Finite Group Databasebeta

← Group #272835

Character table — Group #272835

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222222244444444442244444444444444424444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1111111-1-1-1-1
χ51111111111111111111111-1-111111-1-111111111-11-1-1-1-111-1111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-1-111111111
χ71111111111111111111111-1-1-1-1-1-11-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111
χ9111111111111-1-1-1-11-1-11111111-1-1-1111111-1-1-1-1-1-1-111-111-11-1-111-1-111-1-1
χ10111111111111-1-1-1-11-1-11111111-1-1-111-1-1-1-11111-1-1-111-1-1-1-1111-1-111-1-111
χ11111111111111-1-1-1-11-1-111111-1-111-1111111-1-1-1-1-111-1-11-1-1-1-111-1-11111-1-1
χ12111111111111-1-1-1-11-1-111111-1-111-111-1-1-1-11111-111-1-1111-1-1-1-111-1-1-1-111
χ13111111111111-1-1-1-11-1-1111-1-111-1-1-1-1-11111-1-1-1-11-11-1-111111-1-1-1-111-1-111
χ14111111111111-1-1-1-11-1-1111-1-111-1-1-1-1-1-1-1-1-111111-11-1-11-1-1111111-1-111-1-1
χ15111111111111-1-1-1-11-1-1111-1-1-1-111-1-1-11111-1-1-1-111-111-1-1-11-11111-1-1-1-111
χ16111111111111-1-1-1-11-1-1111-1-1-1-111-1-1-1-1-1-1-1111111-111-1111-1-1-1-1-11111-1-1
χ172222222222222222-2-2-2-2-2-20022-2-2-20000000000020000000-20000000000
χ182222222222222222-2-2-2-2-2-200-2-222-200000000000-2000000020000000000
χ19222222222222-2-2-2-2-222-2-2-2002222200000000000-20000000-20000000000
χ20222222222222-2-2-2-2-222-2-2-200-2-2-2-22000000000002000000020000000000
χ2122222222-2-2-2-222-2-2222-2-22000000-200000000000022-2-200000000000000
χ2222222222-2-2-2-222-2-2222-2-22000000-2000000000000-2-22200000000000000
χ2322222222-2-2-2-222-2-2-2-2-222-22200002-2-20000000020000000-200000000000
χ2422222222-2-2-2-222-2-2-2-2-222-2-2-2000022200000000-20000000200000000000
χ2522222222-2-2-2-2-2-2222-2-2-2-2200000020000000000002-22-200000000000000
χ2622222222-2-2-2-2-2-2222-2-2-2-220000002000000000000-22-2200000000000000
χ2722222222-2-2-2-2-2-222-22222-2220000-2-2-200000000-20000000200000000000
χ2822222222-2-2-2-2-2-222-22222-2-2-20000-2220000000020000000-200000000000
χ292-2-2-222-2222-2-200002002-2-22-2000002-22i2i−2i−2i000000000000000000002i−2i00
χ302-2-2-222-2222-2-200002002-2-22-2000002-2−2i−2i2i2i00000000000000000000−2i2i00
χ312-2-2-222-2222-2-200002002-2-2-2200000-222i2i−2i−2i00000000000000000000−2i2i00
χ322-2-2-222-2222-2-200002002-2-2-2200000-22−2i−2i2i2i000000000000000000002i−2i00
χ332-2-2-222-22-2-2220000-2002-222-200000-22000022-2-20000000000000000002-2
χ342-2-2-222-22-2-2220000-2002-222-200000-220000-2-222000000000000000000-22
χ352-2-2-222-22-2-2220000-2002-22-22000002-2000022-2-2000000000000000000-22
χ362-2-2-222-22-2-2220000-2002-22-22000002-20000-2-2220000000000000000002-2
χ37444-44-4-4-400004-4000000000000000002-22-22-22-200000000000000000000
χ38444-44-4-4-400004-400000000000000000-22-22-22-2200000000000000000000
χ39444-44-4-4-40000-44000000000000000002-22-2-22-2200000000000000000000
χ40444-44-4-4-40000-4400000000000000000-22-222-22-200000000000000000000
χ4144-44-4-4-444-44-4000000000000004i−4i0000000000000000000000000000000
χ4244-44-4-4-444-44-400000000000000−4i4i0000000000000000000000000000000
χ4344-44-4-4-44-44-440000000000004i−4i000000000000000000000000000000000
χ4444-44-4-4-44-44-44000000000000−4i4i000000000000000000000000000000000
χ4544-4-4-444-40000004i−4i000000000000000000000000000002-2002i−2i00000000
χ4644-4-4-444-40000004i−4i00000000000000000000000000000-2200−2i2i00000000
χ4744-4-4-444-4000000−4i4i000000000000000000000000000002-200−2i2i00000000
χ4844-4-4-444-4000000−4i4i00000000000000000000000000000-22002i−2i00000000
χ494-44-4-4-4444-4-440000000000000000000000000000000000000000022−220000
χ504-44-4-4-4444-4-4400000000000000000000000000000000000000000−22220000
χ514-44-4-4-444-444-400000000000000000000000000000000000000022−22000000
χ524-44-4-4-444-444-4000000000000000000000000000000000000000−2222000000
χ534-4-444-44-40000000004i−4i0000000000002i−2i−2i2i2-2-2200000000000000000000
χ544-4-444-44-40000000004i−4i000000000000−2i2i2i−2i-222-200000000000000000000
χ554-4-444-44-4000000000−4i4i0000000000002i−2i−2i2i-222-200000000000000000000
χ564-4-444-44-4000000000−4i4i000000000000−2i2i2i−2i2-2-2200000000000000000000
χ574-4-4-444-4444-4-40000-400-4440000000000000000000000000000000000000
χ584-4-4-444-44-4-4440000400-44-40000000000000000000000000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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