Finite Group Databasebeta

← Group #68772

Character table — Group #68772

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order1222223444466612121212444444446612121212121212121212881212121224242424224444444488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ911-1-1-1111-1-111-1-111-1-1ii−i−i11-1-1-111-11111-1-1-1-1i−iii−i−iii−i−i1-11-1ii−i−ii−i1-1
χ1011-1-1-1111-1-111-1-111-1-1ii−i−i11-1-1-111-11111-1-1-1-1i−iii−i−iii−i−i-11-11−i−iii−ii-11
χ1111-1-1-1111-1-111-1-111-1-1ii−i−i-1-111-111-1-1-1-1-11111−iiii−i−i−i−iii1-11-1ii−i−i−ii-11
χ1211-1-1-1111-1-111-1-111-1-1ii−i−i-1-111-111-1-1-1-1-11111−iiii−i−i−i−iii-11-11−i−iiii−i1-1
χ1311-1-1-1111-1-111-1-111-1-1−i−iii11-1-1-111-11111-1-1-1-1−ii−i−iii−i−iii1-11-1−i−iii−ii1-1
χ1411-1-1-1111-1-111-1-111-1-1−i−iii11-1-1-111-11111-1-1-1-1−ii−i−iii−i−iii-11-11ii−i−ii−i-11
χ1511-1-1-1111-1-111-1-111-1-1−i−iii-1-111-111-1-1-1-1-11111i−i−i−iiiii−i−i1-11-1−i−iiii−i-11
χ1611-1-1-1111-1-111-1-111-1-1−i−iii-1-111-111-1-1-1-1-11111i−i−i−iiiii−i−i-11-11ii−i−i−ii1-1
χ172222222-2-2-2-2222-2-2-2-20000000022-2-200000000000000000000002-22-20000
χ182222222-2-2-2-2222-2-2-2-20000000022-2-20000000000000000000000-22-220000
χ19222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-1-1-11111000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111221111-1-1-1-1000000000000
χ232222-2-222-22-2222222200000000-2-2-2-200000000000000000022-2-200000000
χ242222-2-222-22-2222222200000000-2-2-2-2000000000000000000-2-22200000000
χ252222-2-22-22-22222-2-2-2-22-22-20000-2-22200000000002-22-20000000000000000
χ262222-2-22-22-22222-2-2-2-2-22-220000-2-2220000000000-22-220000000000000000
χ272222-2-2-1-22-22-1-1-111112-22-2000011-1-133−3−333−3−300-11-113−33−3000000000000
χ282222-2-2-1-22-22-1-1-111112-22-2000011-1-1−3−333−3−33300-11-11−33−33000000000000
χ292222-2-2-1-22-22-1-1-11111-22-22000011-1-133−3−333−3−3001-11-1−33−33000000000000
χ302222-2-2-1-22-22-1-1-11111-22-22000011-1-1−3−333−3−333001-11-13−33−3000000000000
χ3122-2-22-2222-2-22-2-222-2-2000000002-2-220000000000000000002-2-2200000000
χ3222-2-22-2222-2-22-2-222-2-2000000002-2-22000000000000000000-222-200000000
χ3322-2-22-22-2-2222-2-2-2-2222i−2i−2i2i00002-22-200000000002i−2i−2i2i0000000000000000
χ3422-2-22-22-2-2222-2-2-2-222−2i2i2i−2i00002-22-20000000000−2i2i2i−2i0000000000000000
χ3522-2-22-2-1-2-222-11111-1-12i−2i−2i2i0000-11-1133−3−3−3−33300−iii−ii3−i3−i3i3000000000000
χ3622-2-22-2-1-2-222-11111-1-12i−2i−2i2i0000-11-11−3−33333−3−300−iii−i−i3i3i3−i3000000000000
χ3722-2-22-2-1-2-222-11111-1-1−2i2i2i−2i0000-11-1133−3−3−3−33300i−i−ii−i3i3i3−i3000000000000
χ3822-2-22-2-1-2-222-11111-1-1−2i2i2i−2i0000-11-11−3−33333−3−300i−i−iii3−i3−i3i3000000000000
χ3922-2-2-222-222-22-2-2-2-22200000000-22-2200000000000000000000002i−2i−2i2i0000
χ4022-2-2-222-222-22-2-2-2-22200000000-22-220000000000000000000000−2i2i2i−2i0000
χ4122-2-2-22-12-2-22-111-1-1112i2i−2i−2i22-2-21-1-11-1-1-1-111112i−2i−i−iii−i−iii000000000000
χ4222-2-2-22-12-2-22-111-1-1112i2i−2i−2i-2-2221-1-111111-1-1-1-1−2i2i−i−iiiii−i−i000000000000
χ4322-2-2-22-12-2-22-111-1-111−2i−2i2i2i22-2-21-1-11-1-1-1-11111−2i2iii−i−iii−i−i000000000000
χ4422-2-2-22-12-2-22-111-1-111−2i−2i2i2i-2-2221-1-111111-1-1-1-12i−2iii−i−i−i−iii000000000000
χ45444444-2-4-4-4-4-2-2-2222200000000-2-222000000000000000000000000000000
χ464444-4-4-24-44-4-2-2-2-2-2-2-2000000002222000000000000000000000000000000
χ4744-4-44-4-244-4-4-222-2-22200000000-222-2000000000000000000000000000000
χ4844-4-4-44-2-444-4-22222-2-2000000002-22-2000000000000000000000000000000
χ494-44-40040000-44-4000000002i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i0000000000000000000000
χ504-44-40040000-44-400000000−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i0000000000000000000000
χ514-44-400-200002-2223−2323−2300002i−2i2i−2i0000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ524-44-400-200002-2223−2323−230000−2i2i−2i2i0000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ534-44-400-200002-22−2323−232300002i−2i2i−2i0000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ544-44-400-200002-22−2323−23230000−2i2i−2i2i0000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ554-4-440040000-4-44000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ564-4-440040000-4-4400000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ574-4-4400-2000022-223−23−232300002i−2i−2i2i0000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ584-4-4400-2000022-223−23−23230000−2i2i2i−2i0000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ594-4-4400-2000022-2−232323−2300002i−2i−2i2i0000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ604-4-4400-2000022-2−232323−230000−2i2i2i−2i0000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000

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