Finite Group Databasebeta

← Group #7388

Character table — Group #7388

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size111122222222222222222244444444444444444444441616161616161616
order124424888888881616161616161616441616161632323232323232323232323232323232248816161616
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
χ5111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i
χ6111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii
χ7111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii
χ8111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i
χ911-1-1-11i−i11-1-1i−iiiii−i−i−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ61-1i−iζ2−ζ2ζ6−ζ6
χ1011-1-1-11i−i11-1-1i−iiiii−i−i−i−ii−i11-1-1ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-11−ii−ζ2ζ2−ζ6ζ6
χ1111-1-1-11i−i11-1-1i−iiiii−i−i−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ61-1i−i−ζ2ζ2−ζ6ζ6
χ1211-1-1-11i−i11-1-1i−iiiii−i−i−i−ii−i11-1-1−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-11−iiζ2−ζ2ζ6−ζ6
χ1311-1-1-11−ii11-1-1−ii−i−i−i−iiiii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ21-1−iiζ6−ζ6ζ2−ζ2
χ1411-1-1-11−ii11-1-1−ii−i−i−i−iiiii−ii11-1-1ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-11i−i−ζ6ζ6−ζ2ζ2
χ1511-1-1-11−ii11-1-1−ii−i−i−i−iiiii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ21-1−ii−ζ6ζ6−ζ2ζ2
χ1611-1-1-11−ii11-1-1−ii−i−i−i−iiiii−ii11-1-1−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-11i−iζ6−ζ6ζ2−ζ2
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ1822222222-2-2-2-22200000000-2-2000022−2−222−2−222−2−222−2−200000000
χ1922222222-2-2-2-22200000000-2-20000−2−222−2−222−2−222−2−22200000000
χ20222222-2-22222-2-222222222-2-2-2-2-2-2000000000000000000000000
χ21222222-2-2-2-2-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ22222222-2-2-2-2-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ232222-2-2220000-2-222−2−222−2−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000
χ242222-2-2220000-2-222−2−222−2−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000
χ252222-2-2220000-2-2−2−222−2−22200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000
χ262222-2-2220000-2-2−2−222−2−22200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000
χ272222-2-2-2-200002222−2−222−2−200−22−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ500000000
χ282222-2-2-2-200002222−2−222−2−200−22−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ500000000
χ292222-2-2-2-2000022−2−222−2−222002−22−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ700000000
χ302222-2-2-2-2000022−2−222−2−222002−22−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ700000000
χ3122-2-22-22i−2i0000−2i2ii2i2−i2−i2−i2−i2i2i2002−2−22ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ300000000
χ3222-2-22-22i−2i0000−2i2ii2i2−i2−i2−i2−i2i2i2002−2−22−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ300000000
χ3322-2-22-22i−2i0000−2i2i−i2−i2i2i2i2i2−i2−i200−222−2ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ700000000
χ3422-2-22-22i−2i0000−2i2i−i2−i2i2i2i2i2−i2−i200−222−2−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ700000000
χ3522-2-22-2−2i2i00002i−2ii2i2−i2−i2−i2−i2i2i200−222−2ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ300000000
χ3622-2-22-2−2i2i00002i−2ii2i2−i2−i2−i2−i2i2i200−222−2−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ300000000
χ3722-2-22-2−2i2i00002i−2i−i2−i2i2i2i2i2−i2−i2002−2−22ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ700000000
χ3822-2-22-2−2i2i00002i−2i−i2−i2i2i2i2i2−i2−i2002−2−22−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ700000000
χ3922-2-2-222i−2i22-2-22i−2i−2i−2i−2i−2i2i2i2i2i2i−2i-2-222000000000000000000000000
χ4022-2-2-222i−2i-2-2222i−2i00000000−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00000000
χ4122-2-2-222i−2i-2-2222i−2i00000000−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00000000
χ4222-2-2-22−2i2i22-2-2−2i2i2i2i2i2i−2i−2i−2i−2i−2i2i-2-222000000000000000000000000
χ4322-2-2-22−2i2i-2-222−2i2i000000002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00000000
χ4422-2-2-22−2i2i-2-222−2i2i000000002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00000000
χ454-44i−4i000022−222i2−2i2002ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3000000000000000000000000000000
χ464-44i−4i000022−222i2−2i200−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3000000000000000000000000000000
χ474-44i−4i0000−2222−2i22i2002ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000
χ484-44i−4i0000−2222−2i22i200−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000
χ494-4−4i4i000022−22−2i22i2002ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000
χ504-4−4i4i000022−22−2i22i200−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000
χ514-4−4i4i0000−22222i2−2i2002ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3000000000000000000000000000000
χ524-4−4i4i0000−22222i2−2i200−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3000000000000000000000000000000

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