Finite Group Databasebeta

← Group #308533

Character table — Group #308533

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-111-1-1-1
χ31111111111111111111111111111-1-1111111-1-1111111-1-1-1-1-1-11-1-111-111-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-111-1-111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1111
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111-1-11
χ101111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-111-1-111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-111111-1-1-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111111-1-1-1-111111-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1111-1-1-111-1-11111-1
χ17222222222-2-2222-2-22222-2-20000-2-22200000022000000-2-2000000000-2000000000
χ18222222222-2-2222-2-22222-2-20000-2-2-2-2000000-2-2000000220000000002000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-200002222000000-2-200000022000000000-2000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2000022-2-200000022000000-2-20000000002000000000
χ2122222222-222-2-2-2220000-2-22222000022-2-2-2-200-2-20000000000200000000000000
χ2222222222-222-2-2-2220000-2-222220000-2-2222200-2-20000000000-200000000000000
χ2322222222-222-2-2-2220000-2-2-2-2-2-200002222-2-200220000000000-200000000000000
χ2422222222-222-2-2-2220000-2-2-2-2-2-20000-2-2-2-22200220000000000200000000000000
χ25222-22-2-2-2222-22-2-2-222-2-22-200002-2000000000000000000000002-2000002-200000
χ26222-22-2-2-2222-22-2-2-222-2-22-200002-200000000000000000000000-2200000-2200000
χ27222-22-2-2-2222-22-2-2-2-2-2222-20000-22000000000000000000000002-200000-2200000
χ28222-22-2-2-2222-22-2-2-2-2-2222-20000-2200000000000000000000000-22000002-200000
χ29222-22-2-2-22-2-2-22-22222-2-2-220000-22002i−2i002i−2i000000000000000000002i−2i0000000
χ30222-22-2-2-22-2-2-22-22222-2-2-220000-2200−2i2i00−2i2i00000000000000000000−2i2i0000000
χ31222-22-2-2-22-2-2-22-222-2-222-2200002-2002i−2i002i−2i00000000000000000000−2i2i0000000
χ32222-22-2-2-22-2-2-22-222-2-222-2200002-200−2i2i00−2i2i000000000000000000002i−2i0000000
χ33222-22-2-2-2-2-2-22-222200002-2000000002i−2i00−2i2i000022-2-20000000002i−2i0000000000
χ34222-22-2-2-2-2-2-22-222200002-2000000002i−2i00−2i2i0000-2-222000000000−2i2i0000000000
χ35222-22-2-2-2-2-2-22-222200002-200000000−2i2i002i−2i000022-2-2000000000−2i2i0000000000
χ36222-22-2-2-2-2-2-22-222200002-200000000−2i2i002i−2i0000-2-2220000000002i−2i0000000000
χ3722-2-2-22-22200-2-22002-22-200i2i2−i2−i2002i−2i0000002i−2ii2−i2i2−i2i2−i20022−2−200000000002−2000
χ3822-2-2-22-22200-2-22002-22-200i2i2−i2−i200−2i2i000000−2i2ii2−i2i2−i2i2−i200−2−2220000000000−22000
χ3922-2-2-22-22200-2-22002-22-200−i2−i2i2i2002i−2i0000002i−2i−i2i2−i2i2−i2i200−2−2220000000000−22000
χ4022-2-2-22-22200-2-22002-22-200−i2−i2i2i200−2i2i000000−2i2i−i2i2−i2i2−i2i20022−2−200000000002−2000
χ4122-2-2-22-22200-2-2200-22-2200i2i2−i2−i2002i−2i000000−2i2ii2−i2−i2i2−i2i200−2−22200000000002−2000
χ4222-2-2-22-22200-2-2200-22-2200i2i2−i2−i200−2i2i0000002i−2ii2−i2−i2i2−i2i20022−2−20000000000−22000
χ4322-2-2-22-22200-2-2200-22-2200−i2−i2i2i2002i−2i000000−2i2i−i2i2i2−i2i2−i20022−2−20000000000−22000
χ4422-2-2-22-22200-2-2200-22-2200−i2−i2i2i200−2i2i0000002i−2i−i2i2i2−i2i2−i200−2−22200000000002−2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-4-4444-44-4-40000-440000000000000000000000000000000000000000000
χ4744-44-4-44-44004-4-4004-4-44000000000000000000000000000000000000000000000
χ4844-44-4-44-44004-4-400-444-4000000000000000000000000000000000000000000000
χ4944-44-4-44-4-400-444000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5044-44-4-44-4-400-44400000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5144-4-4-44-44-40044-4000000002i22i2−2i2−2i2000000000000−2i22i20000000000000000000000000
χ5244-4-4-44-44-40044-400000000−2i2−2i22i22i20000000000002i2−2i20000000000000000000000000
χ534-444-4-4-4404-40004-400000000000000000000000000000000000000000000002i2−2i20
χ544-444-4-4-4404-40004-40000000000000000000000000000000000000000000000−2i22i20
χ554-444-4-4-440-44000-4400000000000000004i−4i0000000000000000000000000000000
χ564-444-4-4-440-44000-440000000000000000−4i4i0000000000000000000000000000000
χ574-44-4-444-404-4000-440000004i−4i4i−4i000000000000000000000000000000000000000
χ584-44-4-444-404-4000-44000000−4i4i−4i4i000000000000000000000000000000000000000
χ594-44-4-444-40-440004-40000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ604-44-4-444-40-440004-4000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ614-4-4444-4-40000000000000022−22−22220000000000000000002i2−2i22i−2i−2i2i000000000000000
χ624-4-4444-4-40000000000000022−22−2222000000000000000000−2i22i2−2i2i2i−2i000000000000000
χ634-4-4444-4-400000000000000−222222−220000000000000000002i2−2i2−2i2i2i−2i000000000000000
χ644-4-4444-4-400000000000000−222222−22000000000000000000−2i22i22i−2i−2i2i000000000000000
χ658-8-8-88-888000000000000000000000000000000000000000000000000000000000

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