Finite Group Databasebeta

← Group #337637

Character table — Group #337637

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888882444444488888888444
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11
χ31111111111111111111111-1-1-1-11111-1-1-1-11-1-111111-1-1-1-111-1-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1111-1-1
χ511111111111111111111-1-11111111111111-1-1-1-1-1111111-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1111111-1
χ711111111111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1-1111-11
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-111
χ9111111111111111111-1-111111111111111-1111-1-1-1-1-1-1-1-11111-1-1-1
χ10111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-111-1
χ11111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-1-1-1111111-1-11-11
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-11-1-11111-1-1-1-111-111
χ13111111111111111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-11111-1-111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1111111-1-111-1-11-1-1
χ172222222222-22-2-2-22-2-22200000022-2-20000-2000002-200000000000
χ182222222222-22-2-2-22-2-222000000-2-2220000-200000-2200000000000
χ192222222222-22-2-2-22-2-2-2-200000022-2-20000200000-2200000000000
χ202222222222-22-2-2-22-2-2-2-2000000-2-22200002000002-200000000000
χ2122222222-2-22-2222-2-2-2002222-2-20000000002-2-2000000000000000
χ2222222222-2-22-2222-2-2-20022-2-222000000000-22-2000000000000000
χ2322222222-2-22-2222-2-2-200-2-222-2-2000000000-222000000000000000
χ2422222222-2-22-2222-2-2-200-2-2-2-2220000000002-22000000000000000
χ252-2222-2-2-2-2-2-2222-222-2000000000000000000002i−2i00002i−2i002-2000
χ262-2222-2-2-2-2-2-2222-222-2000000000000000000002i−2i0000−2i2i00-22000
χ272-2222-2-2-2-2-2-2222-222-200000000000000000000−2i2i00002i−2i00-22000
χ282-2222-2-2-2-2-2-2222-222-200000000000000000000−2i2i0000−2i2i002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ3044-44-44-4-400404-4-4000000000000000000000000000000022−2200000
χ3144-44-44-4-400404-4-40000000000000000000000000000000−222200000
χ3244-44-44-4-400-40-444000004i−4i0000000000000000000000000000000
χ3344-44-44-4-400-40-44400000−4i4i0000000000000000000000000000000
χ3444-4-44-44-44-404000-4000000000000002222−22−220000000000000000000
χ3544-4-44-44-44-404000-400000000000000−22−2222220000000000000000000
χ3644-4-44-44-4-440-4000400000000004i−4i0000000000000000000000000
χ3744-4-44-44-4-440-400040000000000−4i4i0000000000000000000000000
χ384-4444-4-4-4444-4-4-44-44-400000000000000000000000000000000000
χ394-4444-4-4-444-4-444-4-4-4400000000000000000000000000000000000
χ404-4444-4-4-4-4-444-4-444-4400000000000000000000000000000000000
χ414-44-4-444-4000000000000002i2−2i2000022−222i−2i2i−2i0000000000000000000
χ424-44-4-444-4000000000000002i2−2i20000−2222−2i2i−2i2i0000000000000000000
χ434-44-4-444-400000000000000−2i22i2000022−22−2i2i−2i2i0000000000000000000
χ444-44-4-444-400000000000000−2i22i20000−22222i−2i2i−2i0000000000000000000
χ454-4-44-4-4440040-44-40000000000000002i2−2i2−2i22i20000000000000000000
χ464-4-44-4-4440040-44-4000000000000000−2i22i22i2−2i20000000000000000000
χ474-4-44-4-44400-404-440000000004-4000000000000000000000000000
χ484-4-44-4-44400-404-44000000000-44000000000000000000000000000
χ494-4-4-444-444-40-400040000000000000000000000000022−22000000000
χ504-4-4-444-444-40-4000400000000000000000000000000−2222000000000
χ514-4-4-444-44-4404000-4004i−4i000000000000000000000000000000000
χ524-4-4-444-44-4404000-400−4i4i000000000000000000000000000000000
χ53888-8-8-8-88000000000000000000000000000000000000000000000

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