Finite Group Databasebeta

← Group #5196

Character table — Group #5196

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42
size1111222222222233334444444444666666888812121212
order124423468888121288882244612242424244444886612128888
χ1111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-11111111-11-111-1-1-1-1-1-1-1-1111-11-111-1-1
χ611111111-1-1-1-1111111-11-1111-1-1-1-1-1-1-1-111-11-11-1-111
χ711111111-1-1-1-111-1-1-1-11-11-111-1-1-1-11111-1-11-11-1-1-111
χ811111111-1-1-1-111-1-1-1-1-11-1111-1-1-1-11111-1-1-11-1111-1-1
χ911-1-1-111111-1-1-1-1ii−i−i11-1-1-1111-1-1ii−i−ii−i11-1-1i−ii−i
χ1011-1-1-111111-1-1-1-1ii−i−i-1-111-1111-1-1ii−i−ii−i-1-111−ii−ii
χ1111-1-1-111111-1-1-1-1−i−iii11-1-1-1111-1-1−i−iii−ii11-1-1−ii−ii
χ1211-1-1-111111-1-1-1-1−i−iii-1-111-1111-1-1−i−iii−ii-1-111i−ii−i
χ1311-1-1-1111-1-111-1-1ii−i−i1-1-11-11-1-111−i−iiii−i1-1-11i−i−ii
χ1411-1-1-1111-1-111-1-1ii−i−i-111-1-11-1-111−i−iiii−i-111-1−iii−i
χ1511-1-1-1111-1-111-1-1−i−iii1-1-11-11-1-111ii−i−i−ii1-1-11−iii−i
χ1611-1-1-1111-1-111-1-1−i−iii-111-1-11-1-111ii−i−i−ii-111-1i−i−ii
χ1722222-12-12222-1-100002222-1-1-1-1-1-1000000-1-1-1-10000
χ1822222-12-12222-1-10000-2-2-2-2-1-1-1-1-1-100000011110000
χ1922222-12-1-2-2-2-2-1-100002-22-2-1-11111000000-11-110000
χ2022222-12-1-2-2-2-2-1-10000-22-22-1-111110000001-11-10000
χ212222-22-2200002222220000-2-200000000-2-200000000
χ222222-22-22000022-2-2-2-20000-2-2000000002200000000
χ2322-2-222-220000-2-22i2i−2i−2i00002-200000000−2i2i00000000
χ2422-2-222-220000-2-2−2i−2i2i2i00002-2000000002i−2i00000000
χ2522-2-2-2-12-122-2-211000022-2-21-1-1-111000000-1-1110000
χ2622-2-2-2-12-122-2-2110000-2-2221-1-1-11100000011-1-10000
χ2722-2-2-2-12-1-2-2221100002-2-221-111-1-1000000-111-10000
χ2822-2-2-2-12-1-2-222110000-222-21-111-1-10000001-1-110000
χ292-22i−2i020-22−2i2−i22i−2i2ζ−2ζ2ζ3−2ζ30000002−2i2−i21+i−1−i1−i−1+i0000000000
χ302-22i−2i020-22−2i2−i22i−2i−2ζ2ζ−2ζ32ζ30000002−2i2−i2−1−i1+i−1+i1−i0000000000
χ312-22i−2i020-2−22−i2i22i−2i2ζ−2ζ2ζ3−2ζ3000000−22−i2i2−1−i1+i−1+i1−i0000000000
χ322-22i−2i020-2−22−i2i22i−2i−2ζ2ζ−2ζ32ζ3000000−22−i2i21+i−1−i1−i−1+i0000000000
χ332-2−2i2i020-22−2−i2i2−2i2i2ζ3−2ζ32ζ−2ζ0000002−2−i2i2−1+i1−i−1−i1+i0000000000
χ342-2−2i2i020-22−2−i2i2−2i2i−2ζ32ζ3−2ζ2ζ0000002−2−i2i21−i−1+i1+i−1−i0000000000
χ352-2−2i2i020-2−22i2−i2−2i2i2ζ3−2ζ32ζ−2ζ000000−22i2−i21−i−1+i1+i−1−i0000000000
χ362-2−2i2i020-2−22i2−i2−2i2i−2ζ32ζ3−2ζ2ζ000000−22i2−i2−1+i1−i−1−i1+i0000000000
χ374444-4-2-4-20000-2-20000000022000000000000000000
χ3844-4-44-2-4-200002200000000-22000000000000000000
χ394-44i−4i0-20222−222i2−2i2−2i2i0000000000−22−i2i200000000000000
χ404-44i−4i0-202−2222−2i22i2−2i2i00000000002−2i2−i200000000000000
χ414-4−4i4i0-20222−22−2i22i22i−2i0000000000−22i2−i200000000000000
χ424-4−4i4i0-202−22222i2−2i22i−2i00000000002−2−i2i200000000000000

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