Finite Group Databasebeta

← Group #7060

Character table — Group #7060

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size1111111122224444444488888888888888888888888888
order12224444224488888888224444888816161616161616161616161616161616
χ11111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-111-1-1iiii−i−i−i−i111-1-1-1ii−i−iζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ101111-1-1-1-111-1-1iiii−i−i−i−i111-1-1-1ii−i−i−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ111111-1-1-1-111-1-1iiii−i−i−i−i-1-11-111−i−iiiζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6
χ121111-1-1-1-111-1-1iiii−i−i−i−i-1-11-111−i−iii−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6
χ131111-1-1-1-111-1-1−i−i−i−iiiii111-1-1-1−i−iiiζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ141111-1-1-1-111-1-1−i−i−i−iiiii111-1-1-1−i−iii−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ151111-1-1-1-111-1-1−i−i−i−iiiii-1-11-111ii−i−iζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2
χ161111-1-1-1-111-1-1−i−i−i−iiiii-1-11-111ii−i−i−ζ6−ζ6ζ6ζ6−ζ2−ζ2ζ2ζ2ζ6ζ6−ζ6−ζ6ζ2ζ2−ζ2−ζ2
χ1722222222222222-2-222-2-200-2-20000000000000000000000
χ18222222222222-2-222-2-22200-2-20000000000000000000000
χ192222-2-2-2-222-2-22i2i−2i−2i−2i−2i2i2i00-220000000000000000000000
χ202222-2-2-2-222-2-2−2i−2i2i2i2i2i−2i−2i00-220000000000000000000000
χ2122-2-22i−2i2i−2i2-22i−2i002ζ6−2ζ6002ζ2−2ζ20000000000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ700000000
χ2222-2-22i−2i2i−2i2-22i−2i002ζ6−2ζ6002ζ2−2ζ20000000000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ700000000
χ2322-2-22i−2i2i−2i2-22i−2i00−2ζ62ζ600−2ζ22ζ20000000000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ700000000
χ2422-2-22i−2i2i−2i2-22i−2i00−2ζ62ζ600−2ζ22ζ20000000000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ700000000
χ2522-2-22i−2i2i−2i-22−2i2i2ζ2−2ζ2002ζ6−2ζ600000000000000000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5
χ2622-2-22i−2i2i−2i-22−2i2i2ζ2−2ζ2002ζ6−2ζ600000000000000000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5
χ2722-2-22i−2i2i−2i-22−2i2i−2ζ22ζ200−2ζ62ζ600000000000000000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5
χ2822-2-22i−2i2i−2i-22−2i2i−2ζ22ζ200−2ζ62ζ600000000000000000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5
χ2922-2-2−2i2i−2i2i2-2−2i2i002ζ2−2ζ2002ζ6−2ζ60000000000ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ500000000
χ3022-2-2−2i2i−2i2i2-2−2i2i002ζ2−2ζ2002ζ6−2ζ60000000000−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ500000000
χ3122-2-2−2i2i−2i2i2-2−2i2i00−2ζ22ζ200−2ζ62ζ60000000000ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ500000000
χ3222-2-2−2i2i−2i2i2-2−2i2i00−2ζ22ζ200−2ζ62ζ60000000000−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ500000000
χ3322-2-2−2i2i−2i2i-222i−2i2ζ6−2ζ6002ζ2−2ζ200000000000000000000ζ+ζ5−ζ−ζ5ζ−ζ5−ζ+ζ5−ζ3+ζ7ζ3−ζ7−ζ3−ζ7ζ3+ζ7
χ3422-2-2−2i2i−2i2i-222i−2i2ζ6−2ζ6002ζ2−2ζ200000000000000000000−ζ−ζ5ζ+ζ5−ζ+ζ5ζ−ζ5ζ3−ζ7−ζ3+ζ7ζ3+ζ7−ζ3−ζ7
χ3522-2-2−2i2i−2i2i-222i−2i−2ζ62ζ600−2ζ22ζ200000000000000000000ζ−ζ5−ζ+ζ5−ζ−ζ5ζ+ζ5−ζ3−ζ7ζ3+ζ7ζ3−ζ7−ζ3+ζ7
χ3622-2-2−2i2i−2i2i-222i−2i−2ζ62ζ600−2ζ22ζ200000000000000000000−ζ+ζ5ζ−ζ5ζ+ζ5−ζ−ζ5ζ3+ζ7−ζ3−ζ7−ζ3+ζ7ζ3−ζ7
χ3744444444-4-4-4-40000000000000000000000000000000000
χ384444-4-4-4-4-4-4440000000000000000000000000000000000
χ394-44-44i−4i−4i4i0000000000002-2002i−2i00000000000000000000
χ404-44-44i−4i−4i4i000000000000-2200−2i2i00000000000000000000
χ414-44-4−4i4i4i−4i0000000000002-200−2i2i00000000000000000000
χ424-44-4−4i4i4i−4i000000000000-22002i−2i00000000000000000000
χ434-4-4444-4-40000000000000000002i−2i2i−2i0000000000000000
χ444-4-4444-4-4000000000000000000−2i2i−2i2i0000000000000000
χ454-4-44-4-4440000000000000000002-2-220000000000000000
χ464-4-44-4-444000000000000000000-222-20000000000000000

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