Finite Group Databasebeta

← Group #337624

Character table — Group #337624

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888884444444488888888444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-11-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-11-111-1111-1-1-1-111-1-1-1-11
χ41111111111111111111111-1-1-1-1-1-1-1-11111-1-1-11-1111-1-111-1-111-11-1
χ511111111111111111111-1-1111111111111-11-1-111-1-1-1-1-1-11111-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-1-1-1-111
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111111-1-111-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-111111-11-1-11-1-111-1-1-1-1111-11
χ9111111111111111111-1-1111111111111111-111-1-1-1-11111-1-1-1-1-1-1-1
χ10111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-111
χ11111111111111111111-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-11111-1-11-11
χ13111111111111111111-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-111-1-11111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-1111111-1-111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-11111-1-111-1-1-11-1
χ172222222222-2-22-2-22-2-20022000022-2-2000020-2-2000000000000000
χ182222222222-2-22-2-22-2-200220000-2-2220000-202-2000000000000000
χ192222222222-2-22-2-22-2-200-2-2000022-2-20000-2022000000000000000
χ202222222222-2-22-2-22-2-200-2-20000-2-222000020-22000000000000000
χ2122222222-2-222-222-2-2-2220022-2-2000000000200-2-20000000000000
χ2222222222-2-222-222-2-2-22200-2-222000000000-2002-20000000000000
χ2322222222-2-222-222-2-2-2-2-20022-2-2000000000-200220000000000000
χ2422222222-2-222-222-2-2-2-2-200-2-222000000000200-220000000000000
χ252-22-2-222-2-2-2222-2-222-200000000000000000000002i−2i002i−2i002-2000
χ262-22-2-222-2-2-2222-2-222-200000000000000000000002i−2i00−2i2i00-22000
χ272-22-2-222-2-2-2222-2-222-20000000000000000000000−2i2i002i−2i00-22000
χ282-22-2-222-2-2-2222-2-222-20000000000000000000000−2i2i00−2i2i002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ304444-4-4-4-4004-404-40000000000000002222−22−220000000000000000000
χ314444-4-4-4-4004-404-4000000000000000−22−2222220000000000000000000
χ324444-4-4-4-400-440-4400000004-400000000000000000000000000000
χ334444-4-4-4-400-440-440000000-4400000000000000000000000000000
χ3444-4-44-44-44-400400-400000000004-40000000000000000000000000
χ3544-4-44-44-44-400400-40000000000-440000000000000000000000000
χ3644-4-44-44-4-4400-4004000000000000002i2−2i22i2−2i20000000000000000000
χ3744-4-44-44-4-4400-400400000000000000−2i22i2−2i22i20000000000000000000
χ3844-4-4-44-4400000000000000002i2−2i20022−222i−2i−2i2i0000000000000000000
χ3944-4-4-44-4400000000000000002i2−2i200−2222−2i2i2i−2i0000000000000000000
χ4044-4-4-44-440000000000000000−2i22i20022−22−2i2i2i−2i0000000000000000000
χ4144-4-4-44-440000000000000000−2i22i200−22222i−2i−2i2i0000000000000000000
χ424-44-44-4-44004-40-440004i−4i000000000000000000000000000000000
χ434-44-44-4-44004-40-44000−4i4i000000000000000000000000000000000
χ444-44-44-4-4400-4404-400000000000000000000000000000002i2−2i200000
χ454-44-44-4-4400-4404-40000000000000000000000000000000−2i22i200000
χ464-44-4-444-44444-4-4-4-4-4400000000000000000000000000000000000
χ474-44-4-444-444-4-4-444-44-400000000000000000000000000000000000
χ484-44-4-444-4-4-4-4-44444-4400000000000000000000000000000000000
χ494-4-44-4-4444-400-400400004-40000000000000000000000000000000
χ504-4-44-4-4444-400-40040000-440000000000000000000000000000000
χ514-4-44-4-444-4400400-4000000000000000000000000002i2−2i2000000000
χ524-4-44-4-444-4400400-400000000000000000000000000−2i22i2000000000
χ538-8-8888-8-8000000000000000000000000000000000000000000000

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