Finite Group Databasebeta

← Group #166324

Character table — Group #166324

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444442244444448888888824444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-111-1-111111111-1-1-11-11-111-111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111
χ51111111111111111111111-1-1111-1-11111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-111-1-1-1-11111
χ71111111111111111111111-1-11-1-1-1-1-1-1111111111-1-1-11-11-1-11-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111111111-1-1-1-1
χ911111111-1-1-1-11-1-11-1-1111111-111-1-1-1-11111-1-1-1-111-1-111-111-1-1-111-1-111-1-1
χ1011111111-1-1-1-11-1-11-1-1111111-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-11-1-11-1-1111111-1-1-1-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-111-1-111
χ1211111111-1-1-1-11-1-11-1-1111111-1-1-1-1-111-1-1-1-11111-1-11-1-111-1-111111-1-111-1-1
χ1311111111-1-1-1-11-1-11-1-11111-1-1-11111-1-11111-1-1-1-1-11-11-1-11-1-111111-1-1-1-111
χ1411111111-1-1-1-11-1-11-1-11111-1-1-11111-1-1-1-1-1-11111-11-11-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-11-1-11-1-11111-1-1-1-1-111111111-1-1-1-11-1111-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11-1-11-1-11111-1-1-1-1-11111-1-1-1-111111-1111-1-111-1-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-22-2-2002000000000000002000-20200-20000000000
χ182222222222222-2-2-2-2-2-22-2-200200000000000000-200020-20020000000000
χ19222222222222-2222-2-2-2-22-222-200-2-2000000000000020-200000000000000
χ20222222222222-2222-2-2-2-22-2-2-2-200220000000000000-20200000000000000
χ21222222222222-2-2-2-2222-2-2200-2220022000000000-2-200000000000000000
χ22222222222222-2-2-2-2222-2-2200-2-2-200-2-20000000002200000000000000000
χ2322222222-2-2-2-2222-222-22-2-200-2000000000000002000-20-20020000000000
χ2422222222-2-2-2-2222-222-22-2-200-200000000000000-200020200-20000000000
χ2522222222-2-2-2-2-222-2-2-22-2-220022200-2-2000000000-2200000000000000000
χ2622222222-2-2-2-2-222-2-2-22-2-22002-2-200220000000002-200000000000000000
χ2722222222-2-2-2-2-2-2-2222-2-22-222200220000000000000-20-200000000000000
χ2822222222-2-2-2-2-2-2-2222-2-22-2-2-2200-2-2000000000000020200000000000000
χ292-2-2-2-222222-2-200002-2-20020002-2002-222−2−222−2−20000000000002−22−20000
χ302-2-2-2-222222-2-200002-2-20020002-2002-2−2−222−2−222000000000000−22−220000
χ312-2-2-2-222222-2-200002-2-2002000-2200-2222−2−222−2−2000000000000−22−220000
χ322-2-2-2-222222-2-200002-2-2002000-2200-22−2−222−2−2220000000000002−22−20000
χ332-2-2-2-2222-2-2220000-22-20020002-200-2222−2−2−2−2220000000000002−2−220000
χ342-2-2-2-2222-2-2220000-22-20020002-200-22−2−22222−2−2000000000000−222−20000
χ352-2-2-2-2222-2-2220000-22-2002000-22002-222−2−2−2−222000000000000−222−20000
χ362-2-2-2-2222-2-2220000-22-2002000-22002-2−2−22222−2−20000000000002−2−220000
χ37444-4-4-44-400004000000-40000000000022−2222−22000000000000000000000000
χ38444-4-4-44-400004000000-400000000000−2222−2222000000000000000000000000
χ39444-4-4-44-40000-400000040000000000000002i2−2i22i2−2i200000000000000000000
χ40444-4-4-44-40000-40000004000000000000000−2i22i2−2i22i200000000000000000000
χ4144-44-44-4-4000000040000-404-400000000000000000000000000000000000
χ4244-44-44-4-4000000040000-40-4400000000000000000000000000000000000
χ4344-44-44-4-40000000-4000040000004i−4i000000000000000000000000000000
χ4444-44-44-4-40000000-400004000000−4i4i000000000000000000000000000000
χ4544-4-44-4-444i−4i4i−4i00000000000000000000000000000000000000000002-22i−2i
χ4644-4-44-4-444i−4i4i−4i0000000000000000000000000000000000000000000-22−2i2i
χ4744-4-44-4-44−4i4i−4i4i00000000000000000000000000000000000000000002-2−2i2i
χ4844-4-44-4-44−4i4i−4i4i0000000000000000000000000000000000000000000-222i−2i
χ494-444-4-4-444i−4i−4i4i00000000000000000000000000000000002i−2i02-200000000
χ504-444-4-4-444i−4i−4i4i0000000000000000000000000000000000−2i2i0-2200000000
χ514-444-4-4-44−4i4i4i−4i00000000000000000000000000000000002i−2i0-2200000000
χ524-444-4-4-44−4i4i4i−4i0000000000000000000000000000000000−2i2i02-200000000
χ534-4-444-44-4000004i−4i00000000000000002-2-222i−2i−2i2i00000000000000000000
χ544-4-444-44-4000004i−4i0000000000000000-222-2−2i2i2i−2i00000000000000000000
χ554-4-444-44-400000−4i4i00000000000000002-2-22−2i2i2i−2i00000000000000000000
χ564-4-444-44-400000−4i4i0000000000000000-222-22i−2i−2i2i00000000000000000000
χ574-4-4-4-444444-4-40000-44400-40000000000000000000000000000000000000
χ584-4-4-4-4444-4-44400004-4400-40000000000000000000000000000000000000
χ598-88-888-8-8000000000000000000000000000000000000000000000000000

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