Finite Group Databasebeta

← Group #12995

Character table — Group #12995

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112222222222444444444444448888888888888816161616
order1244222444888822448816161616161616168888888888161616162488
χ11111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ811111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ911-1-11-1-1-11111-1-11-11-11-1iiii−i−i−i−iii−i−iii−i−i1-1ii−i−i1-11-1
χ1011-1-11-1-1-11111-1-11-11-11-1iiii−i−i−i−i−i−iii−i−iii1-1ii−i−i-11-11
χ1111-1-11-1-1-11111-1-11-11-11-1−i−i−i−iiiiiii−i−iii−i−i1-1−i−iii-11-11
χ1211-1-11-1-1-11111-1-11-11-11-1−i−i−i−iiiii−i−iii−i−iii1-1−i−iii1-11-1
χ1311-1-11-1-1-11111-1-1-11-111-1iiii−i−i−i−iii−i−i−i−iii-11−i−iii1-1-11
χ1411-1-11-1-1-11111-1-1-11-111-1iiii−i−i−i−i−i−iiiii−i−i-11−i−iii-111-1
χ1511-1-11-1-1-11111-1-1-11-111-1−i−i−i−iiiiiii−i−i−i−iii-11ii−i−i-111-1
χ1611-1-11-1-1-11111-1-1-11-111-1−i−i−i−iiiii−i−iiiii−i−i-11ii−i−i1-1-11
χ172222222222-2-2-2-22222-2-20000000000000000-2-200000000
χ182222222222-2-2-2-2-2-2-2-2-2-200000000000000002200000000
χ192222-22-2-22-200002-2-220022−2−222−2−200000000002−22−20000
χ202222-22-2-22-200002-2-2200−2−222−2−2220000000000−22−220000
χ212222-22-2-22-20000-222-20022−2−222−2−20000000000−22−220000
χ222222-22-2-22-20000-222-200−2−222−2−22200000000002−22−20000
χ232222-2-22-2-2222220000-2-20000000000002-22-20000000000
χ242222-2-22-2-2222220000-2-2000000000000-22-220000000000
χ252222-2-22-2-22-2-2-2-2000022000000002-22-200000000000000
χ262222-2-22-2-22-2-2-2-200002200000000-22-2200000000000000
χ2722-2-22-2-2-222-2-2222-22-2-220000000000000000-2200000000
χ2822-2-22-2-2-222-2-222-22-22-2200000000000000002-200000000
χ2922-2-2-22-22-2222-2-20000-220000000000002i−2i−2i2i0000000000
χ3022-2-2-22-22-2222-2-20000-22000000000000−2i2i2i−2i0000000000
χ3122-2-2-22-22-22-2-22200002-2000000002i−2i−2i2i00000000000000
χ3222-2-2-22-22-22-2-22200002-200000000−2i2i2i−2i00000000000000
χ3322-2-2-2-2222-2000022-2-200i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ3422-2-2-2-2222-2000022-2-200−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ3522-2-2-2-2222-20000-2-22200i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ3622-2-2-2-2222-20000-2-22200−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ3744444-4-44-4-4000000000000000000000000000000000000
χ3844-4-4444-4-4-4000000000000000000000000000000000000
χ394-44i−4i00000022−222i2−2i2000000ζ+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−ζ7000000000000000000
χ404-44i−4i00000022−222i2−2i2000000−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+ζ7000000000000000000
χ414-44i−4i000000−2222−2i22i2000000ζ+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+ζ7000000000000000000
χ424-44i−4i000000−2222−2i22i2000000−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−ζ7000000000000000000
χ434-4−4i4i00000022−22−2i22i2000000ζ−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+ζ7000000000000000000
χ444-4−4i4i00000022−22−2i22i2000000−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−ζ7000000000000000000
χ454-4−4i4i000000−22222i2−2i2000000ζ−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−ζ7000000000000000000
χ464-4−4i4i000000−22222i2−2i2000000−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+ζ7000000000000000000

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