Finite Group Databasebeta

← Group #166388

Character table — Group #166388

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122224444444444888888888888888881616161616161616161616161616161616161616
order12222222444444444444444444444448888888822444444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111-1-11-1-11-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-11-1-1111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1111111-1-1-1-1
χ911111111-1-1-1-1-1-11-1-11111111-1-1-111-1-11111-1-1-1-11-1-1111-1-11-11-111-1-111-1-1
χ1011111111-1-1-1-1-1-11-1-11111111-1-1-111-1-1-1-1-1-111111-1-1-1-11111-11-1-1-111-1-111
χ1111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1111111-1-1-1-1-11-1-1-1111-11-1111-1-1-1-111
χ1211111111-1-1-1-1-1-11-1-11111111-1-1-1-1-111-1-1-1-11111-11-1111-1-1-11-11-1-11111-1-1
χ1311111111-1-1-1-1-1-11-1-111111-1-1-11111-1-11111-1-1-1-1-11111-1-1-11-1-11-1-111-1-111
χ1411111111-1-1-1-1-1-11-1-111111-1-1-11111-1-1-1-1-1-11111-111-1-1-1111-1-1111-1-111-1-1
χ1511111111-1-1-1-1-1-11-1-111111-1-1-111-1-1111111-1-1-1-11-11-1-1-111-111-1-1-11111-1-1
χ1611111111-1-1-1-1-1-11-1-111111-1-1-111-1-111-1-1-1-111111-1111-1-1-1-111-111-1-1-1-111
χ1722222222222222-2-2-222-2-2-200-20022-2-20000000000000000-220000000000
χ1822222222222222-2-2-222-2-2-200-200-2-22200000000000000002-20000000000
χ19222222222222-2-2222-2-2-2-2222-22200000000000000-200-200000000000000
χ20222222222222-2-2222-2-2-2-22-2-2-2-2-200000000000000200200000000000000
χ21222222222222-2-2-2-2-2-2-222-2002000000000000002-200000000-2200000000
χ22222222222222-2-2-2-2-2-2-222-200200000000000000-22000000002-200000000
χ2322222222-2-2-2-2222-2-2-2-2-2-22222-2-200000000000000200-200000000000000
χ2422222222-2-2-2-2222-2-2-2-2-2-22-2-222200000000000000-200200000000000000
χ2522222222-2-2-2-222-222-2-222-200-2000000000000002200000000-2-200000000
χ2622222222-2-2-2-222-222-2-222-200-200000000000000-2-2000000002200000000
χ2722222222-2-2-2-2-2-2-22222-2-2-20020022220000000000000000-2-20000000000
χ2822222222-2-2-2-2-2-2-22222-2-2-200200-2-2-2-20000000000000000220000000000
χ292-22-2-22-2222-2-20022-20000-22-202-20000i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i20000
χ302-22-2-22-2222-2-20022-20000-22-202-20000−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i20000
χ312-22-2-22-2222-2-20022-20000-2-220-220000i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i20000
χ322-22-2-22-2222-2-20022-20000-2-220-220000−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i20000
χ332-22-2-22-22-2-222002-220000-22-20-220000i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i20000
χ342-22-2-22-22-2-222002-220000-22-20-220000−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i20000
χ352-22-2-22-22-2-222002-220000-2-2202-20000i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i20000
χ362-22-2-22-22-2-222002-220000-2-2202-20000−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i20000
χ374444-4-4-4-400004-4000000000000000002-22-22-22-200000000000000000000
χ384444-4-4-4-400004-400000000000000000-22-22-22-2200000000000000000000
χ394444-4-4-4-40000-44000000000000000002-22-2-22-2200000000000000000000
χ404444-4-4-4-40000-4400000000000000000-22-222-22-200000000000000000000
χ4144-4-44-4-440000000004-400000000004i−4i0000000000000000000000000000
χ4244-4-44-4-440000000004-40000000000−4i4i0000000000000000000000000000
χ4344-4-44-4-44000000000-44000000004i−4i000000000000000000000000000000
χ4444-4-44-4-44000000000-4400000000−4i4i000000000000000000000000000000
χ4544-4-4-444-44i−4i4i−4i0000000000000000000000000000002i−2i02-2000000000000
χ4644-4-4-444-44i−4i4i−4i000000000000000000000000000000−2i2i0-22000000000000
χ4744-4-4-444-4−4i4i−4i4i0000000000000000000000000000002i−2i0-22000000000000
χ4844-4-4-444-4−4i4i−4i4i000000000000000000000000000000−2i2i02-2000000000000
χ494-44-44-44-4000000000004-4000000000000002i2−2i2−2i22i200000000000000000000
χ504-44-44-44-4000000000004-400000000000000−2i22i22i2−2i200000000000000000000
χ514-44-44-44-400000000000-4400000000002i2−2i2−2i22i2000000000000000000000000
χ524-44-44-44-400000000000-440000000000−2i22i22i2−2i2000000000000000000000000
χ534-44-4-44-4444-4-400-4-44000040000000000000000000000000000000000000
χ544-44-4-44-44-4-44400-44-4000040000000000000000000000000000000000000
χ554-4-4444-4-44i−4i−4i4i00000000000000000000000000000000000000000002i−2i2-2
χ564-4-4444-4-44i−4i−4i4i0000000000000000000000000000000000000000000−2i2i-22
χ574-4-4444-4-4−4i4i4i−4i00000000000000000000000000000000000000000002i−2i-22
χ584-4-4444-4-4−4i4i4i−4i0000000000000000000000000000000000000000000−2i2i2-2
χ598-8-88-8-888000000000000000000000000000000000000000000000000000

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