Finite Group Databasebeta

← Group #337633

Character table — Group #337633

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888882444444488888888444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11-111111-111-1-1-1-1-1-1-11-1
χ31111111111111111111111-1-1-1-11111-1-1-1-111-111-111-1-1-1-111-1-1-1-11
χ41111111111111111111111-1-1-1-1-1-1-1-111111-1-111-11-1-1-111-1-1111-1-1
χ511111111111111111111-1-1111111111111-1-11-1-111-1-1-1-1-11111-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1-1-11-11
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1111111-1-111-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111-111
χ9111111111111111111-1-11111111111111111-1-1-1-1-111111-1-1-1-1-1-1-1
χ10111111111111111111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-111111-11
χ11111111111111111111-1-111-1-1-1-11111-1-1-1-1111-1-11-11-1-1-1-1-1-11111-1
χ12111111111111111111-1-111-1-1-1-1-1-1-1-111111-11-1-11-1-1-1-11111-1-1-111
χ13111111111111111111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-111-1-11-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1111-1-111-1-11-1-1
χ172222222222-22-2-2-22-2-20022000022-2-20000-2200000-200000000000
χ182222222222-22-2-2-22-2-200220000-2-2220000-2-200000200000000000
χ192222222222-22-2-2-22-2-200-2-2000022-2-200002-200000200000000000
χ202222222222-22-2-2-22-2-200-2-20000-2-22200002200000-200000000000
χ2122222222-2-22-2222-2-2-2220022-2-20000000000200-2-2000000000000
χ2222222222-2-22-2222-2-2-22200-2-2220000000000-2002-2000000000000
χ2322222222-2-22-2222-2-2-2-2-20022-2-20000000000-20022000000000000
χ2422222222-2-22-2222-2-2-2-2-200-2-2220000000000200-22000000000000
χ252-2-22-222-2-2-2-2222-222-200000000000000000002i−2i000002i−2i002-2000
χ262-2-22-222-2-2-2-2222-222-200000000000000000002i−2i00000−2i2i00-22000
χ272-2-22-222-2-2-2-2222-222-20000000000000000000−2i2i000002i−2i00-22000
χ282-2-22-222-2-2-2-2222-222-20000000000000000000−2i2i00000−2i2i002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ304444-4-4-4-40000000000000022−22000022−2222-2-20000000000000000000
χ314444-4-4-4-40000000000000022−220000−2222-2-2220000000000000000000
χ324444-4-4-4-400000000000000−2222000022−22-2-2220000000000000000000
χ334444-4-4-4-400000000000000−22220000−222222-2-20000000000000000000
χ3444-4-444-4-400404-4-40004-4000000000000000000000000000000000
χ3544-4-444-4-400404-4-4000-44000000000000000000000000000000000
χ3644-4-444-4-400-40-44400000000000000000000000000000002i2−2i200000
χ3744-4-444-4-400-40-4440000000000000000000000000000000−2i22i200000
χ3844-4-4-4-4444-404000-400004i−4i0000000000000000000000000000000
χ3944-4-4-4-4444-404000-40000−4i4i0000000000000000000000000000000
χ4044-4-4-4-444-440-400040000000000000000000000000022−22000000000
χ4144-4-4-4-444-440-4000400000000000000000000000000−2222000000000
χ424-44-44-44-44-40-4000400000000004i−4i0000000000000000000000000
χ434-44-44-44-44-40-400040000000000−4i4i0000000000000000000000000
χ444-44-44-44-4-4404000-40000000000000022−2222−220000000000000000000
χ454-44-44-44-4-4404000-400000000000000−2222−22220000000000000000000
χ464-44-4-44-440040-44-40000000004i−4i000000000000000000000000000
χ474-44-4-44-440040-44-4000000000−4i4i000000000000000000000000000
χ484-44-4-44-4400-404-4400000000000000022−22−22220000000000000000000
χ494-44-4-44-4400-404-44000000000000000−222222−220000000000000000000
χ504-4-44-444-4444-4-4-44-44-400000000000000000000000000000000000
χ514-4-44-444-444-4-444-4-4-4400000000000000000000000000000000000
χ524-4-44-444-4-4-444-4-444-4400000000000000000000000000000000000
χ538-8-888-8-88000000000000000000000000000000000000000000000

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