Finite Group Databasebeta

← Group #308556

Character table — Group #308556

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1111-1-1-111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-11-1-1-1-1-1-111-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111
χ71111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111
χ1011111111111111111-1-1-1-111111-1-1111111-1-1111111-1-1-1-111111-1-1-1-1-1-1-11111-1-1-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-111111-1-1-1-111-1-1-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-111-1-1-1-1-111-1-1111
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-111111-1-1-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-11-1-111-111-1-11111-1
χ17222222222-2-22-222-2-22222-20000-2-200000022-2-222000000000000000-2000000000
χ18222222222-2-22-222-2-22222-20000-2-2000000-2-222-2-20000000000000002000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000220000002222-2-2000000000000000-2000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022000000-2-2-2-2220000000000000002000000000
χ2122222222-222-22-2-22-20000-222220022-2-222000000-2-200000000-200000000000000
χ2222222222-222-22-2-22-20000-2222200-2-222-2-2000000-2-200000000200000000000000
χ2322222222-222-22-2-22-20000-2-2-2-2-20022-2-2-2-20000002200000000200000000000000
χ2422222222-222-22-2-22-20000-2-2-2-2-200-2-222220000002200000000-200000000000000
χ25222-2-22-2-2222-2-22-2-2222-2-2-200002-200000000000000000000000002-20002-200000
χ26222-2-22-2-2222-2-22-2-2222-2-2-200002-20000000000000000000000000-22000-2200000
χ27222-2-22-2-2222-2-22-2-22-2-222-20000-2200000000000000000000000002-2000-2200000
χ28222-2-22-2-2222-2-22-2-22-2-222-20000-220000000000000000000000000-220002-200000
χ29222-2-22-2-22-2-2-222-22-222-2-220000-222i−2i2i−2i0000000000000000000000002i−2i0000000
χ30222-2-22-2-22-2-2-222-22-222-2-220000-22−2i2i−2i2i000000000000000000000000−2i2i0000000
χ31222-2-22-2-22-2-2-222-22-2-2-222200002-22i−2i2i−2i000000000000000000000000−2i2i0000000
χ32222-2-22-2-22-2-2-222-22-2-2-222200002-2−2i2i−2i2i0000000000000000000000002i−2i0000000
χ33222-2-22-2-2-2-2-222-22220000-20000002i−2i−2i2i000000000022-2-2000002i−2i000000000000
χ34222-2-22-2-2-2-2-222-22220000-20000002i−2i−2i2i0000000000-2-22200000−2i2i000000000000
χ35222-2-22-2-2-2-2-222-22220000-2000000−2i2i2i−2i000000000022-2-200000−2i2i000000000000
χ36222-2-22-2-2-2-2-222-22220000-2000000−2i2i2i−2i0000000000-2-222000002i−2i000000000000
χ3722-22-2-22-2-200-2022002i−2i2i−2i022−2−2000000002i−2i002-22−2i2−i2i2−i222−2−2000000000000i2−i20
χ3822-22-2-22-2-200-2022002i−2i2i−2i022−2−200000000−2i2i00-222−2i2−i2i2−i2−2−222000000000000−i2i20
χ3922-22-2-22-2-200-2022002i−2i2i−2i0−2−222000000002i−2i002-2−22−i2i2−i2i2−2−222000000000000−i2i20
χ4022-22-2-22-2-200-2022002i−2i2i−2i0−2−22200000000−2i2i00-22−22−i2i2−i2i222−2−2000000000000i2−i20
χ4122-22-2-22-2-200-202200−2i2i−2i2i022−2−2000000002i−2i00-222−2−i2i2−i2i2−2−222000000000000i2−i20
χ4222-22-2-22-2-200-202200−2i2i−2i2i022−2−200000000−2i2i002-22−2−i2i2−i2i222−2−2000000000000−i2i20
χ4322-22-2-22-2-200-202200−2i2i−2i2i0−2−222000000002i−2i00-22−22i2−i2i2−i222−2−2000000000000−i2i20
χ4422-22-2-22-2-200-202200−2i2i−2i2i0−2−22200000000−2i2i002-2−22i2−i2i2−i2−2−222000000000000i2−i20
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-4-4444-4-44-4-4000040000000000000000000000000000000000000000000
χ4744-44-4-44-440040-4-400000002222−22−2200000000000000−222200000000000000000000000
χ4844-44-4-44-440040-4-40000000−22−2222220000000000000022−2200000000000000000000000
χ4944-4-44-4-44400-40-440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5044-4-44-4-44400-40-44000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5144-4-44-4-44-400404-4004i−4i−4i4i00000000000000000000000000000000000000000000
χ5244-4-44-4-44-400404-400−4i4i4i−4i00000000000000000000000000000000000000000000
χ534-444-4-4-44000000000000002i2−2i22i2−2i200000000002i2−2i2000000002-22-2000000000000000
χ544-444-4-4-44000000000000002i2−2i22i2−2i20000000000−2i22i200000000-22-22000000000000000
χ554-444-4-4-4400000000000000−2i22i2−2i22i200000000002i2−2i200000000-22-22000000000000000
χ564-444-4-4-4400000000000000−2i22i2−2i22i20000000000−2i22i2000000002-22-2000000000000000
χ574-4-4444-4-404-40400-400000000000000000000000000000022−22−2222000000000000000
χ584-4-4444-4-404-40400-4000000000000000000000000000000−222222−22000000000000000
χ594-4-4444-4-40-440-40040000004i−4i−4i4i000000000000000000000000000000000000000
χ604-4-4444-4-40-440-4004000000−4i4i4i−4i000000000000000000000000000000000000000
χ614-4-4-4-444404-40-400400000000000000004-40000000000000000000000000000000
χ624-4-4-4-444404-40-40040000000000000000-440000000000000000000000000000000
χ634-4-4-4-44440-440400-4000000000000000000000000000000000000000000002i2−2i2000
χ644-4-4-4-44440-440400-400000000000000000000000000000000000000000000−2i22i2000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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