Finite Group Databasebeta

← Group #70365

Character table — Group #70365

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order12222234444666121212122244444466121212121212121212126688121224242424444444444488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ91-11-11-111-1-11-1-1111-1-11-11-1ii−i−i1-11-1iiii−i−i−i−i1-1i−i1-1ii−i−ii−ii−iii−i−i1-11-1
χ101-11-11-111-1-11-1-1111-1-11-11-1ii−i−i1-11-1iiii−i−i−i−i1-1i−i1-1ii−i−i−ii−ii−i−iii-11-11
χ111-11-11-111-1-11-1-1111-1-11-11-1−i−iii1-11-1−i−i−i−iiiii1-1−ii1-1−i−iiii−ii−iii−i−i-11-11
χ121-11-11-111-1-11-1-1111-1-11-11-1−i−iii1-11-1−i−i−i−iiiii1-1−ii1-1−i−iii−ii−ii−i−iii1-11-1
χ131-11-11-111-1-11-1-1111-1-1-11-11ii−i−i1-11-1iiii−i−i−i−i-11−ii-11−i−iiii−ii−i−i−iii-111-1
χ141-11-11-111-1-11-1-1111-1-1-11-11ii−i−i1-11-1iiii−i−i−i−i-11−ii-11−i−iii−ii−iiii−i−i1-1-11
χ151-11-11-111-1-11-1-1111-1-1-11-11−i−iii1-11-1−i−i−i−iiiii-11i−i-11ii−i−ii−ii−i−i−iii1-1-11
χ161-11-11-111-1-11-1-1111-1-1-11-11−i−iii1-11-1−i−i−i−iiiii-11i−i-11ii−i−i−ii−iiii−i−i-111-1
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
χ19222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-2-2-1-11111000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-111-2-2111111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111112211-1-1-1-1000000000000
χ232222-2-222-22-2222222200000000-2-2-2-200000000000000000022-2-200000000
χ242222-2-222-22-2222222200000000-2-2-2-2000000000000000000-2-22200000000
χ252222-2-22-22-22222-2-2-2-222-2-20000-2-222000000002200-2-20000000000000000
χ262222-2-22-22-22222-2-2-2-2-2-2220000-2-22200000000-2-200220000000000000000
χ272222-2-2-1-22-22-1-1-1111122-2-2000011-1-133−3−333−3−3-1-100113−33−3000000000000
χ282222-2-2-1-22-22-1-1-1111122-2-2000011-1-1−3−333−3−333-1-10011−33−33000000000000
χ292222-2-2-1-22-22-1-1-11111-2-222000011-1-133−3−333−3−31100-1-1−33−33000000000000
χ302222-2-2-1-22-22-1-1-11111-2-222000011-1-1−3−333−3−3331100-1-13−33−3000000000000
χ312-22-22-22-222-2-2-22-2-222000000002-2-2200000000000000000000002i−2i−2i2i0000
χ322-22-22-22-222-2-2-22-2-222000000002-2-220000000000000000000000−2i2i2i−2i0000
χ332-22-22-2-12-2-2211-1-1-1112-22-22i2i−2i−2i-11-11−i−i−i−iiiii-112i−2i-11−i−iii000000000000
χ342-22-22-2-12-2-2211-1-1-1112-22-2−2i−2i2i2i-11-11iiii−i−i−i−i-11−2i2i-11ii−i−i000000000000
χ352-22-22-2-12-2-2211-1-1-111-22-222i2i−2i−2i-11-11−i−i−i−iiiii1-1−2i2i1-1ii−i−i000000000000
χ362-22-22-2-12-2-2211-1-1-111-22-22−2i−2i2i2i-11-11iiii−i−i−i−i1-12i−2i1-1−i−iii000000000000
χ372-22-2-22222-2-2-2-2222-2-200000000-22-220000000000000000002i−2i−2i2i00000000
χ382-22-2-22222-2-2-2-2222-2-200000000-22-22000000000000000000−2i2i2i−2i00000000
χ392-22-2-222-2-222-2-22-2-2222-2-220000-222-2000000002-200-220000000000000000
χ402-22-2-222-2-222-2-22-2-222-222-20000-222-200000000-22002-20000000000000000
χ412-22-2-22-1-2-22211-111-1-12-2-2200001-1-11−i3−i3i3i3i3i3−i3−i3-11001-1−i3i3i3−i3000000000000
χ422-22-2-22-1-2-22211-111-1-12-2-2200001-1-11i3i3−i3−i3−i3−i3i3i3-11001-1i3−i3−i3i3000000000000
χ432-22-2-22-1-2-22211-111-1-1-222-200001-1-11−i3−i3i3i3i3i3−i3−i31-100-11i3−i3−i3i3000000000000
χ442-22-2-22-1-2-22211-111-1-1-222-200001-1-11i3i3−i3−i3−i3−i3i3i31-100-11−i3i3i3−i3000000000000
χ45444444-2-4-4-4-4-2-2-2222200000000-2-222000000000000000000000000000000
χ464444-4-4-24-44-4-2-2-2-2-2-2-2000000002222000000000000000000000000000000
χ4744-4-400400004-4-4000000002-22-200002-22-22-22-20000000000000000000000
χ4844-4-400400004-4-400000000-22-220000-22-22-22-220000000000000000000000
χ4944-4-400-20000-22223−2323−2300002-22-20000−1+31−3−1−31+3−1+31−3−1−31+30000000000000000000000
χ5044-4-400-20000-22223−2323−230000-22-2200001−3−1+31+3−1−31−3−1+31+3−1−30000000000000000000000
χ5144-4-400-20000-222−2323−232300002-22-20000−1−31+3−1+31−3−1−31+3−1+31−30000000000000000000000
χ5244-4-400-20000-222−2323−23230000-22-2200001+3−1−31−3−1+31+3−1−31−3−1+30000000000000000000000
χ534-44-44-4-2-444-422-222-2-200000000-222-2000000000000000000000000000000
χ544-44-4-44-244-4-422-2-2-222000000002-22-2000000000000000000000000000000
χ554-4-440040000-44-4000000002i−2i−2i2i00002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ564-4-440040000-44-400000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ574-4-4400-200002-2223−23−232300002i−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
χ584-4-4400-200002-2223−23−23230000−2i2i2i−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
χ594-4-4400-200002-22−232323−2300002i−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
χ604-4-4400-200002-22−232323−230000−2i2i2i−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

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