Finite Group Databasebeta

← Group #305749

Character table — Group #305749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444442222448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1111111-1-11111-1-1-1-1-1-11-111-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-11111-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-11111-111111-1-1-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-111-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-111-1
χ172222222222-2-22-22-22222-2-20000000022-2-20000220000-2-200000-20000000000000
χ182222222222-2-22-22-22222-2-200000000-2-2-2-20000-2-20000220000020000000000000
χ192222222222-2-22-22-2-2-2-2-2-2-20000000022220000-2-200002200000-20000000000000
χ202222222222-2-22-22-2-2-2-2-2-2-200000000-2-2220000220000-2-20000020000000000000
χ2122222222-2-222-22-220000-2-2222222-2-20000-2-2-2-2000000000000200000000000000
χ2222222222-2-222-22-220000-2-22222-2-222000022-2-2000000000000-200000000000000
χ2322222222-2-222-22-220000-2-2-2-2-2-222220000-2-222000000000000-200000000000000
χ2422222222-2-222-22-220000-2-2-2-2-2-2-2-2-2-200002222000000000000200000000000000
χ25222-2-22-2-22-200-202022-2-20022−2−200002i−2i00002−22i−2i22−2−200i2i2−i2−i200000000i2−i200000
χ26222-2-22-2-22-200-202022-2-20022−2−20000−2i2i00002−2−2i2i22−2−200−i2−i2i2i200000000−i2i200000
χ27222-2-22-2-22-200-202022-2-200−2−22200002i−2i0000−222i−2i−2−22200−i2−i2i2i200000000−i2i200000
χ28222-2-22-2-22-200-202022-2-200−2−2220000−2i2i0000−22−2i2i−2−22200i2i2−i2−i200000000i2−i200000
χ29222-2-22-2-22-200-2020-2-2220022−2−200002i−2i00002−2−2i2i−2−22200−i2−i2i2i200000000i2−i200000
χ30222-2-22-2-22-200-2020-2-2220022−2−20000−2i2i00002−22i−2i−2−22200i2i2−i2−i200000000−i2i200000
χ31222-2-22-2-22-200-2020-2-22200−2−22200002i−2i0000−22−2i2i22−2−200i2i2−i2−i200000000−i2i200000
χ32222-2-22-2-22-200-2020-2-22200−2−2220000−2i2i0000−222i−2i22−2−200−i2−i2i2i200000000i2−i200000
χ3322-2-22-2-222222-2-2-2-22-22-22-200002-200002-22-2000000000000000000002-20000000
χ3422-2-22-2-222222-2-2-2-22-22-22-20000-2200002-2-2200000000000000000000-220000000
χ3522-2-22-2-222222-2-2-2-2-22-222-200002-20000-222-200000000000000000000-220000000
χ3622-2-22-2-222222-2-2-2-2-22-222-20000-220000-22-22000000000000000000002-20000000
χ3722-2-22-2-2222-2-2-22-222-22-2-220000000000-22000000000000000000002i−2i00002i−2i000
χ3822-2-22-2-2222-2-2-22-222-22-2-220000000000-2200000000000000000000−2i2i0000−2i2i000
χ3922-2-22-2-2222-2-2-22-22-22-22-2200000000002-2000000000000000000002i−2i0000−2i2i000
χ4022-2-22-2-2222-2-2-22-22-22-22-2200000000002-200000000000000000000−2i2i00002i−2i000
χ4122-2-22-2-22-2-2222-22-20000-2200002-2000000-2200002i−2i2i−2i000000002i−2i00000000000
χ4222-2-22-2-22-2-2222-22-20000-2200002-2000000-220000−2i2i−2i2i00000000−2i2i00000000000
χ4322-2-22-2-22-2-2222-22-20000-220000-220000002-200002i−2i2i−2i00000000−2i2i00000000000
χ4422-2-22-2-22-2-2222-22-20000-220000-220000002-20000−2i2i−2i2i000000002i−2i00000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-4-440040-400000002222−22−220000000000−2222000000000000000000000000000
χ47444-4-44-4-4-440040-40000000−22−222222000000000022−22000000000000000000000000000
χ4844-44-4-44-44-40040-404-4-44000000000000000000000000000000000000000000000
χ4944-44-4-44-44-40040-40-444-4000000000000000000000000000000000000000000000
χ5044-44-4-44-4-4400-40400000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5144-44-4-44-4-4400-4040000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ5244-4-44-4-44-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ534-4444-4-4-40000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ544-4444-4-4-40000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ554-4444-4-4-400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ564-4444-4-4-400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ574-44-4-4-444004-4040-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ584-44-4-4-444004-4040-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ594-44-4-4-44400-440-4040000004-4-44000000000000000000000000000000000000000
χ604-44-4-4-44400-440-404000000-444-4000000000000000000000000000000000000000
χ614-4-44-44-44004-40-404000000000000000000000000000000000000000000000022−220
χ624-4-44-44-44004-40-4040000000000000000000000000000000000000000000000−22220
χ634-4-44-44-4400-44040-40000000000004i−4i00000000000000000000000000000000000
χ644-4-44-44-4400-44040-4000000000000−4i4i00000000000000000000000000000000000
χ658-8-8-8888-8000000000000000000000000000000000000000000000000000000000

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