Finite Group Databasebeta

← Group #280049

Character table — Group #280049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-1111-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111
χ511111111111111111111-1-1-1-11111111111-1-11111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-111111-1-1-1-111-1
χ91111111111111111-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-11-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111111-111-1-111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111-1-11-1-111-1-1-1-11
χ17222222222-22-2-222-222220000-2-20000222200-2-2220000-2-2000000000000-2000000000000
χ18222222222-22-2-222-222220000-2-20000-2-2-2-200-2-2-2-20000220000000000002000000000000
χ19222222222-22-2-222-2-2-2-2-20000-2-2000022220022-2-20000-2-20000000000002000000000000
χ20222222222-22-2-222-2-2-2-2-20000-2-20000-2-2-2-2002222000022000000000000-2000000000000
χ2122222222-22-222-2-2200002222-2-222220000-2-2000022-2-200000000000000000-2000000000
χ2222222222-22-222-2-2200002222-2-2-2-2-2-20000-2-20000-2-222000000000000000002000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-222220000220000-2-2-2-2000000000000000002000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-2-2-20000220000222200000000000000000-2000000000
χ25222-2-22-2-20-202-200200002i2i−2i−2i0022-2-222−2−20000002i−2i002−2i2i2−i2−i2000022−2−200000000i2−i2000
χ26222-2-22-2-20-202-200200002i2i−2i−2i0022-2-2−2−2220000002i−2i00−22−i2−i2i2i20000−2−22200000000−i2i2000
χ27222-2-22-2-20-202-200200002i2i−2i−2i00-2-22222−2−2000000−2i2i002−2i2i2−i2−i20000−2−22200000000−i2i2000
χ28222-2-22-2-20-202-200200002i2i−2i−2i00-2-222−2−222000000−2i2i00−22−i2−i2i2i2000022−2−200000000i2−i2000
χ29222-2-22-2-20-202-20020000−2i−2i2i2i0022-2-222−2−2000000−2i2i002−2−i2−i2i2i2000022−2−200000000−i2i2000
χ30222-2-22-2-20-202-20020000−2i−2i2i2i0022-2-2−2−222000000−2i2i00−22i2i2−i2−i20000−2−22200000000i2−i2000
χ31222-2-22-2-20-202-20020000−2i−2i2i2i00-2-22222−2−20000002i−2i002−2−i2−i2i2i20000−2−22200000000i2−i2000
χ32222-2-22-2-20-202-20020000−2i−2i2i2i00-2-222−2−2220000002i−2i00−22i2i2−i2−i2000022−2−200000000−i2i2000
χ3322-22-2-2-22-202002-2022-2-2000000i2−i2i2−i22i−2i2i−2i00002i−2i00i2−i2000000i2i2−i2−i22−22−200000000002−20
χ3422-22-2-2-22-202002-2022-2-2000000i2−i2i2−i2−2i2i−2i2i0000−2i2i00i2−i2000000i2i2−i2−i2−22−220000000000−220
χ3522-22-2-2-22-202002-2022-2-2000000−i2i2−i2i22i−2i2i−2i00002i−2i00−i2i2000000−i2−i2i2i2−22−220000000000−220
χ3622-22-2-2-22-202002-2022-2-2000000−i2i2−i2i2−2i2i−2i2i0000−2i2i00−i2i2000000−i2−i2i2i22−22−200000000002−20
χ3722-22-2-2-22-202002-20-2-222000000i2−i2i2−i22i−2i2i−2i0000−2i2i00i2−i2000000−i2−i2i2i22−22−20000000000−220
χ3822-22-2-2-22-202002-20-2-222000000i2−i2i2−i2−2i2i−2i2i00002i−2i00i2−i2000000−i2−i2i2i2−22−2200000000002−20
χ3922-22-2-2-22-202002-20-2-222000000−i2i2−i2i22i−2i2i−2i0000−2i2i00−i2i2000000i2i2−i2−i2−22−2200000000002−20
χ4022-22-2-2-22-202002-20-2-222000000−i2i2−i2i2−2i2i−2i2i00002i−2i00−i2i2000000i2i2−i2−i22−22−20000000000−220
χ412-2-22-222-222-2-2-22-222i−2i2i−2i00002-200000000002i−2i000000002i−2i2i−2i0000000000002-20000000
χ422-2-22-222-222-2-2-22-222i−2i2i−2i00002-200000000002i−2i00000000−2i2i−2i2i000000000000-220000000
χ432-2-22-222-222-2-2-22-22−2i2i−2i2i00002-20000000000−2i2i000000002i−2i2i−2i000000000000-220000000
χ442-2-22-222-222-2-2-22-22−2i2i−2i2i00002-20000000000−2i2i00000000−2i2i−2i2i0000000000002-20000000
χ452-2-22-222-22-2-2222-2-22i−2i2i−2i2-22-2-22000000002-2−2i2i000000000000000000000000002i−2i00000
χ462-2-22-222-22-2-2222-2-22i−2i2i−2i-22-22-2200000000-22−2i2i00000000000000000000000000−2i2i00000
χ472-2-22-222-22-2-2222-2-2−2i2i−2i2i2-22-2-22000000002-22i−2i00000000000000000000000000−2i2i00000
χ482-2-22-222-22-2-2222-2-2−2i2i−2i2i-22-22-2200000000-222i−2i000000000000000000000000002i−2i00000
χ492-2-22-222-2-2-2222-22-200002-22-22-200000000-22000000000000002i−2i2i−2i000002i−2i0000000000
χ502-2-22-222-2-2-2222-22-200002-22-22-200000000-2200000000000000−2i2i−2i2i00000−2i2i0000000000
χ512-2-22-222-2-2-2222-22-20000-22-222-2000000002-2000000000000002i−2i2i−2i00000−2i2i0000000000
χ522-2-22-222-2-2-2222-22-20000-22-222-2000000002-200000000000000−2i2i−2i2i000002i−2i0000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-44-4-4040-4400-4000000000000002222−22−220000000000−22220000000000000000000000000
χ55444-4-44-4-4040-4400-400000000000000−22−222222000000000022−220000000000000000000000000
χ5644-44-4-4-4440-400-44000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ5744-44-4-4-4440-400-4400000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ5844-4-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ5944-4-44-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ6044-4-44-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ6144-4-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ624-4444-4-4-440400-4-40000000000000000000000000000000000022−22−222200000000000000000
χ634-4444-4-4-440400-4-400000000000000000000000000000000000−222222−2200000000000000000
χ644-4444-4-4-4-40-4004404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ654-4444-4-4-4-40-400440−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ664-4-44-444-4-444-4-4-44400000000-44000000000000000000000000000000000000000000000
χ674-4-4-444-440404-400-400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ684-4-4-444-440404-400-40000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ694-4-4-444-440-40-4400400000000000000000000000000000022−22−2222000000000000000000000
χ704-4-4-444-440-40-44004000000000000000000000000000000−222222−22000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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