Finite Group Databasebeta

← Group #70368

Character table — Group #70368

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11112222222222222244444444444444448888888888882424242424242424
order12442223444666121212124444661212121212121212121224668812122424242444444488
χ1111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1
χ8111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111
χ92222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000
χ102222222-1222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000
χ112222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-2-2-1-1111100000000
χ122222222-1222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2112211-1-1-1-100000000
χ1322222-2-22-2-2222222220000-2-2-2-2000000000000000000002i−2i000000
χ1422222-2-22-2-2222222220000-2-2-2-200000000000000000000−2i2i000000
χ152222-22-222-2-2-2-2222-2-200002-22-20000000000002i−2i002i2i−2i−2i00000000
χ162222-22-222-2-2-2-2222-2-200002-22-2000000000000−2i2i00−2i−2i2i2i00000000
χ172222-22-2-12-2-211-1-1-1110000-11-113333−3−3−3−300−i3i32i−2i−i3i3−i−iii00000000
χ182222-22-2-12-2-211-1-1-1110000-11-113333−3−3−3−300i3−i3−2i2ii3−i3ii−i−i00000000
χ192222-22-2-12-2-211-1-1-1110000-11-11−3−3−3−3333300−i3i3−2i2i−i3i3ii−i−i00000000
χ202222-22-2-12-2-211-1-1-1110000-11-11−3−3−3−3333300i3−i32i−2ii3−i3−i−iii00000000
χ212222-2-222-22-2-2-2222-2-20000-22-220000000000000000000000002-200
χ222222-2-222-22-2-2-2222-2-20000-22-22000000000000000000000000-2200
χ2322-2-22222-2-2-2222-2-2-2-2000022-2-200000000000000000000002-20000
χ2422-2-22222-2-2-2222-2-2-2-2000022-2-20000000000000000000000-220000
χ2522-2-22-2-2222-2222-2-2-2-20000-2-222000000002-22200-2-2000000000000
χ2622-2-22-2-2222-2222-2-2-2-20000-2-22200000000-22-2-20022000000000000
χ2722-2-22-2-2-122-2-1-1-11111000011-1-133−3−333−3−32-2-1-100113−33−300000000
χ2822-2-22-2-2-122-2-1-1-11111000011-1-133−3−333−3−3-221100-1-1−33−3300000000
χ2922-2-22-2-2-122-2-1-1-11111000011-1-1−3−333−3−3332-2-1-10011−33−3300000000
χ3022-2-22-2-2-122-2-1-1-11111000011-1-1−3−333−3−333-221100-1-13−33−300000000
χ3122-2-2-22-22-222-2-22-2-22200002-2-22000000000000000000000000002i−2i
χ3222-2-2-22-22-222-2-22-2-22200002-2-2200000000000000000000000000−2i2i
χ3322-2-2-2-2222-22-2-22-2-22222-2-2-222-222-2-2-2-22200000000000000000000
χ3422-2-2-2-2222-22-2-22-2-222-2-222-222-2-2-22222-2-200000000000000000000
χ3522-2-2-2-22-12-2211-111-1-122-2-21-1-11-1-11111-1-100−i3i300i3−i3−i3i3i3−i300000000
χ3622-2-2-2-22-12-2211-111-1-122-2-21-1-11-1-11111-1-100i3−i300−i3i3i3−i3−i3i300000000
χ3722-2-2-2-22-12-2211-111-1-1-2-2221-1-1111-1-1-1-11100−i3i300i3−i3i3−i3−i3i300000000
χ3822-2-2-2-22-12-2211-111-1-1-2-2221-1-1111-1-1-1-11100i3−i300−i3i3−i3i3i3−i300000000
χ3944444-4-4-2-4-44-2-2-2-2-2-2-2000022220000000000000000000000000000
χ404444-4-44-2-44-422-2-2-22200002-22-20000000000000000000000000000
χ4144-4-4444-2-4-4-4-2-2-222220000-2-2220000000000000000000000000000
χ4244-4-4-44-4-2-44422-222-2-20000-222-20000000000000000000000000000
χ434-44i−4i000400000-44i−4i002-22i−2i00002-22i−2i2i−2i2-200000000000000000000
χ444-44i−4i000400000-44i−4i00-22−2i2i0000-22−2i2i−2i2i-2200000000000000000000
χ454-44i−4i000-2000−2i32i32−2i2i23−232-22i−2i0000−1+31−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−1−31+300000000000000000000
χ464-44i−4i000-2000−2i32i32−2i2i23−23-22−2i2i00001−3−1+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ111+3−1−300000000000000000000
χ474-44i−4i000-20002i3−2i32−2i2i−23232-22i−2i0000−1−31+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−1+31−300000000000000000000
χ484-44i−4i000-20002i3−2i32−2i2i−2323-22−2i2i00001+3−1−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ111−3−1+300000000000000000000
χ494-4−4i4i000400000-4−4i4i002-2−2i2i00002-2−2i2i−2i2i2-200000000000000000000
χ504-4−4i4i000400000-4−4i4i00-222i−2i0000-222i−2i2i−2i-2200000000000000000000
χ514-4−4i4i000-2000−2i32i322i−2i−23232-2−2i2i0000−1−31+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−1+31−300000000000000000000
χ524-4−4i4i000-2000−2i32i322i−2i−2323-222i−2i00001+3−1−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ111−3−1+300000000000000000000
χ534-4−4i4i000-20002i3−2i322i−2i23−232-2−2i2i0000−1+31−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−1−31+300000000000000000000
χ544-4−4i4i000-20002i3−2i322i−2i23−23-222i−2i00001−3−1+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ111+3−1−300000000000000000000

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