Finite Group Databasebeta

← Group #282778

Character table — Group #282778

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-11111111111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111111-1-1-111-1-111-1
χ131111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111111-1
χ151111111111111111-1-1-1-11-1-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1111-1-11111-1
χ161111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ172222222222-22-2-2-222222-20000-200002222-2-2002200000000-2-20000000000-20000000000
χ182222222222-22-2-2-222222-20000-20000-2-2-2-2-2-200-2-20000000022000000000020000000000
χ192222222222-22-2-2-22-2-2-2-2-20000-2000022222200-2-200000000-2-2000000000020000000000
χ202222222222-22-2-2-22-2-2-2-2-20000-20000-2-2-2-222002200000000220000000000-20000000000
χ2122222222-2-22-2222-20000-22222-222220000002200-2-2-2-20000000000000000000-20000000
χ2222222222-2-22-2222-20000-22222-2-2-2-2-2000000-2-200-2-222000000000000000000020000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-22222000000-2-20022-2-2000000000000000000020000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-2-2-2-2-2000000220022220000000000000000000-20000000
χ252222-2-2-2-22-20-2000222-2-200000022−2−22i2i−2i−2i00002i−2i002−222−2−2000000i2i2−i2−i200000000i2−i2000
χ262222-2-2-2-22-20-2000222-2-200000022−2−2−2i−2i2i2i0000−2i2i002−222−2−2000000−i2−i2i2i200000000−i2i2000
χ272222-2-2-2-22-20-2000222-2-2000000−2−2222i2i−2i−2i00002i−2i00−22−2−222000000−i2−i2i2i200000000−i2i2000
χ282222-2-2-2-22-20-2000222-2-2000000−2−222−2i−2i2i2i0000−2i2i00−22−2−222000000i2i2−i2−i200000000i2−i2000
χ292222-2-2-2-22-20-20002-2-22200000022−2−22i2i−2i−2i0000−2i2i002−2−2−222000000i2i2−i2−i200000000−i2i2000
χ302222-2-2-2-22-20-20002-2-22200000022−2−2−2i−2i2i2i00002i−2i002−2−2−222000000−i2−i2i2i200000000i2−i2000
χ312222-2-2-2-22-20-20002-2-222000000−2−2222i2i−2i−2i0000−2i2i00−2222−2−2000000−i2−i2i2i200000000i2−i2000
χ322222-2-2-2-22-20-20002-2-222000000−2−222−2i−2i2i2i00002i−2i00−2222−2−2000000i2i2−i2−i200000000−i2i2000
χ3322-2-2-2-22200202-2-20000002i2i−2i−2i02-22-22−22−2002i−2i00000000002−2i2i2−i2−i22−22−20000000000i2−i20
χ3422-2-2-2-22200202-2-20000002i2i−2i−2i02-22-2−22−22002i−2i0000000000−22−i2−i2i2i2−22−220000000000−i2i20
χ3522-2-2-2-22200202-2-20000002i2i−2i−2i0-22-222−22−200−2i2i00000000002−2i2i2−i2−i2−22−220000000000−i2i20
χ3622-2-2-2-22200202-2-20000002i2i−2i−2i0-22-22−22−2200−2i2i0000000000−22−i2−i2i2i22−22−20000000000i2−i20
χ3722-2-2-2-22200202-2-2000000−2i−2i2i2i02-22-22−22−200−2i2i00000000002−2−i2−i2i2i22−22−20000000000−i2i20
χ3822-2-2-2-22200202-2-2000000−2i−2i2i2i02-22-2−22−2200−2i2i0000000000−22i2i2−i2−i2−22−220000000000i2−i20
χ3922-2-2-2-22200202-2-2000000−2i−2i2i2i0-22-222−22−2002i−2i00000000002−2−i2−i2i2i2−22−220000000000i2−i20
χ4022-2-2-2-22200202-2-2000000−2i−2i2i2i0-22-22−22−22002i−2i0000000000−22i2i2−i2−i22−22−20000000000−i2i20
χ412-2-22-22-22222-2-2-22-22i−2i2i−2i22-22-2-2000000002i−2i00002-200000000000000000002i−2i00000000
χ422-2-22-22-22222-2-2-22-22i−2i2i−2i2-22-22-2000000002i−2i0000-220000000000000000000−2i2i00000000
χ432-2-22-22-22222-2-2-22-2−2i2i−2i2i22-22-2-200000000−2i2i00002-20000000000000000000−2i2i00000000
χ442-2-22-22-22222-2-2-22-2−2i2i−2i2i2-22-22-200000000−2i2i0000-2200000000000000000002i−2i00000000
χ452-2-22-22-2222-2-222-2-22i−2i2i−2i-20000200000000−2i2i000000000000002i−2i2i−2i00002-200000000000
χ462-2-22-22-2222-2-222-2-22i−2i2i−2i-20000200000000−2i2i00000000000000−2i2i−2i2i0000-2200000000000
χ472-2-22-22-2222-2-222-2-2−2i2i−2i2i-200002000000002i−2i000000000000002i−2i2i−2i0000-2200000000000
χ482-2-22-22-2222-2-222-2-2−2i2i−2i2i-200002000000002i−2i00000000000000−2i2i−2i2i00002-200000000000
χ492-2-22-22-22-2-222-2-2220000-22-22-2200000000000000-22002-22-200000000000000002-200000
χ502-2-22-22-22-2-222-2-2220000-22-22-2200000000000000-2200-22-220000000000000000-2200000
χ512-2-22-22-22-2-222-2-2220000-2-22-222000000000000002-2002-22-20000000000000000-2200000
χ522-2-22-22-22-2-222-2-2220000-2-22-222000000000000002-200-22-2200000000000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000400004000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4404000-400000000002222−22−22000000000000−2222000000000000000000000000000
χ554444-4-4-4-4-4404000-40000000000−22−22222200000000000022−22000000000000000000000000000
χ5644-4-444-4-400000000000000000022−22−22222i2−2i2−2i22i2000000000000000000002i−2i−2i2i0000000000000
χ5744-4-444-4-400000000000000000022−22−2222−2i22i22i2−2i200000000000000000000−2i2i2i−2i0000000000000
χ5844-4-444-4-4000000000000000000−222222−222i2−2i2−2i22i200000000000000000000−2i2i2i−2i0000000000000
χ5944-4-444-4-4000000000000000000−222222−22−2i22i22i2−2i2000000000000000000002i−2i−2i2i0000000000000
χ6044-4-4-4-44400-40-44400000000000000022−2222−2200000000000000−2222000000000000000000000
χ6144-4-4-4-44400-40-444000000000000000−2222−22220000000000000022−22000000000000000000000
χ624-44-44-4-440040-44-40000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ634-44-44-4-440040-44-4000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ644-44-44-4-4400-404-440000000000000000000000000000000000022−22−222200000000000000000
χ654-44-44-4-4400-404-4400000000000000000000000000000000000−222222−2200000000000000000
χ664-4-444-44-44-404000-44i−4i−4i4i000000000000000000000000000000000000000000000000000
χ674-4-444-44-44-404000-4−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ684-4-444-44-4-440-40004000000000000000000000000000022−22−222200000000000000000000000
χ694-4-444-44-4-440-400040000000000000000000000000000−222222−2200000000000000000000000
χ704-4-44-44-44-4-4-4444-44000040000-4000000000000000000000000000000000000000000000
χ718-88-8-888-8000000000000000000000000000000000000000000000000000000000000000

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