Finite Group Databasebeta

← Group #73113

Character table — Group #73113

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222333366666688888888888888882424242424242424
order12224488882222448888366612121212242424242424242422444444
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ4111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ51-11-11-1ii−i−i1-11-11-1ii−i−i1-1-1111-1-1iiii−i−i−i−i1-1i−i1-1i−i
χ61-11-11-1ii−i−i1-11-11-1ii−i−i1-1-1111-1-1iiii−i−i−i−i-11−ii-11−ii
χ71-11-11-1−i−iii1-11-11-1−i−iii1-1-1111-1-1−i−i−i−iiiii1-1−ii1-1−ii
χ81-11-11-1−i−iii1-11-11-1−i−iii1-1-1111-1-1−i−i−i−iiiii-11i−i-11i−i
χ922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ10222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ112222-2-200002222-2-200002222-2-2-2-20000000000000000
χ122222-2-200002222-2-20000-1-1-1-1111133−3−333−3−300000000
χ132222-2-200002222-2-20000-1-1-1-11111−3−333−3−33300000000
χ1422-2-200−i2i2−i2i2-222-200−i2i2−i2i222-2-20000−i2i2−i2i2−i2i2−i2i200000000
χ1522-2-200−i2i2−i2i2-222-200−i2i2−i2i2-1-1113−33−3ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000
χ1622-2-200−i2i2−i2i2-222-200−i2i2−i2i2-1-111−33−33ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000
χ1722-2-200i2−i2i2−i2-222-200i2−i2i2−i222-2-20000i2−i2i2−i2i2−i2i2−i200000000
χ1822-2-200i2−i2i2−i2-222-200i2−i2i2−i2-1-1113−33−3−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000
χ1922-2-200i2−i2i2−i2-222-200i2−i2i2−i2-1-111−33−33−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000
χ202-22-22-22i2i−2i−2i2-22-22-22i2i−2i−2i-111-1-1-111−i−i−i−iiiii00000000
χ212-22-22-2−2i−2i2i2i2-22-22-2−2i−2i2i2i-111-1-1-111iiii−i−i−i−i00000000
χ222-22-2-2200002-22-2-2200002-2-22-2-2220000000000000000
χ232-22-2-2200002-22-2-220000-111-111-1-1−i3−i3i3i3i3i3−i3−i300000000
χ242-22-2-2200002-22-2-220000-111-111-1-1i3i3−i3−i3−i3−i3i3i300000000
χ252-2-22002−2−22-2-222002−2−222-22-200002−22−2−22−2200000000
χ262-2-22002−2−22-2-222002−2−22-11-113−3−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000
χ272-2-22002−2−22-2-222002−2−22-11-11−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000
χ282-2-2200−222−2-2-22200−222−22-22-20000−22−222−22−200000000
χ292-2-2200−222−2-2-22200−222−2-11-113−3−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000
χ302-2-2200−222−2-2-22200−222−2-11-11−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000
χ313333333333-1-1-1-1-1-1-1-1-1-100000000000000001111-1-1-1-1
χ323333333333-1-1-1-1-1-1-1-1-1-10000000000000000-1-1-1-11111
χ33333333-3-3-3-3-1-1-1-1-1-11111000000000000000011-1-1-1-111
χ34333333-3-3-3-3-1-1-1-1-1-111110000000000000000-1-11111-1-1
χ353-33-33-33i3i−3i−3i-11-11-11−i−iii00000000000000001-1i−i-11−ii
χ363-33-33-33i3i−3i−3i-11-11-11−i−iii0000000000000000-11−ii1-1i−i
χ373-33-33-3−3i−3i3i3i-11-11-11ii−i−i00000000000000001-1−ii-11i−i
χ383-33-33-3−3i−3i3i3i-11-11-11ii−i−i0000000000000000-11i−i1-1−ii
χ396666-6-60000-2-2-2-2220000000000000000000000000000
χ4066-6-600−3i23i2−3i23i22-2-2200i2−i2i2−i2000000000000000000000000
χ4166-6-6003i2−3i23i2−3i22-2-2200−i2i2−i2i2000000000000000000000000
χ426-66-6-660000-22-222-20000000000000000000000000000
χ436-6-660032−32−323222-2-200−222−2000000000000000000000000
χ446-6-6600−323232−3222-2-2002−2−22000000000000000000000000

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