Finite Group Databasebeta

← Group #70375

Character table — Group #70375

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111122222222222222444444444444444444448888888888121212121212121224242424
order12442223444666121212122244444466121212121212121212126688121224242424888888884488
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
χ5111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ911-1-1-11-111-11-1-11-1-1111-11-111-1-1-111-11111-1-1-1-11-11-11-111-1-1ii−i−iii−i−ii−ii−i
χ1011-1-1-11-111-11-1-11-1-1111-11-111-1-1-111-11111-1-1-1-11-11-11-111-1-1−i−iii−i−iii−ii−ii
χ1111-1-1-11-111-11-1-11-1-1111-11-1-1-111-111-1-1-1-1-111111-1-111-1-1-111ii−i−iii−i−i−ii−ii
χ1211-1-1-11-111-11-1-11-1-1111-11-1-1-111-111-1-1-1-1-111111-1-111-1-1-111−i−iii−i−iiii−ii−i
χ1311-1-1-11-111-11-1-11-1-111-11-1111-1-1-111-11111-1-1-1-1-11-11-11-1-111ii−i−i−i−iiii−i−ii
χ1411-1-1-11-111-11-1-11-1-111-11-1111-1-1-111-11111-1-1-1-1-11-11-11-1-111−i−iiiii−i−i−iii−i
χ1511-1-1-11-111-11-1-11-1-111-11-11-1-111-111-1-1-1-1-11111-111-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611-1-1-11-111-11-1-11-1-111-11-11-1-111-111-1-1-1-1-11111-111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ172222222-1222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-2-2-1-11111000000000000
χ192222222-1222-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-111-2-2111111000000000000
χ202222222-1222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111112211-1-1-1-1000000000000
χ2122222-2-22-2-22222222200000000-2-2-2-20000000000000000002-22-200000000
χ2222222-2-22-2-22222222200000000-2-2-2-2000000000000000000-22-2200000000
χ232222-22-22-22-2-2-2222-2-200000000-22-2200000000000000000000002-22-20000
χ242222-22-22-22-2-2-2222-2-200000000-22-220000000000000000000000-22-220000
χ252222-2-2222-2-2-2-2222-2-22-2-2200002-22-2000000002-200-220000000000000000
χ262222-2-2222-2-2-2-2222-2-2-222-200002-22-200000000-22002-20000000000000000
χ272222-2-22-12-2-211-1-1-1112-2-220000-11-1133−3−333−3−3-11001-13−33−3000000000000
χ282222-2-22-12-2-211-1-1-1112-2-220000-11-11−3−333−3−333-11001-1−33−33000000000000
χ292222-2-22-12-2-211-1-1-111-222-20000-11-1133−3−333−3−31-100-11−33−33000000000000
χ302222-2-22-12-2-211-1-1-111-222-20000-11-11−3−333−3−3331-100-113−33−3000000000000
χ3122-2-22222-2-2-2222-2-2-2-20000000022-2-200000000000000000000002i−2i−2i2i0000
χ3222-2-22222-2-2-2222-2-2-2-20000000022-2-20000000000000000000000−2i2i2i−2i0000
χ3322-2-22-2-2222-2222-2-2-2-222-2-20000-2-222000000002200-2-20000000000000000
χ3422-2-22-2-2222-2222-2-2-2-2-2-2220000-2-22200000000-2-200220000000000000000
χ3522-2-22-2-2-122-2-1-1-1111122-2-2000011-1-133−3−3−3−333-1-100113−3−33000000000000
χ3622-2-22-2-2-122-2-1-1-1111122-2-2000011-1-1−3−33333−3−3-1-10011−333−3000000000000
χ3722-2-22-2-2-122-2-1-1-11111-2-222000011-1-133−3−3−3−3331100-1-1−333−3000000000000
χ3822-2-22-2-2-122-2-1-1-11111-2-222000011-1-1−3−33333−3−31100-1-13−3−33000000000000
χ3922-2-2-22-2-12-2211-111-1-12-22-222-2-21-1-11-1-1-1-11111-112-2-11-1-111000000000000
χ4022-2-2-22-2-12-2211-111-1-12-22-2-2-2221-1-111111-1-1-1-1-11-22-1111-1-1000000000000
χ4122-2-2-22-2-12-2211-111-1-1-22-2222-2-21-1-11-1-1-1-111111-1-221-111-1-1000000000000
χ4222-2-2-22-2-12-2211-111-1-1-22-22-2-2221-1-111111-1-1-1-11-12-21-1-1-111000000000000
χ4322-2-2-2-222-222-2-22-2-222000000002-2-220000000000000000002i−2i−2i2i00000000
χ4422-2-2-2-222-222-2-22-2-222000000002-2-22000000000000000000−2i2i2i−2i00000000
χ4544444-4-4-2-4-44-2-2-2-2-2-2-2000000002222000000000000000000000000000000
χ464444-44-4-2-44-422-2-2-222000000002-22-2000000000000000000000000000000
χ4744-4-4444-2-4-4-4-2-2-2222200000000-2-222000000000000000000000000000000
χ4844-4-4-4-44-2-44422-222-2-200000000-222-2000000000000000000000000000000
χ494-44i−4i000400000-44i−4i0000002-22i−2i00002-22-22i−2i2i−2i0000000000000000000000
χ504-44i−4i000400000-44i−4i000000-22−2i2i0000-22-22−2i2i−2i2i0000000000000000000000
χ514-44i−4i000-2000−2i32i32−2i2i23−2300002-22i−2i0000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000000000000000000
χ524-44i−4i000-2000−2i32i32−2i2i23−230000-22−2i2i00001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ534-44i−4i000-20002i3−2i32−2i2i−232300002-22i−2i0000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ544-44i−4i000-20002i3−2i32−2i2i−23230000-22−2i2i00001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ554-4−4i4i000400000-4−4i4i0000002-2−2i2i00002-22-2−2i2i−2i2i0000000000000000000000
χ564-4−4i4i000400000-4−4i4i000000-222i−2i0000-22-222i−2i2i−2i0000000000000000000000
χ574-4−4i4i000-2000−2i32i322i−2i−232300002-2−2i2i0000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000000000000000000
χ584-4−4i4i000-2000−2i32i322i−2i−23230000-222i−2i00001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000000000000000000
χ594-4−4i4i000-20002i3−2i322i−2i23−2300002-2−2i2i0000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000000000000000000
χ604-4−4i4i000-20002i3−2i322i−2i23−230000-222i−2i00001−3−1+31+3−1−3ζ2+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.