Finite Group Databasebeta

← Group #244792

Character table — Group #244792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222222244888888882244444488888888888888882222444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-11-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ17222222222-22-22-22-222220000-2-2222200002200-2-200-2-20000000000000000000-20000000
χ18222222222-22-22-22-222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000000020000000
χ19222222222-22-22-22-2-2-2-2-20000-2-222220000-2-2002200-2-2000000000000000000020000000
χ20222222222-22-22-22-2-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000000-20000000
χ2122222222-22-22-22-2200002222-2-20000222200-2-2002200-2-20000000000000000-200000000
χ2222222222-22-22-22-2200002222-2-20000-2-2-2-200-2-200-2-200220000000000000000200000000
χ2322222222-22-22-22-220000-2-2-2-2-2-200002222002200-2-200-2-20000000000000000200000000
χ2422222222-22-22-22-220000-2-2-2-2-2-20000-2-2-2-20022002200220000000000000000-200000000
χ25222-22-2-2-220-20-202022-2-200000022-2-2i2i2−i2−i22-200000000i2−i20000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-22-2-2-220-20-202022-2-200000022-2-2−i2−i2i2i22-200000000−i2i20000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-22-2-2-220-20-202022-2-2000000-2-222i2i2−i2−i2-2200000000i2−i20000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-22-2-2-220-20-202022-2-2000000-2-222−i2−i2i2i2-2200000000−i2i20000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-22-2-2-220-20-2020-2-22200000022-2-2i2i2−i2−i2-2200000000i2−i20000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-22-2-2-220-20-2020-2-22200000022-2-2−i2−i2i2i2-2200000000−i2i20000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-22-2-2-220-20-2020-2-222000000-2-222i2i2−i2−i22-200000000i2−i20000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-22-2-2-220-20-2020-2-222000000-2-222−i2−i2i2i22-200000000−i2i20000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-2-2-2-2220-20-20202000022-2-2002−22−22-22-20000002-22−20022−2−200002−22−200000000002−20
χ3422-2-2-2-2220-20-20202000022-2-2002−22−2-22-22000000-222−20022−2−20000−22−220000000000−220
χ3522-2-2-2-2220-20-20202000022-2-200−22−222-22-20000002-2−2200−2−2220000−22−220000000000−220
χ3622-2-2-2-2220-20-20202000022-2-200−22−22-22-22000000-22−2200−2−22200002−22−200000000002−20
χ3722-2-2-2-2220-20-202020000-2-222002−22−22-22-2000000-222−200−2−22200002−22−20000000000−220
χ3822-2-2-2-2220-20-202020000-2-222002−22−2-22-220000002-22−200−2−2220000−22−2200000000002−20
χ3922-2-2-2-2220-20-202020000-2-22200−22−222-22-2000000-22−220022−2−20000−22−2200000000002−20
χ4022-2-2-2-2220-20-202020000-2-22200−22−22-22-220000002-2−220022−2−200002−22−20000000000−220
χ412-2-2-222-222-2-222-2-2200002-22-2-2200000000002-20000000000002-22-200000000002-200000
χ422-2-2-222-222-2-222-2-2200002-22-2-2200000000002-2000000000000-22-220000000000-2200000
χ432-2-2-222-222-2-222-2-220000-22-22-220000000000-220000000000002-22-20000000000-2200000
χ442-2-2-222-222-2-222-2-220000-22-22-220000000000-22000000000000-22-2200000000002-200000
χ452-2-2-222-22-222-2-222-22-22-20000-220000000000002-20000002-22-200000000002-2000000000
χ462-2-2-222-22-222-2-222-22-22-20000-220000000000002-2000000-22-220000000000-22000000000
χ472-2-2-222-22-222-2-222-2-22-220000-22000000000000-220000002-22-20000000000-22000000000
χ482-2-2-222-22-222-2-222-2-22-220000-22000000000000-22000000-22-2200000000002-2000000000
χ492-2-2-222-22-2-222-2-2222-22-22-22-22-20000000000-22-220000000000000000002-200000000000
χ502-2-2-222-22-2-222-2-2222-22-2-22-222-200000000002-2-22000000000000000000-2200000000000
χ512-2-2-222-22-2-222-2-222-22-222-22-22-20000000000-222-2000000000000000000-2200000000000
χ522-2-2-222-22-2-222-2-222-22-22-22-222-200000000002-22-20000000000000000002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-44-4-4-4-404040-40000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ55444-44-4-4-4-404040-4000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-44-44-4-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5744-44-44-4-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ5844-44-44-4-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5944-44-44-4-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ6044-4-4-4-44404040-40-4000000000022−2222−22000000000000−2222000000000000000000000000000
χ6144-4-4-4-44404040-40-40000000000−2222−222200000000000022−22000000000000000000000000000
χ624-444-4-4-44040-40-40400004-4-4400000000000000000000000000000000000000000000000
χ634-444-4-4-44040-40-4040000-444-400000000000000000000000000000000000000000000000
χ644-444-4-4-440-404040-400000000000000000000000000000022−22−2222000000000000000000000
χ654-444-4-4-440-404040-4000000000000000000000000000000−222222−22000000000000000000000
χ664-4-444-44-44040-40-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ674-4-444-44-44040-40-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ684-4-444-44-4-40-4040404-4-44000000000000000000000000000000000000000000000000000
χ694-4-444-44-4-40-404040-444-4000000000000000000000000000000000000000000000000000
χ704-4-4-444-4444-4-444-4-4000000004-4000000000000000000000000000000000000000000000
χ718-88-8-888-8000000000000000000000000000000000000000000000000000000000000000

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