Finite Group Databasebeta

← Group #93739

Character table — Group #93739

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order122244442244444444448888888888888888888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iii−i−iζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6
χ101111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iii−i−i−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6
χ111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−iiiζ6ζ6−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ2ζ2−ζ2−ζ2
χ121111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−iii−ζ6−ζ6ζ6ζ6−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ2−ζ2ζ2ζ2
χ131111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−iiiζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6
χ141111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−iii−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6
χ151111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−iζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ2ζ2
χ161111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ2−ζ2
χ172222222222222222-2-2-2-20000000022-2-222-2-200000000000000000000
χ182222222222222222-2-2-2-200000000-2-222-2-22200000000000000000000
χ192222-2-2-2-222-2-2-2-222-2-222000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ202222-2-2-2-222-2-2-2-222-2-22200000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2122-2-22i2i−2i−2i2-22i−2i2i−2i2-2000000000000002ζ6−2ζ6002ζ2−2ζ20000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ50000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ70000
χ2222-2-22i2i−2i−2i2-22i−2i2i−2i2-2000000000000002ζ6−2ζ6002ζ2−2ζ20000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ50000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ70000
χ2322-2-22i2i−2i−2i2-22i−2i2i−2i2-200000000000000−2ζ62ζ600−2ζ22ζ20000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ50000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ70000
χ2422-2-22i2i−2i−2i2-22i−2i2i−2i2-200000000000000−2ζ62ζ600−2ζ22ζ20000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ50000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ70000
χ2522-2-22i2i−2i−2i2-22i−2i−2i2i-220000000000002ζ2−2ζ2002ζ6−2ζ60000000000ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ70000ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ5
χ2622-2-22i2i−2i−2i2-22i−2i−2i2i-220000000000002ζ2−2ζ2002ζ6−2ζ60000000000−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ70000−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ5
χ2722-2-22i2i−2i−2i2-22i−2i−2i2i-22000000000000−2ζ22ζ200−2ζ62ζ60000000000ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ70000ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ5
χ2822-2-22i2i−2i−2i2-22i−2i−2i2i-22000000000000−2ζ22ζ200−2ζ62ζ60000000000−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ70000−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ5
χ2922-2-2−2i−2i2i2i2-2−2i2i2i−2i-220000000000002ζ6−2ζ6002ζ2−2ζ20000000000ζ−ζ5−ζ+ζ5ζ+ζ5−ζ−ζ50000−ζ3−ζ7ζ3+ζ7−ζ3+ζ7ζ3−ζ7
χ3022-2-2−2i−2i2i2i2-2−2i2i2i−2i-220000000000002ζ6−2ζ6002ζ2−2ζ20000000000−ζ+ζ5ζ−ζ5−ζ−ζ5ζ+ζ50000ζ3+ζ7−ζ3−ζ7ζ3−ζ7−ζ3+ζ7
χ3122-2-2−2i−2i2i2i2-2−2i2i2i−2i-22000000000000−2ζ62ζ600−2ζ22ζ20000000000ζ+ζ5−ζ−ζ5−ζ+ζ5ζ−ζ50000−ζ3+ζ7ζ3−ζ7ζ3+ζ7−ζ3−ζ7
χ3222-2-2−2i−2i2i2i2-2−2i2i2i−2i-22000000000000−2ζ62ζ600−2ζ22ζ20000000000−ζ−ζ5ζ+ζ5ζ−ζ5−ζ+ζ50000ζ3−ζ7−ζ3+ζ7−ζ3−ζ7ζ3+ζ7
χ3322-2-2−2i−2i2i2i2-2−2i2i−2i2i2-2000000000000002ζ2−2ζ2002ζ6−2ζ60000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ70000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ50000
χ3422-2-2−2i−2i2i2i2-2−2i2i−2i2i2-2000000000000002ζ2−2ζ2002ζ6−2ζ60000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ70000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ50000
χ3522-2-2−2i−2i2i2i2-2−2i2i−2i2i2-200000000000000−2ζ22ζ200−2ζ62ζ60000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ70000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ50000
χ3622-2-2−2i−2i2i2i2-2−2i2i−2i2i2-200000000000000−2ζ22ζ200−2ζ62ζ60000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ70000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ50000
χ37444444444444-4-4-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-40000000022-2-222-2-20000000000000000000000000000
χ3944444444-4-4-4-400000000-2-222-2-2220000000000000000000000000000
χ404444-4-4-4-444-4-444-4-40000000000000000000000000000000000000000
χ414444-4-4-4-4-4-4440000000022-2-2-2-2220000000000000000000000000000
χ424444-4-4-4-4-4-44400000000-2-22222-2-20000000000000000000000000000
χ4344-4-44i4i−4i−4i-44−4i4i0000000000000000000000002ζ6−2ζ62ζ2−2ζ20000000000000000
χ4444-4-44i4i−4i−4i-44−4i4i000000000000000000000000−2ζ62ζ6−2ζ22ζ20000000000000000
χ4544-4-4−4i−4i4i4i-444i−4i0000000000000000000000002ζ2−2ζ22ζ6−2ζ60000000000000000
χ4644-4-4−4i−4i4i4i-444i−4i000000000000000000000000−2ζ22ζ2−2ζ62ζ60000000000000000
χ474-44-44-44-4000000002-22-2002i2−2i2002i2−2i20000000000000000000000000000
χ484-44-44-44-4000000002-22-200−2i22i200−2i22i20000000000000000000000000000
χ494-44-44-44-400000000-22-222i2−2i2002i2−2i2000000000000000000000000000000
χ504-44-44-44-400000000-22-22−2i22i200−2i22i2000000000000000000000000000000
χ514-44-4-44-44000000002-2-22002i2−2i200−2i22i20000000000000000000000000000
χ524-44-4-44-44000000002-2-2200−2i22i2002i2−2i20000000000000000000000000000
χ534-44-4-44-4400000000-222-22i2−2i200−2i22i2000000000000000000000000000000
χ544-44-4-44-4400000000-222-2−2i22i2002i2−2i2000000000000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.