Finite Group Databasebeta

← Group #4823

Character table — Group #4823

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36
size111122222244444444444466668888121212121212
order1244234612122444688121212121288886122424248888
χ1111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111-1-11-1-11-1-1-1-1111111-1-1-1-111-1-1
χ4111111111111-1-11-1-11-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111-1-1111-1-1111111111-1-1-1-1-1-1-1-111
χ61111111111-1-1111-1-111111-1-1-1-1-1-1-1-11111-1-1
χ71111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111
χ911-1-1-1111-1-11-1i−i-1i−i1ii−i−iii−i−i1-1i−i1-1i−i1-1
χ1011-1-1-1111-1-11-1i−i-1i−i1ii−i−i−i−iii1-1i−i-11−ii-11
χ1111-1-1-1111-1-11-1−ii-1−ii1−i−iiiii−i−i1-1−ii-11i−i-11
χ1211-1-1-1111-1-11-1−ii-1−ii1−i−iii−i−iii1-1−ii1-1−ii1-1
χ1311-1-1-1111-1-1-11i−i-1−ii1ii−i−iii−i−i-11−ii-11−ii1-1
χ1411-1-1-1111-1-1-11i−i-1−ii1ii−i−i−i−iii-11−ii1-1i−i-11
χ1511-1-1-1111-1-1-11−ii-1i−i1−i−iiiii−i−i-11i−i1-1−ii-11
χ1611-1-1-1111-1-1-11−ii-1i−i1−i−iii−i−iii-11i−i-11i−i1-1
χ1722222-12-1-1-12222-122-1-1-1-1-10000-1-1-1-1000000
χ1822222-12-1-1-122-2-2-1-2-2-111110000-1-111000000
χ1922222-12-1-1-1-2-222-1-2-2-1-1-1-1-100001111000000
χ2022222-12-1-1-1-2-2-2-2-122-11111000011-1-1000000
χ212222-22-22220000-200-200002-22-20000000000
χ222222-22-22220000-200-20000-22-220000000000
χ2322-2-222-22-2-20000200-200002i−2i−2i2i0000000000
χ2422-2-222-22-2-20000200-20000−2i2i2i−2i0000000000
χ2522-2-2-2-12-1112-22i−2i12i−2i-1−i−iii0000-11−ii000000
χ2622-2-2-2-12-1112-2−2i2i1−2i2i-1ii−i−i0000-11i−i000000
χ2722-2-2-2-12-111-222i−2i1−2i2i-1−i−iii00001-1i−i000000
χ2822-2-2-2-12-111-22−2i2i12i−2i-1ii−i−i00001-1−ii000000
χ294444-4-2-4-2-2-200002002000000000000000000
χ3044-4-44-2-4-2220000-2002000000000000000000
χ314-44i−4i040-44i−4i00000000000000000000000000
χ324-44i−4i0-202−2i2i00000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000000000
χ334-44i−4i0-202−2i2i00000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000000000
χ344-4−4i4i040-4−4i4i00000000000000000000000000
χ354-4−4i4i0-2022i−2i00000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000000000
χ364-4−4i4i0-2022i−2i00000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.