Finite Group Databasebeta

← Group #13513

Character table — Group #13513

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40
size111122222222224444444444888888881616161616161616
order1244222444888888161616161616161644881616161644888888
χ11111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ92222222222-2-2-2-2-2-20000000022-2-2000000000000
χ102222222222-2-2-2-2-2-200000000-2-222000000000000
χ112222-22-2-22-22222-2-200000000000000002i−2i000000
χ122222-22-2-22-22222-2-20000000000000000−2i2i000000
χ132222-22-2-22-2-2-2-2-222000000000000000000002i−2i00
χ142222-22-2-22-2-2-2-2-22200000000000000000000−2i2i00
χ152222-2-222-2-20000002222−2−2−2−22i−2i00i2i2−i2−i200000000
χ162222-2-222-2-20000002222−2−2−2−2−2i2i00−i2−i2i2i200000000
χ172222-2-222-2-2000000−2−2−2−222222i−2i00−i2−i2i2i200000000
χ182222-2-222-2-2000000−2−2−2−22222−2i2i00i2i2−i2−i200000000
χ1922-2-22-2-222-222-2-2-2222-2-222-2-20000000000000000
χ2022-2-22-2-222-222-2-2-22-2-222-2-2220000000000000000
χ2122-2-22-2-222-2-2-2222-20000000000002-22-200000000
χ2222-2-22-2-222-2-2-2222-2000000000000-22-2200000000
χ2322-2-2-22-22-2200000022−2−2−2−222002i−2ii2−i2−i2i200000000
χ2422-2-2-22-22-2200000022−2−2−2−22200−2i2i−i2i2i2−i200000000
χ2522-2-2-22-22-22000000−2−22222−2−2002i−2i−i2i2i2−i200000000
χ2622-2-2-22-22-22000000−2−22222−2−200−2i2ii2−i2−i2i200000000
χ2722-2-2-2-22-22222-2-22-20000000000000000002i−2i0000
χ2822-2-2-2-22-22222-2-22-2000000000000000000−2i2i0000
χ2922-2-2-2-22-222-2-222-2200000000000000000000002-2
χ3022-2-2-2-22-222-2-222-220000000000000000000000-22
χ3144444-4-4-4-44000000000000000000000000000000
χ3244-4-4444-4-4-4000000000000000000000000000000
χ334-44i−4i00000022−222i2−2i200ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000
χ344-44i−4i00000022−222i2−2i200−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000
χ354-44i−4i000000−2222−2i22i200ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000
χ364-44i−4i000000−2222−2i22i200−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000
χ374-4−4i4i00000022−22−2i22i200ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ70000000000000000
χ384-4−4i4i00000022−22−2i22i200−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ70000000000000000
χ394-4−4i4i000000−22222i2−2i200ζ−ζ3−ζ5+ζ7−ζ+ζ3+ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ70000000000000000
χ404-4−4i4i000000−22222i2−2i200−ζ+ζ3+ζ5−ζ7ζ−ζ3−ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3+ζ5+ζ7−ζ−ζ3−ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ70000000000000000

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