Finite Group Databasebeta

← Group #93708

Character table — Group #93708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444888888888888161616161616161616161616161616161616161616161616
order122222444422442244888888884444888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ10111111-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ11111111-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ12111111-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ13111111-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ14111111-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ15111111-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ16111111-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ1722222222222222-2-2-2-222-2-222-2-2000000000000000000000000
χ1822222222222222-2-2-2-2-2-222-2-222000000000000000000000000
χ19222222-2-2-2-222-2-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ20222222-2-2-2-222-2-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ2122-2-22-22i2i−2i−2i2-22i−2i0000002ζ6−2ζ6002ζ2−2ζ200000000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ700000000
χ2222-2-22-22i2i−2i−2i2-22i−2i0000002ζ6−2ζ6002ζ2−2ζ200000000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ700000000
χ2322-2-22-22i2i−2i−2i2-22i−2i000000−2ζ62ζ600−2ζ22ζ200000000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ700000000
χ2422-2-22-22i2i−2i−2i2-22i−2i000000−2ζ62ζ600−2ζ22ζ200000000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ700000000
χ2522-2-22-22i2i−2i−2i-22−2i2i00002ζ2−2ζ2002ζ6−2ζ6000000000000000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5
χ2622-2-22-22i2i−2i−2i-22−2i2i00002ζ2−2ζ2002ζ6−2ζ6000000000000000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5
χ2722-2-22-22i2i−2i−2i-22−2i2i0000−2ζ22ζ200−2ζ62ζ6000000000000000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5
χ2822-2-22-22i2i−2i−2i-22−2i2i0000−2ζ22ζ200−2ζ62ζ6000000000000000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5
χ2922-2-22-2−2i−2i2i2i2-2−2i2i0000002ζ2−2ζ2002ζ6−2ζ600000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ500000000
χ3022-2-22-2−2i−2i2i2i2-2−2i2i0000002ζ2−2ζ2002ζ6−2ζ600000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ500000000
χ3122-2-22-2−2i−2i2i2i2-2−2i2i000000−2ζ22ζ200−2ζ62ζ600000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ500000000
χ3222-2-22-2−2i−2i2i2i2-2−2i2i000000−2ζ22ζ200−2ζ62ζ600000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ500000000
χ3322-2-22-2−2i−2i2i2i-222i−2i00002ζ6−2ζ6002ζ2−2ζ2000000000000000000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7
χ3422-2-22-2−2i−2i2i2i-222i−2i00002ζ6−2ζ6002ζ2−2ζ2000000000000000000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7
χ3522-2-22-2−2i−2i2i2i-222i−2i0000−2ζ62ζ600−2ζ22ζ2000000000000000000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7
χ3622-2-22-2−2i−2i2i2i-222i−2i0000−2ζ62ζ600−2ζ22ζ2000000000000000000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7
χ374444444444-4-4-4-4000000000000000000000000000000000000
χ38444444-4-4-4-4-4-444000000000000000000000000000000000000
χ394444-4-44-44-400000000000000002i−2i2i−2i00000000000000000000
χ404444-4-44-44-40000000000000000−2i2i−2i2i00000000000000000000
χ414444-4-4-44-4400000000000000002i−2i−2i2i00000000000000000000
χ424444-4-4-44-440000000000000000−2i2i2i−2i00000000000000000000
χ4344-4-4-444i−4i−4i4i000000000000000000002ζ6−2ζ62ζ2−2ζ20000000000000000
χ4444-4-4-444i−4i−4i4i00000000000000000000−2ζ62ζ6−2ζ22ζ20000000000000000
χ4544-4-4-44−4i4i4i−4i000000000000000000002ζ2−2ζ22ζ6−2ζ60000000000000000
χ4644-4-4-44−4i4i4i−4i00000000000000000000−2ζ22ζ2−2ζ62ζ60000000000000000
χ478-88-80000000000004i−4i00000000000000000000000000000000
χ488-88-8000000000000−4i4i00000000000000000000000000000000
χ498-8-8800000000004-40000000000000000000000000000000000
χ508-8-880000000000-440000000000000000000000000000000000

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