Finite Group Databasebeta

← Group #337654

Character table — Group #337654

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111111112222222244888888888888888816161616161616161616161616161616323232
order12222222444444444444448888888888884444444488888888244
χ111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-1-1-1-11-1
χ31111111111111111111111-1-1-1-11111-1-1-1-11-1-111111-1-1-1-111-1-1-1-11
χ41111111111111111111111-1-1-1-1-1-1-1-111111-1-111-11-1-1-111-1-1111-1-1
χ511111111111111111111-1-1111111111111-111-1-1-11-1-1-1-1-11111-1-1-1
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
χ811111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111-111
χ9111111111111111111-1-1111111111111111-1-1-1-11-111111-1-1-1-1-1-1-1
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
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-111
χ13111111111111111111-1-1-1-1111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1111
χ14111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-11111-1-111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1111-1-111-1-11-1-1
χ1722222222222-2-2-2-22-2-20022000022-2-20000-2000020-200000000000
χ1822222222222-2-2-2-22-2-200220000-2-2220000-20000-20200000000000
χ1922222222222-2-2-2-22-2-200-2-2000022-2-2000020000-20200000000000
χ2022222222222-2-2-2-22-2-200-2-20000-2-22200002000020-200000000000
χ2122222222-2-2-22222-2-2-2220022-2-20000000002-2000-2000000000000
χ2222222222-2-2-22222-2-2-22200-2-222000000000-22000-2000000000000
χ2322222222-2-2-22222-2-2-2-2-20022-2-2000000000-220002000000000000
χ2422222222-2-2-22222-2-2-2-2-200-2-2220000000002-20002000000000000
χ252-2-2222-2-2-2-2222-2-222-200000000000000000002i−2i000002i−2i002-2000
χ262-2-2222-2-2-2-2222-2-222-200000000000000000002i−2i00000−2i2i00-22000
χ272-2-2222-2-2-2-2222-2-222-20000000000000000000−2i2i000002i−2i00-22000
χ282-2-2222-2-2-2-2222-2-222-20000000000000000000−2i2i00000−2i2i002-2000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000
χ304444-4-4-4-40004-44-4000000000000000000000000000000022−2200000
χ314444-4-4-4-40004-44-40000000000000000000000000000000−222200000
χ324444-4-4-4-4000-44-440004-4000000000000000000000000000000000
χ334444-4-4-4-4000-44-44000-44000000000000000000000000000000000
χ3444-4-44-44-44-440000-4000000000000002222−22−220000000000000000000
χ3544-4-44-44-44-440000-400000000000000−22−2222220000000000000000000
χ3644-4-44-44-4-44-40000400000000004i−4i0000000000000000000000000
χ3744-4-44-44-4-44-4000040000000000−4i4i0000000000000000000000000
χ384-44-44-4-444-4-4000040000000000000000000000000022−22000000000
χ394-44-44-4-444-4-40000400000000000000000000000000−2222000000000
χ404-44-44-4-44-4440000-400004i−4i0000000000000000000000000000000
χ414-44-44-4-44-4440000-40000−4i4i0000000000000000000000000000000
χ424-44-4-444-4000000000000002i2−2i200002i2−2i22-22-20000000000000000000
χ434-44-4-444-4000000000000002i2−2i20000−2i22i2-22-220000000000000000000
χ444-44-4-444-400000000000000−2i22i200002i2−2i2-22-220000000000000000000
χ454-44-4-444-400000000000000−2i22i20000−2i22i22-22-20000000000000000000
χ464-4-4444-4-444-444-4-4-4-4400000000000000000000000000000000000
χ474-4-4444-4-444-4-4-444-44-400000000000000000000000000000000000
χ484-4-4444-4-4-4-44-4-4444-4400000000000000000000000000000000000
χ494-4-44-4-4440004-4-440000000004-4000000000000000000000000000
χ504-4-44-4-4440004-4-44000000000-44000000000000000000000000000
χ514-4-44-4-444000-444-400000000000000022−22−22220000000000000000000
χ524-4-44-4-444000-444-4000000000000000−222222−220000000000000000000
χ5388-8-8-88-88000000000000000000000000000000000000000000000

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