Finite Group Databasebeta

← Group #7463

Character table — Group #7463

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order12224444448888161616161616161688161616163232323232323232323232323232323288888888
χ11111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ6111111-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ7111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ8111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ911-1-11-1ii−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−iζ2−ζ2ζ6−ζ6ζ2−ζ2ζ6−ζ6
χ1011-1-11-1ii−i−i11-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1iiii−i−i−i−i−ζ2ζ2−ζ6ζ6−ζ2ζ2−ζ6ζ6
χ1111-1-11-1ii−i−i11-1-11111-1-1-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiiiζ2−ζ2ζ6−ζ6−ζ2ζ2−ζ6ζ6
χ1211-1-11-1ii−i−i11-1-11111-1-1-1-1i−iii−i−i-1-1-1-11111−i−i−i−iiiii−ζ2ζ2−ζ6ζ6ζ2−ζ2ζ6−ζ6
χ1311-1-11-1−i−iii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiiiζ6−ζ6ζ2−ζ2ζ6−ζ6ζ2−ζ2
χ1411-1-11-1−i−iii11-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−i−i−i−iiiii−ζ6ζ6−ζ2ζ2−ζ6ζ6−ζ2ζ2
χ1511-1-11-1−i−iii11-1-11111-1-1-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−iζ6−ζ6ζ2−ζ2−ζ6ζ6−ζ2ζ2
χ1611-1-11-1−i−iii11-1-11111-1-1-1-1−ii−i−iii-1-1-1-11111iiii−i−i−i−i−ζ6ζ6−ζ2ζ2ζ6−ζ6ζ2−ζ2
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222-2-2-2-200000000-2-2000022−2−222−2−222−2−222−2−200000000
χ192222222222-2-2-2-200000000-2-20000−2−222−2−222−2−222−2−22200000000
χ20222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ21222222-2-2-2-2-2-2-2-20000000022000022−2−222−2−2−2−222−2−22200000000
χ22222222-2-2-2-2-2-2-2-200000000220000−2−222−2−22222−2−222−2−200000000
χ232222-2-22-22-2000022−2−222−2−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ242222-2-22-22-2000022−2−222−2−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ252222-2-22-22-20000−2−222−2−22200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ262222-2-22-22-20000−2−222−2−22200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ272222-2-2-22-22000022−2−222−2−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ282222-2-2-22-22000022−2−222−2−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ292222-2-2-22-220000−2−222−2−222002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ302222-2-2-22-220000−2−222−2−222002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ3122-2-22-22i2i−2i−2i22-2-2-2-2-2-222222i−2i−2i−2i2i2i000000000000000000000000
χ3222-2-22-22i2i−2i−2i-2-22200000000−2i2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ3322-2-22-22i2i−2i−2i-2-22200000000−2i2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ3422-2-22-2−2i−2i2i2i22-2-2-2-2-2-22222−2i2i2i2i−2i−2i000000000000000000000000
χ3522-2-22-2−2i−2i2i2i-2-222000000002i−2i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ3622-2-22-2−2i−2i2i2i-2-222000000002i−2i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ3722-2-2-222i−2i−2i2i000022−2−2−2−22200i2−i2−i2i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000
χ3822-2-2-222i−2i−2i2i000022−2−2−2−22200i2−i2−i2i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ700000000
χ3922-2-2-222i−2i−2i2i0000−2−22222−2−200−i2i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ500000000
χ4022-2-2-222i−2i−2i2i0000−2−22222−2−200−i2i2i2−i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ500000000
χ4122-2-2-22−2i2i2i−2i000022−2−2−2−22200−i2i2i2−i2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ700000000
χ4222-2-2-22−2i2i2i−2i000022−2−2−2−22200−i2i2i2−i2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000
χ4322-2-2-22−2i2i2i−2i0000−2−22222−2−200i2−i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ500000000
χ4422-2-2-22−2i2i2i−2i0000−2−22222−2−200i2−i2−i2i2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ500000000
χ454-44-400000022−2222−222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000
χ464-44-400000022−2222−22−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000
χ474-44-4000000−2222−22222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000
χ484-44-4000000−2222−2222−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000
χ494-4-4400000022−22−22222ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000
χ504-4-4400000022−22−2222−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000
χ514-4-44000000−222222−222ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000
χ524-4-44000000−222222−22−2ζ3−2ζ52ζ3+2ζ52ζ+2ζ7−2ζ−2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000

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