000000-20000000-20000000000
χ22222222-2-22222-200-2-200220-22-22-2-2000000-2000000020000000000
χ23222222-2-22222-200-2-200-2-202-22-2-2-20000002000000020000000000
χ24222222-2-22222-200-2-200-2-20-22-222200000020000000-20000000000
χ25222222-2-2-2-2-2-2-20022000002i−2i−2i2i000000000002-200002i−2i00000000
χ26222222-2-2-2-2-2-2-20022000002i−2i−2i2i00000000000-220000−2i2i00000000
χ27222222-2-2-2-2-2-2-2002200000−2i2i2i−2i000000000002-20000−2i2i00000000
χ28222222-2-2-2-2-2-2-2002200000−2i2i2i−2i00000000000-2200002i−2i00000000
χ292222-2-22222-2-2-2222-22-200-20000002222-2-200000000000-20000000
χ302222-2-22222-2-2-2222-22-200-2000000-2-2-2-2220000000000020000000
χ312222-2-22222-2-2-2-2-22-2-2200200000022-2-22200000000000-20000000
χ322222-2-22222-2-2-2-2-22-2-22002000000-2-222-2-20000000000020000000
χ332222-2-222-2-222-222-22-2200-200000000000002-200200000000-20000
χ342222-2-222-2-222-222-22-2200-20000000000000-2200-20000000020000
χ352222-2-222-2-222-2-2-2-222-200200000000000002-200-20000000020000
χ362222-2-222-2-222-2-2-2-222-20020000000000000-2200200000000-20000
χ374444-4-4-4-444-4-4400-44000000000000000000000000000000000000
χ384444-4-4-4-4-4-4444004-4000000000000000000000000000000000000
χ3944-4-400-44000004i−4i00000000000002i2−2i222−22000000000000000000000
χ4044-4-400-44000004i−4i0000000000000−2i22i2−2222000000000000000000000
χ4144-4-400-4400000−4i4i00000000000002i2−2i2−2222000000000000000000000
χ4244-4-400-4400000−4i4i0000000000000−2i22i222−22000000000000000000000
χ434-44-44-4004-44-400000000000000000000000000000000000002i2−2i200
χ444-44-44-4004-44-40000000000000000000000000000000000000−2i22i200
χ454-44-44-400-44-4400000000000000000000000000000000002i2−2i200000
χ464-44-44-400-44-440000000000000000000000000000000000−2i22i200000
χ474-44-4-44004-4-44000000000000004i−4i0000000000000000000000000
χ484-44-4-44004-4-4400000000000000−4i4i0000000000000000000000000
χ494-44-4-4400-444-400000004i−4i00000000000000000000000000000000
χ504-44-4-4400-444-40000000−4i4i00000000000000000000000000000000
χ5188-8-8008-8000000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004-40000000000000000000
χ538-8-880000000000000000000000000000-440000000000000000000

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