Finite Group Databasebeta

← Group #310176

Character table — Group #310176

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882224444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111111-1-11-1-1-1-1-1-11
χ172222222222-2-22-2-2200002222-2-200002222000022-2-200-2-200000000000000-20000000000
χ182222222222-2-22-2-2200002222-2-20000-2-2-2-20000-2-2-2-200220000000000000020000000000
χ192222222222-2-22-2-220000-2-2-2-2-2-2000022220000-2-22200-2-20000000000000020000000000
χ202222222222-2-22-2-220000-2-2-2-2-2-20000-2-2-2-200002222002200000000000000-20000000000
χ2122222222-2-222-222-222220000-2-222220000-2-2220000-2-20000000000000000000-20000000
χ2222222222-2-222-222-222220000-2-2-2-2-2-20000-2-2-2-2000022000000000000000000020000000
χ2322222222-2-222-222-2-2-2-2-20000-2-22222000022-2-20000-2-2000000000000000000020000000
χ2422222222-2-222-222-2-2-2-2-20000-2-2-2-2-2-2000022220000220000000000000000000-20000000
χ25222-2-2-2-222-200-200200002i2i−2i−2i00i2i2−i2−i222-2-200002i−2i00i2−i20022−2−20000i2i2−i2−i2000000002−2000
χ26222-2-2-2-222-200-200200002i2i−2i−2i00i2i2−i2−i2-2-2220000−2i2i00i2−i20022−2−20000−i2−i2i2i200000000−22000
χ27222-2-2-2-222-200-200200002i2i−2i−2i00−i2−i2i2i222-2-200002i−2i00−i2i200−2−2220000−i2−i2i2i200000000−22000
χ28222-2-2-2-222-200-200200002i2i−2i−2i00−i2−i2i2i2-2-2220000−2i2i00−i2i200−2−2220000i2i2−i2−i2000000002−2000
χ29222-2-2-2-222-200-20020000−2i−2i2i2i00i2i2−i2−i222-2-20000−2i2i00i2−i200−2−2220000i2i2−i2−i200000000−22000
χ30222-2-2-2-222-200-20020000−2i−2i2i2i00i2i2−i2−i2-2-22200002i−2i00i2−i200−2−2220000−i2−i2i2i2000000002−2000
χ31222-2-2-2-222-200-20020000−2i−2i2i2i00−i2−i2i2i222-2-20000−2i2i00−i2i20022−2−20000−i2−i2i2i2000000002−2000
χ32222-2-2-2-222-200-20020000−2i−2i2i2i00−i2−i2i2i2-2-22200002i−2i00−i2i20022−2−20000i2i2−i2−i200000000−22000
χ3322-2-2-222-22-2222-2-2-22i2i−2i−2i2i−2i2i−2i-22000000002i−2i00002i−2i00000000000000002-200000000000
χ3422-2-2-222-22-2222-2-2-22i2i−2i−2i−2i2i−2i2i-22000000002i−2i0000−2i2i0000000000000000-2200000000000
χ3522-2-2-222-22-2222-2-2-2−2i−2i2i2i2i−2i2i−2i-2200000000−2i2i00002i−2i0000000000000000-2200000000000
χ3622-2-2-222-22-2222-2-2-2−2i−2i2i2i−2i2i−2i2i-2200000000−2i2i0000−2i2i00000000000000002-200000000000
χ3722-2-2-222-22-2-2-2222-200002i−2i2i−2i2-200000000000000−2i2i0000000022-2-200000000002i−2i00000
χ3822-2-2-222-22-2-2-2222-200002i−2i2i−2i2-200000000000000−2i2i00000000-2-2220000000000−2i2i00000
χ3922-2-2-222-22-2-2-2222-20000−2i2i−2i2i2-2000000000000002i−2i0000000022-2-20000000000−2i2i00000
χ4022-2-2-222-22-2-2-2222-20000−2i2i−2i2i2-2000000000000002i−2i00000000-2-22200000000002i−2i00000
χ4122-2-2-222-2-2222-2-2-222i2i−2i−2i00002-200000000−2i2i00000000002i−2i2i−2i000000000002-200000000
χ4222-2-2-222-2-2222-2-2-222i2i−2i−2i00002-200000000−2i2i0000000000−2i2i−2i2i00000000000-2200000000
χ4322-2-2-222-2-2222-2-2-22−2i−2i2i2i00002-2000000002i−2i00000000002i−2i2i−2i00000000000-2200000000
χ4422-2-2-222-2-2222-2-2-22−2i−2i2i2i00002-2000000002i−2i0000000000−2i2i−2i2i000000000002-200000000
χ452-222-2-22-2002-202-202i−2i2i−2i0000002i−2i2i−2ii2−i2i2−i2002-2000000i2−i200002−22−22−22−20000000000i2−i20
χ462-222-2-22-2002-202-202i−2i2i−2i0000002i−2i2i−2i−i2i2−i2i2002-2000000−i2i20000−22−22−22−220000000000−i2i20
χ472-222-2-22-2002-202-202i−2i2i−2i000000−2i2i−2i2ii2−i2i2−i200-22000000i2−i200002−22−2−22−220000000000−i2i20
χ482-222-2-22-2002-202-202i−2i2i−2i000000−2i2i−2i2i−i2i2−i2i200-22000000−i2i20000−22−222−22−20000000000i2−i20
χ492-222-2-22-2002-202-20−2i2i−2i2i0000002i−2i2i−2ii2−i2i2−i200-22000000i2−i20000−22−222−22−20000000000−i2i20
χ502-222-2-22-2002-202-20−2i2i−2i2i0000002i−2i2i−2i−i2i2−i2i200-22000000−i2i200002−22−2−22−220000000000i2−i20
χ512-222-2-22-2002-202-20−2i2i−2i2i000000−2i2i−2i2ii2−i2i2−i2002-2000000i2−i20000−22−22−22−220000000000i2−i20
χ522-222-2-22-2002-202-20−2i2i−2i2i000000−2i2i−2i2i−i2i2−i2i2002-2000000−i2i200002−22−22−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4400400-400000000002i22i2−2i2−2i2000000000000−2i22i2000000000000000000000000000
χ55444-4-4-4-44-4400400-40000000000−2i2−2i22i22i20000000000002i2−2i2000000000000000000000000000
χ5644-444-4-4-44400-400-400004-4-4400000000000000000000000000000000000000000000000
χ5744-444-4-4-44400-400-40000-444-400000000000000000000000000000000000000000000000
χ5844-444-4-4-4-4-40040040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5944-444-4-4-4-4-4004004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ6044-4-4-444-4-44-4-4-444400000000-44000000000000000000000000000000000000000000000
χ614-444-4-44-400-440-440000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ624-444-4-44-400-440-44000000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
χ634-44-444-4-400000000000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ644-44-444-4-400000000000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ654-44-444-4-4000000000000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ664-44-444-4-4000000000000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ674-4-4-44-444004-40-4404-4-44000000000000000000000000000000000000000000000000000
χ684-4-4-44-444004-40-440-444-4000000000000000000000000000000000000000000000000000
χ694-4-4-44-44400-4404-40000000000000000000000000000000000022−22−222200000000000000000
χ704-4-4-44-44400-4404-400000000000000000000000000000000000−222222−2200000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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