Finite Group Databasebeta

← Group #279924

Character table — Group #279924

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-11111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111111-111-1-1-1
χ91111111111111111-1-1-1-11111111111111111-1-111-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-111-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-11111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-11-1-11-1-1-1-11
χ17222222222-22-2-222-200002222-2-2222200002200-2-20000-2-20000000000000000-200000000
χ18222222222-22-2-222-200002222-2-2-2-2-2-20000-2-200-2-20000220000000000000000200000000
χ19222222222-22-2-222-20000-2-2-2-2-2-222220000-2-200220000-2-20000000000000000200000000
χ20222222222-22-2-222-20000-2-2-2-2-2-2-2-2-2-200002200220000220000000000000000-200000000
χ2122222222-22-222-2-2222220000-2-200002222002200-2-2-2-2000000000000000000000-200000
χ2222222222-22-222-2-2222220000-2-20000-2-2-2-200-2-200-2-222000000000000000000000200000
χ2322222222-22-222-2-22-2-2-2-20000-2-20000222200-2-20022-2-2000000000000000000000200000
χ2422222222-22-222-2-22-2-2-2-20000-2-20000-2-2-2-20022002222000000000000000000000-200000
χ25222-22-2-2-20202-200-222-2-200000022−2−222-2-2002-20000002−222−2−2000022−2−2000000002−2000
χ26222-22-2-2-20202-200-222-2-200000022−2−2-2-22200-220000002−222−2−20000−2−22200000000−22000
χ27222-22-2-2-20202-200-222-2-2000000−2−22222-2-2002-2000000−22−2−2220000−2−22200000000−22000
χ28222-22-2-2-20202-200-222-2-2000000−2−222-2-22200-22000000−22−2−222000022−2−2000000002−2000
χ29222-22-2-2-20202-200-2-2-22200000022−2−222-2-200-220000002−2−2−222000022−2−200000000−22000
χ30222-22-2-2-20202-200-2-2-22200000022−2−2-2-222002-20000002−2−2−2220000−2−222000000002−2000
χ31222-22-2-2-20202-200-2-2-222000000−2−22222-2-200-22000000−2222−2−20000−2−222000000002−2000
χ32222-22-2-2-20202-200-2-2-222000000−2−222-2-222002-2000000−2222−2−2000022−2−200000000−22000
χ3322-22-2-22-2-20-20022000002i2i−2i−2i002i−2i2i−2i2−22−22-20000002−2000000i2i2−i2−i2i2−i2i2−i200000000002−20
χ3422-22-2-22-2-20-20022000002i2i−2i−2i002i−2i2i−2i−22−222-2000000−22000000−i2−i2i2i2−i2i2−i2i20000000000−220
χ3522-22-2-22-2-20-20022000002i2i−2i−2i00−2i2i−2i2i2−22−2-220000002−2000000i2i2−i2−i2−i2i2−i2i20000000000−220
χ3622-22-2-22-2-20-20022000002i2i−2i−2i00−2i2i−2i2i−22−22-22000000−22000000−i2−i2i2i2i2−i2i2−i200000000002−20
χ3722-22-2-22-2-20-2002200000−2i−2i2i2i002i−2i2i−2i2−22−2-220000002−2000000−i2−i2i2i2i2−i2i2−i20000000000−220
χ3822-22-2-22-2-20-2002200000−2i−2i2i2i002i−2i2i−2i−22−22-22000000−22000000i2i2−i2−i2−i2i2−i2i200000000002−20
χ3922-22-2-22-2-20-2002200000−2i−2i2i2i00−2i2i−2i2i2−22−22-20000002−2000000−i2−i2i2i2−i2i2−i2i200000000002−20
χ4022-22-2-22-2-20-2002200000−2i−2i2i2i00−2i2i−2i2i−22−222-2000000−22000000i2i2−i2−i2i2−i2i2−i20000000000−220
χ412-2-222-2-2222-2-2-22-2200002i−2i2i−2i2-20000000000002i−2i0000002i−2i2i−2i00000000000002-2000000
χ422-2-222-2-2222-2-2-22-2200002i−2i2i−2i2-20000000000002i−2i000000−2i2i−2i2i0000000000000-22000000
χ432-2-222-2-2222-2-2-22-220000−2i2i−2i2i2-2000000000000−2i2i0000002i−2i2i−2i0000000000000-22000000
χ442-2-222-2-2222-2-2-22-220000−2i2i−2i2i2-2000000000000−2i2i000000−2i2i−2i2i00000000000002-2000000
χ452-2-222-2-222-2-2222-2-22-22-22i−2i2i−2i-22000000000000−2i2i2-200000000000000002i−2i00000000000
χ462-2-222-2-222-2-2222-2-22-22-2−2i2i−2i2i-220000000000002i−2i2-20000000000000000−2i2i00000000000
χ472-2-222-2-222-2-2222-2-2-22-222i−2i2i−2i-22000000000000−2i2i-220000000000000000−2i2i00000000000
χ482-2-222-2-222-2-2222-2-2-22-22−2i2i−2i2i-220000000000002i−2i-2200000000000000002i−2i00000000000
χ492-2-222-2-22-2-2222-22-22-22-200002-200000000000000-22000000002i−2i2i−2i0000002i−2i000000000
χ502-2-222-2-22-2-2222-22-22-22-200002-200000000000000-2200000000−2i2i−2i2i000000−2i2i000000000
χ512-2-222-2-22-2-2222-22-2-22-2200002-2000000000000002-2000000002i−2i2i−2i000000−2i2i000000000
χ522-2-222-2-22-2-2222-22-2-22-2200002-2000000000000002-200000000−2i2i−2i2i0000002i−2i000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-44-4-4-40-40-4400400000000002222−22−2200000000000000−22220000000000000000000000000
χ55444-44-4-4-40-40-440040000000000−22−2222220000000000000022−220000000000000000000000000
χ5644-44-4-44-440400-4-400000000000000022−2222−2200000000−2222000000000000000000000000000
χ5744-44-4-44-440400-4-4000000000000000−2222−22220000000022−22000000000000000000000000000
χ5844-4-4-44-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ5944-4-4-44-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ6044-4-4-44-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ6144-4-4-44-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ624-444-44-4-440-400-440000000000000000000000000000000000022−22−222200000000000000000
χ634-444-44-4-440-400-4400000000000000000000000000000000000−222222−2200000000000000000
χ644-444-44-4-4-404004-4000004-4-4400000000000000000000000000000000000000000000000
χ654-444-44-4-4-404004-400000-444-400000000000000000000000000000000000000000000000
χ664-4-444-4-44-444-4-4-44400000000-44000000000000000000000000000000000000000000000
χ674-4-4-4444-4040-4400-40000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ684-4-4-4444-4040-4400-4000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ694-4-4-4444-40-404-40044-4-44000000000000000000000000000000000000000000000000000
χ704-4-4-4444-40-404-4004-444-4000000000000000000000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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