Finite Group Databasebeta

← Group #285351

Character table — Group #285351

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444422444244448888888888882444488888888888828
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-111-1-1-1-1-1111-11-111-1-1-1-111-1-1-1-1
χ31111111111111111111111-1-1-1-111-1-11111-1111-1-1-1-1-1111-1-1-1-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-1-1-1-1-11-1-111-11
χ511111111111111111111-1-1111111-1-111111-1-1-11-11111-1-11-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11111
χ711111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11-1-1-11-1-1-11111-11
χ811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1111-1-1-111111-1-11-1
χ9111111111111-1-1111-1-1-11111111111-1-1-1-111-1-111-1-1-11-1-1-1-1-1-1-111
χ10111111111111-1-1111-1-1-1111111-1-1111111-11-1-1-111-1-1-1111-1-111-1-1
χ11111111111111-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1-11-1-1-1-11111-1-1111111-1
χ12111111111111-1-1111-1-1-111-1-1-1-1-1-1-1-1111111-1-11-1-111-111-111-1-1-11
χ13111111111111-1-1111-1-1-1-1-1111111-1-1-1-1-1-11-1111-1-1-1-1111-11111-1-1
χ14111111111111-1-1111-1-1-1-1-11111-1-1-1-11111-1-111-1-11-1-1-1-1-1111-1-111
χ15111111111111-1-1111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111111111-1-1-1-1-11
χ16111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-11111111-11111-111-1-1-1-1-1-1111-1
χ172222222-22-2-2-2222-2-22-2-2002i2i−2i−2i0000000000000002i−2i0000000000
χ182222222-22-2-2-2222-2-22-2-200−2i−2i2i2i000000000000000−2i2i0000000000
χ192222222-22-2-2-2-2-22-2-2-222002i2i−2i−2i000000000000000−2i2i0000000000
χ202222222-22-2-2-2-2-22-2-2-22200−2i−2i2i2i0000000000000002i−2i0000000000
χ21222222-22-222200-2-2-2000222-22-2002200000-2000-20000000000000
χ22222222-22-222200-2-2-200022-22-2200-2-200000-200020000000000000
χ23222222-22-222200-2-2-2000-2-22-22-200-2-200000200020000000000000
χ24222222-22-222200-2-2-2000-2-2-22-220022000002000-20000000000000
χ25222222-2-2-2-2-2-200-222000002i−2i−2i2i00000000002-20000000002i−2i0000
χ26222222-2-2-2-2-2-200-222000002i−2i−2i2i0000000000-22000000000−2i2i0000
χ27222222-2-2-2-2-2-200-22200000−2i2i2i−2i00000000002-2000000000−2i2i0000
χ28222222-2-2-2-2-2-200-22200000−2i2i2i−2i0000000000-220000000002i−2i0000
χ292222-2-2222-2-2222-22-2-22-2000000000000002000-20-2000002000000
χ302222-2-2222-2-2222-22-2-22-200000000000000-200020200000-2000000
χ312222-2-2222-2-22-2-2-22-22-22000000000000002000-20200000-2000000
χ322222-2-2222-2-22-2-2-22-22-2200000000000000-200020-2000002000000
χ332222-2-22-2222-222-2-22-2-22000000220022-2-2000000000-2000000000
χ342222-2-22-2222-222-2-22-2-22000000-2-200-2-2220000000002000000000
χ352222-2-22-2222-2-2-2-2-2222-20000002200-2-222000000000-2000000000
χ362222-2-22-2222-2-2-2-2-2222-2000000-2-20022-2-20000000002000000000
χ374444-4-4-44-4-4-44004-44000000000000000000000000000000000000
χ384444-4-4-4-4-444-40044-4000000000000000000000000000000000000
χ3944-4-400-4040004-40000000000002i2−2i2002i2−2i2000000000000000000000
χ4044-4-400-4040004-4000000000000−2i22i200−2i22i2000000000000000000000
χ4144-4-400-404000-440000000000002i2−2i200−2i22i2000000000000000000000
χ4244-4-400-404000-44000000000000−2i22i2002i2−2i2000000000000000000000
χ434-44-44-40404-4-400000000000000000000000000000000000002i2−2i200
χ444-44-44-40404-4-40000000000000000000000000000000000000−2i22i200
χ454-44-44-40-40-4440000000000000000000000000000000022−220000000
χ464-44-44-40-40-44400000000000000000000000000000000−22220000000
χ474-44-4-44040-44-4000000004i−4i0000000000000000000000000000000
χ484-44-4-44040-44-400000000−4i4i0000000000000000000000000000000
χ494-44-4-440-404-4400000000000000004-400000000000000000000000
χ504-44-4-440-404-440000000000000000-4400000000000000000000000
χ5188-8-80080-800000000000000000000000000000000000000000000
χ528-8-8800000000000000000000000000004-40000000000000000000
χ538-8-880000000000000000000000000000-440000000000000000000

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