Finite Group Databasebeta

← Group #816

Character table — Group #816

Order 96.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30
size1111222222222222222222222212121212
order122234466688881212121224242424242424244444
χ1111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1
χ31111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ41111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ51-1-1111-1-1-11ii−i−i11-1-1iiii−i−i−i−ii−i1-1
χ61-1-1111-1-1-11ii−i−i11-1-1iiii−i−i−i−i−ii-11
χ71-1-1111-1-1-11−i−iii11-1-1−i−i−i−iiiiii−i-11
χ81-1-1111-1-1-11−i−iii11-1-1−i−i−i−iiiii−ii1-1
χ922222-2-22220000-2-2-2-2000000000000
χ102222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000
χ112222-122-1-1-1-2-2-2-2-1-1-1-1111111110000
χ122222-1-2-2-1-1-10000111133−3−333−3−30000
χ132222-1-2-2-1-1-100001111−3−333−3−3330000
χ1422-2-22002-2-22−22−200002−22−22−22−20000
χ1522-2-22002-2-2−22−220000−22−22−22−220000
χ1622-2-2-100-1112−22−23−33−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ1722-2-2-100-1112−22−2−33−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ1822-2-2-100-111−22−223−33−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ1922-2-2-100-111−22−22−33−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ202-22-2200-22-2−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i20000
χ212-22-2200-22-2i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i20000
χ222-22-2-1001-11−i2i2i2−i23−3−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ232-22-2-1001-11−i2i2i2−i2−333−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ242-22-2-1001-11i2−i2−i2i23−3−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ252-22-2-1001-11i2−i2−i2i2−333−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ262-2-222-22-2-220000-2-222000000000000
χ272-2-22-12-211-12i2i−2i−2i-1-111−i−i−i−iiiii0000
χ282-2-22-12-211-1−2i−2i2i2i-1-111iiii−i−i−i−i0000
χ292-2-22-1-2211-1000011-1-1−i3−i3i3i3i3i3−i3−i30000
χ302-2-22-1-2211-1000011-1-1i3i3−i3−i3−i3−i3i3i30000

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