Finite Group Databasebeta

← Group #93028

Character table — Group #93028

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222222224444888888888888888888888888883232323232323232
order122222444488888888444444448888881616161616161616161616161616161688888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ6111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ7111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ8111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ91111111111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1i−ii−i
χ101111111111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11−ii−ii
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−ii−ii
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-11-11111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11i−ii−i
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−ii-111-1
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i1-1-11
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−ii1-1-11
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i-111-1
χ1722222222222222222222-2-2-2-22-2-2-2-2-222000000000000000000000000
χ18222222222222222222-2-222-2-2-22-2-222-2-2000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000
χ21222222-2-2-2-20000000022222-2-2-200000022−2−222−2−222−2−222−2−200000000
χ22222222-2-2-2-20000000022222-2-2-2000000−2−222−2−222−2−222−2−22200000000
χ23222222-2-2-2-20000000022-2-2-22-22000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ24222222-2-2-2-20000000022-2-2-22-22000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ25222222-2-2-2-200000000-2-222-222-2000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ26222222-2-2-2-200000000-2-222-222-2000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ27222222-2-2-2-200000000-2-2-2-22-22200000022−2−222−2−2−2−222−2−22200000000
χ28222222-2-2-2-200000000-2-2-2-22-222000000−2−222−2−22222−2−222−2−200000000
χ294444-4-444-4-400000000000000004i−4i0000000000000000000000000000
χ304444-4-444-4-40000000000000000−4i4i0000000000000000000000000000
χ314444-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000
χ324444-4-4-4-444-4-44444-4-400000000000000000000000000000000000000
χ3344-4-400004-4440000-4-4000000000000002-22-22-22-20000000000000000
χ3444-4-400004-4440000-4-400000000000000-22-22-22-220000000000000000
χ3544-4-400004-4-4-4000044000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ3644-4-400004-4-4-400004400000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ3744-4-40000-44004i4i−4i−4i00000000000000002ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ60000000000000000
χ3844-4-40000-44004i4i−4i−4i0000000000000000−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ60000000000000000
χ3944-4-40000-4400−4i−4i4i4i00000000000000002ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ20000000000000000
χ4044-4-40000-4400−4i−4i4i4i0000000000000000−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ20000000000000000
χ414-44-4004i−4i002i2−2i222−2222−222i2−2i200000000000000000000002ζ3−2ζ32ζ7−2ζ72ζ5−2ζ52ζ−2ζ00000000
χ424-44-4004i−4i002i2−2i222−2222−222i2−2i20000000000000000000000−2ζ32ζ3−2ζ72ζ7−2ζ52ζ5−2ζ2ζ00000000
χ434-44-4004i−4i00−2i22i2−2222−2222−2i22i200000000000000000000002ζ7−2ζ7−2ζ32ζ32ζ−2ζ−2ζ52ζ500000000
χ444-44-4004i−4i00−2i22i2−2222−2222−2i22i20000000000000000000000−2ζ72ζ72ζ3−2ζ3−2ζ2ζ2ζ5−2ζ500000000
χ454-44-400−4i4i002i2−2i2−2222−22222i2−2i200000000000000000000002ζ−2ζ−2ζ52ζ52ζ7−2ζ7−2ζ32ζ300000000
χ464-44-400−4i4i002i2−2i2−2222−22222i2−2i20000000000000000000000−2ζ2ζ2ζ5−2ζ5−2ζ72ζ72ζ3−2ζ300000000
χ474-44-400−4i4i00−2i22i222−2222−22−2i22i200000000000000000000002ζ5−2ζ52ζ−2ζ2ζ3−2ζ32ζ7−2ζ700000000
χ484-44-400−4i4i00−2i22i222−2222−22−2i22i20000000000000000000000−2ζ52ζ5−2ζ2ζ−2ζ32ζ3−2ζ72ζ700000000
χ494-4-444-400002i2−2i22i2−2i2−2i22i2−2i22i2004-40000002i2−2i200000000000000000000000000
χ504-4-444-400002i2−2i22i2−2i2−2i22i2−2i22i200-44000000−2i22i200000000000000000000000000
χ514-4-444-40000−2i22i2−2i22i22i2−2i22i2−2i2004-4000000−2i22i200000000000000000000000000
χ524-4-444-40000−2i22i2−2i22i22i2−2i22i2−2i200-440000002i2−2i200000000000000000000000000
χ534-4-44-4400002i2−2i2−2i22i22i2−2i2−2i22i24-400000000002i2−2i2000000000000000000000000
χ544-4-44-4400002i2−2i2−2i22i22i2−2i2−2i22i2-440000000000−2i22i2000000000000000000000000
χ554-4-44-440000−2i22i22i2−2i2−2i22i22i2−2i24-40000000000−2i22i2000000000000000000000000
χ564-4-44-440000−2i22i22i2−2i2−2i22i22i2−2i2-4400000000002i2−2i2000000000000000000000000

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