Finite Group Databasebeta

← Group #285357

Character table — Group #285357

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444222248888888888884444488888888888848
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-11-111-11-1-1-1-11111-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-11111111-111-1-1-111-1-1-1-1-11-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-1-1-1-111-11
χ51111111111111111111-1-111111-1-1111111-11-1-11-11-1-1111-1-11-1-1-1-1
χ61111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11111
χ71111111111111111111-1-11-1-1-1-111111111-1-1-1-1-11-1-1-1-1-1-111111-11
χ81111111111111111111-1-11-1-1-1-111-1-1-1-1-1-1-11-1-1111111-1-111-1-1-11-1
χ91111111111111-1-111-1-111-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-111
χ101111111111111-1-111-1-111-1111111-1-111111-1-1-1-111111-1-1-1-1-111-1-1
χ111111111111111-1-111-1-111-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11-1-1111111111-1
χ121111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1111111-1-11-1-111-11111-1-1-1-11
χ131111111111111-1-111-1-1-1-1-11111-1-111-1-1-1-1-11111-1-111-1-1-111111-1-1
χ141111111111111-1-111-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-11-1-111-1-1-111
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11111111-1-11-1-1-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-11111-111111-1-1-1-111-1-1-1111-1
χ172222222-2-22-2-2222-2-2-2-20022i−2i2i−2i0000000000000000002i−2i0000000
χ182222222-2-22-2-2222-2-2-2-2002−2i2i−2i2i000000000000000000−2i2i0000000
χ192222222-2-22-2-22-2-2-2-22200-22i−2i2i−2i000000000000000000−2i2i0000000
χ202222222-2-22-2-22-2-2-2-22200-2−2i2i−2i2i0000000000000000002i−2i0000000
χ21222222-222-222-200-2-20022022-2-2-2-2000000-2000020000000000000
χ22222222-222-222-200-2-200220-2-22222000000-20000-20000000000000
χ23222222-222-222-200-2-200-2-2022-2-22200000020000-20000000000000
χ24222222-222-222-200-2-200-2-20-2-222-2-20000002000020000000000000
χ25222222-2-2-2-2-2-2-20022000002i−2i−2i2i00000000002-2000000002i−2i00000
χ26222222-2-2-2-2-2-2-20022000002i−2i−2i2i0000000000-2200000000−2i2i00000
χ27222222-2-2-2-2-2-2-2002200000−2i2i2i−2i00000000002-200000000−2i2i00000
χ28222222-2-2-2-2-2-2-2002200000−2i2i2i−2i0000000000-22000000002i−2i00000
χ292222-2-222-222-2-2222-22-200-20000002222-2-200000000000000-20000
χ302222-2-222-222-2-2222-22-200-2000000-2-2-2-2220000000000000020000
χ312222-2-222-222-2-2-2-22-2-2200200000022-2-22200000000000000-20000
χ322222-2-222-222-2-2-2-22-2-22002000000-2-222-2-20000000000000020000
χ332222-2-22-222-22-222-22-2200-20000000000000200-20200-2000000000
χ342222-2-22-222-22-222-22-2200-20000000000000-20020-2002000000000
χ352222-2-22-222-22-2-2-2-222-20020000000000000200-20-2002000000000
χ362222-2-22-222-22-2-2-2-222-20020000000000000-20020200-2000000000
χ374444-4-4-44-4-44-4400-44000000000000000000000000000000000000
χ384444-4-4-4-44-4-444004-4000000000000000000000000000000000000
χ3944-4-400-40040004i−4i00000000000002i2−2i222−22000000000000000000000
χ4044-4-400-40040004i−4i0000000000000−2i22i2−2222000000000000000000000
χ4144-4-400-4004000−4i4i00000000000002i2−2i2−2222000000000000000000000
χ4244-4-400-4004000−4i4i0000000000000−2i22i222−22000000000000000000000
χ434-44-44-40440-4-400000004-400000000000000000000000000000000
χ444-44-44-40440-4-40000000-4400000000000000000000000000000000
χ454-44-44-40-4-4044000000000000004-40000000000000000000000000
χ464-44-44-40-4-404400000000000000-440000000000000000000000000
χ474-44-4-4404-40-44000000000000000000000000000002i2−2i20000000000
χ484-44-4-4404-40-4400000000000000000000000000000−2i22i20000000000
χ494-44-4-440-4404-400000000000000000000000000000000000002i2−2i200
χ504-44-4-440-4404-40000000000000000000000000000000000000−2i22i200
χ5188-8-800800-80000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004i−4i0000000000000000000
χ538-8-880000000000000000000000000000−4i4i0000000000000000000

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