Finite Group Databasebeta

← Group #7249

Character table — Group #7249

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size111122222244444444444444448888881616161616161616
order1222224444444444448888888822888888888888
χ11111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ611111111111111-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-111-1-111-1-1iiii−i−i−i−i1-1ii−i−i1-11-1i−ii−i
χ10111111-1-1-1-111-1-111-1-1iiii−i−i−i−i1-1ii−i−i-11-11−ii−ii
χ11111111-1-1-1-111-1-111-1-1−i−i−i−iiiii1-1−i−iii1-11-1−ii−ii
χ12111111-1-1-1-111-1-111-1-1−i−i−i−iiiii1-1−i−iii-11-11i−ii−i
χ13111111-1-1-1-111-1-1-1-111iiii−i−i−i−i-11−i−iiii−i−ii-111-1
χ14111111-1-1-1-111-1-1-1-111iiii−i−i−i−i-11−i−iii−iii−i1-1-11
χ15111111-1-1-1-111-1-1-1-111−i−i−i−iiiii-11ii−i−ii−i−ii1-1-11
χ16111111-1-1-1-111-1-1-1-111−i−i−i−iiiii-11ii−i−i−iii−i-111-1
χ172222222222-2-2-2-222-2-200000000-22000000000000
χ182222222222-2-2-2-2-2-222000000002-2000000000000
χ19222222-2-2-2-2-2-222222200000000-2-2000000000000
χ20222222-2-2-2-2-2-222-2-2-2-20000000022000000000000
χ2122-2-22-20000002-22i−2i2i−2ii2i2−i2−i2i2i2−i2−i2002−22−200000000
χ2222-2-22-20000002-22i−2i2i−2i−i2−i2i2i2−i2−i2i2i200−22−2200000000
χ2322-2-22-20000002-2−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200−22−2200000000
χ2422-2-22-20000002-2−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2002−22−200000000
χ2522-2-22-2000000-222i−2i−2i2i22−2−2−2−22200−i2i2i2−i200000000
χ2622-2-22-2000000-222i−2i−2i2i−2−22222−2−200i2−i2−i2i200000000
χ2722-2-22-2000000-22−2i2i2i−2i22−2−2−2−22200i2−i2−i2i200000000
χ2822-2-22-2000000-22−2i2i2i−2i−2−22222−2−200−i2i2i2−i200000000
χ294444-4-44-4-44000000000000000000000000000000
χ304444-4-4-444-4000000000000000000000000000000
χ3144-4-4-4400004i−4i0000000000000000000000000000
χ3244-4-4-440000−4i4i0000000000000000000000000000
χ334-44-40004i−4i0000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000
χ344-44-40004i−4i000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000
χ354-44-4000−4i4i0000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000
χ364-44-4000−4i4i000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000
χ374-4-4400400-4000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ384-4-4400400-400000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ394-4-4400-4004000000002-2-222-2-2200000000000000
χ404-4-4400-400400000000-222-2-222-200000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.