Finite Group Databasebeta

← Group #4451

Character table — Group #4451

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39
size111122222222222244444444444444444121212122424
order122222344666666644444121212121212121212121212888824
χ1111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−iii−i−i1-1
χ61111-1-11-1-111-1-11-1-11ii−i−i11-1-1iiii−i−i−i−i−i−iii-11
χ71111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiiiii−i−i-11
χ81111-1-11-1-111-1-11-1-11−i−iii11-1-1−i−i−i−iiiii−i−iii1-1
χ92222222-2-22222222-20000-2-2-2-200000000000000
χ10222222-122-1-1-1-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1000000
χ11222222-122-1-1-1-1-1-1-12-2-2-2-2-1-1-1-111111111000000
χ12222222-1-2-2-1-1-1-1-1-1-1-200001111−i3−i3i3i3−i3−i3i3i3000000
χ13222222-1-2-2-1-1-1-1-1-1-1-200001111i3i3−i3−i3i3i3−i3−i3000000
χ142222-2-222222-2-22-2-2-20000-2-22200000000000000
χ152222-2-2-122-1-111-111-2000011-1-133−3−3−3−333000000
χ162222-2-2-122-1-111-111-2000011-1-1−3−33333−3−3000000
χ172222-2-2-1-2-2-1-111-11122i2i−2i−2i-1-111−i−i−i−iiiii000000
χ182222-2-2-1-2-2-1-111-1112−2i−2i2i2i-1-111iiii−i−i−i−i000000
χ1922-2-20022i−2i2-200-20001+i−1−i1−i−1+i002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000
χ2022-2-20022i−2i2-200-2000−1−i1+i−1+i1−i002i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ2122-2-2002−2i2i2-200-20001−i−1+i1+i−1−i00−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000
χ2222-2-2002−2i2i2-200-2000−1+i1−i−1−i1+i00−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000
χ2322-2-200-12i−2i-11−i3i31−i3i301+i−1−i1−i−1+i3−3−ii−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000
χ2422-2-200-12i−2i-11−i3i31−i3i30−1−i1+i−1+i1−i3−3−iiζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000
χ2522-2-200-12i−2i-11i3−i31i3−i301+i−1−i1−i−1+i−33−ii−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000
χ2622-2-200-12i−2i-11i3−i31i3−i30−1−i1+i−1+i1−i−33−iiζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000
χ2722-2-200-1−2i2i-11−i3i31−i3i301−i−1+i1+i−1−i−33i−i−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000
χ2822-2-200-1−2i2i-11−i3i31−i3i30−1+i1−i−1−i1+i−33i−iζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000
χ2922-2-200-1−2i2i-11i3−i31i3−i301−i−1+i1+i−1−i3−3i−i−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000
χ3022-2-200-1−2i2i-11i3−i31i3−i30−1+i1−i−1−i1+i3−3i−iζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000
χ312-2-222-2200-2222-2-2-200000000000000000−i2i2−i2i200
χ322-2-222-2200-2222-2-2-200000000000000000i2−i2i2−i200
χ332-2-22-22200-22-2-2-222000000000000000002−2−2200
χ342-2-22-22200-22-2-2-22200000000000000000−222−200
χ354-44-400400-4-40040000000000000000000000000
χ364-44-400-20022−2i32i3-22i3−2i300000000000000000000000
χ374-44-400-200222i3−2i3-2−2i32i300000000000000000000000
χ384-4-444-4-2002-2-2-222200000000000000000000000
χ394-4-44-44-2002-2222-2-200000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.