Finite Group Databasebeta

← Group #309249

Character table — Group #309249

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888822444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111
χ4111111111111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-111-1-1-11111-1-1
χ51111111111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1111111-1-11-1-11-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1111-1
χ12111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-1111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11111111-1-1-1-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-111-1-1111-1
χ17222222222-2-222-22-2-2-22222000022000022-2-200000000000000-200-200000000
χ18222222222-2-222-22-2-2-222220000-2-20000-2-2-2-200000000000000200200000000
χ19222222222-2-222-22-2-2-2-2-2-2-20000220000-2-22200000000000000200-200000000
χ20222222222-2-222-22-2-2-2-2-2-2-20000-2-20000222200000000000000-200200000000
χ2122222222-222-2-22-22-2-20000222200-2-2-2-20000-2-2000022000000000000000000
χ2222222222-222-2-22-22-2-2000022-2-200-2-2220000220000-2-2000000000000000000
χ2322222222-222-2-22-22-2-20000-2-2220022-2-20000220000-2-2000000000000000000
χ2422222222-222-2-22-22-2-20000-2-2-2-20022220000-2-2000022000000000000000000
χ25222-22-2-2-22-2-2-2-22222-20000002i−2i00002i−2i00000022-2-2002i2i−2i−2i00000000000000
χ26222-22-2-2-22-2-2-2-22222-20000002i−2i00002i−2i000000-2-22200−2i−2i2i2i00000000000000
χ27222-22-2-2-22-2-2-2-22222-2000000−2i2i0000−2i2i00000022-2-200−2i−2i2i2i00000000000000
χ28222-22-2-2-22-2-2-2-22222-2000000−2i2i0000−2i2i000000-2-222002i2i−2i−2i00000000000000
χ29222-22-2-2-2-22222-2-2-22-222-2-20000000000002-20000000000002-202-2000000000
χ30222-22-2-2-2-22222-2-2-22-222-2-20000000000002-2000000000000-220-22000000000
χ31222-22-2-2-2-22222-2-2-22-2-2-222000000000000-220000000000002-20-22000000000
χ32222-22-2-2-2-22222-2-2-22-2-2-222000000000000-22000000000000-2202-2000000000
χ33222-22-2-2-2-2-2-2222-22-2222-2-2002i−2i0000−2i2i00-220000000000000000002i−2i000000
χ34222-22-2-2-2-2-2-2222-22-2222-2-200−2i2i00002i−2i00-22000000000000000000−2i2i000000
χ35222-22-2-2-2-2-2-2222-22-22-2-222002i−2i0000−2i2i002-2000000000000000000−2i2i000000
χ36222-22-2-2-2-2-2-2222-22-22-2-22200−2i2i00002i−2i002-20000000000000000002i−2i000000
χ3722-2-2-22-222002-20-20002i−2i2i−2i00002i−2i00002-2002−200002−2i2−i2i2−i200000000i2−i22−200
χ3822-2-2-22-222002-20-20002i−2i2i−2i00002i−2i00002-200−220000−22−i2i2−i2i200000000−i2i2−2200
χ3922-2-2-22-222002-20-20002i−2i2i−2i0000−2i2i0000-22002−200002−2i2−i2i2−i200000000−i2i2−2200
χ4022-2-2-22-222002-20-20002i−2i2i−2i0000−2i2i0000-2200−220000−22−i2i2−i2i200000000i2−i22−200
χ4122-2-2-22-222002-20-2000−2i2i−2i2i00002i−2i0000-22002−200002−2−i2i2−i2i200000000i2−i2−2200
χ4222-2-2-22-222002-20-2000−2i2i−2i2i00002i−2i0000-2200−220000−22i2−i2i2−i200000000−i2i22−200
χ4322-2-2-22-222002-20-2000−2i2i−2i2i0000−2i2i00002-2002−200002−2−i2i2−i2i200000000−i2i22−200
χ4422-2-2-22-222002-20-2000−2i2i−2i2i0000−2i2i00002-200−220000−22i2−i2i2−i200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-4444-4-4-44-4-4400000000000000000000000000000000000000000000
χ4744-44-4-44-4400-440-40000000000000000000000000000022−22−222200000000000000
χ4844-44-4-44-4400-440-400000000000000000000000000000−222222−2200000000000000
χ4944-44-4-44-4-4004-4040004i−4i−4i4i0000000000000000000000000000000000000000
χ5044-44-4-44-4-4004-404000−4i4i4i−4i0000000000000000000000000000000000000000
χ5144-4-4-44-44-400-440400000000000000000000022−220000−2222000000000000000000
χ5244-4-4-44-44-400-4404000000000000000000000−2222000022−22000000000000000000
χ534-4-444-4-4404-40040-400000000000000000000002i2−2i22i2−2i200000000000000000000
χ544-4-444-4-4404-40040-40000000000000000000000−2i22i2−2i22i200000000000000000000
χ554-4-444-4-440-4400-4040000000000004-400000000000000000000000000000000
χ564-4-444-4-440-4400-404000000000000-4400000000000000000000000000000000
χ574-4-4-4444-404-400-4040000004-400000000000000000000000000000000000000
χ584-4-4-4444-404-400-404000000-4400000000000000000000000000000000000000
χ594-4-4-4444-40-440040-400000000000000000000002i2−2i2−2i22i200000000000000000000
χ604-4-4-4444-40-440040-40000000000000000000000−2i22i22i2−2i200000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-88-8-8-888000000000000000000000000000000000000000000000000000000

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