Finite Group Databasebeta

← Group #70372

Character table — Group #70372

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order12224444223446661212121244446612121212121212121212246688121224242424888888884488
χ1111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111
χ91111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1-111i−i-1-1ii−i−iii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i1-111i−i-1-1ii−i−i−i−iii-1-111-11−ii
χ111111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-11-1-1−ii11−i−iiiii−i−i11-1-1-11−ii
χ121111-1-1-1-1-1-1111111-1-1-1-1ii−i−i-1-111iiii−i−i−i−i-11-1-1−ii11−i−iii−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1-111−ii-1-1−i−iiiii−i−i-1-111-11i−i
χ141111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii1-111−ii-1-1−i−iii−i−iii11-1-11-1−ii
χ151111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−iii−i−i-1-1111-1−ii
χ161111-1-1-1-1-1-1111111-1-1-1-1−i−iii-1-111−i−i−i−iiiii-11-1-1i−i11ii−i−i−i−iii11-1-1-11i−i
χ172222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ182222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ192222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-2-2-1-11111000000000000
χ202222222222-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2112211-1-1-1-1000000000000
χ2122222222-2-22-2-222222220000-2-2-2-2000000000000000000002-22-200000000
χ2222222222-2-22-2-222222220000-2-2-2-200000000000000000000-22-2200000000
χ232222-2-2-2-2222-2-2222-2-2-2-2000022-2-2000000000000000000002i−2i−2i2i00000000
χ242222-2-2-2-2222-2-2222-2-2-2-2000022-2-200000000000000000000−2i2i2i−2i00000000
χ252222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i11-1-1−i−i−i−iiiii2-2-1-12i−2i11−i−iii000000000000
χ262222-2-2-2-2-2-2-122-1-1-111112i2i−2i−2i11-1-1−i−i−i−iiiii-2211−2i2i-1-1ii−i−i000000000000
χ272222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i11-1-1iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i000000000000
χ282222-2-2-2-2-2-2-122-1-1-11111−2i−2i2i2i11-1-1iiii−i−i−i−i-22112i−2i-1-1−i−iii000000000000
χ2922-2-222-2-22-22-22-2-2222-2-22i−2i2i−2i2-22-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ3022-2-222-2-22-22-22-2-2222-2-2−2i2i−2i2i2-22-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3122-2-222-2-22-2-1-2211-1-1-1112i−2i2i−2i-11-11−i−iii−i−iii00−i3i300−i3i33−33−3000000000000
χ3222-2-222-2-22-2-1-2211-1-1-1112i−2i2i−2i-11-11−i−iii−i−iii00i3−i300i3−i3−33−33000000000000
χ3322-2-222-2-22-2-1-2211-1-1-111−2i2i−2i2i-11-11ii−i−iii−i−i00−i3i300−i3i3−33−33000000000000
χ3422-2-222-2-22-2-1-2211-1-1-111−2i2i−2i2i-11-11ii−i−iii−i−i00i3−i300i3−i33−33−3000000000000
χ3522-2-222-2-2-2222-2-2-2222-2-20000-22-220000000000000000000000002i−2i2i−2i0000
χ3622-2-222-2-2-2222-2-2-2222-2-20000-22-22000000000000000000000000−2i2i−2i2i0000
χ3722-2-2-2-2222-222-2-2-22-2-22200002-2-220000000000000000000000002i−2i−2i2i0000
χ3822-2-2-2-2222-222-2-2-22-2-22200002-2-22000000000000000000000000−2i2i2i−2i0000
χ3922-2-2-2-222-222-22-2-22-2-2222-2-22-222-222-2-2-2-222000000000000000000000000
χ4022-2-2-2-222-222-22-2-22-2-222-222-2-222-2-2-22222-2-2000000000000000000000000
χ4122-2-2-2-222-22-1-2211-111-1-12-2-221-1-11-1-11111-1-100−i3i300i3−i3−i3i3i3−i3000000000000
χ4222-2-2-2-222-22-1-2211-111-1-12-2-221-1-11-1-11111-1-100i3−i300−i3i3i3−i3−i3i3000000000000
χ4322-2-2-2-222-22-1-2211-111-1-1-222-21-1-1111-1-1-1-11100−i3i300i3−i3i3−i3−i3i3000000000000
χ4422-2-2-2-222-22-1-2211-111-1-1-222-21-1-1111-1-1-1-11100i3−i300−i3i3−i3i3i3−i3000000000000
χ4544444444-4-4-2-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ464444-4-4-4-444-2-4-4-2-2-222220000-2-22200000000000000000000000000000000
χ4744-4-444-4-4-44-24-422-2-2-22200002-22-200000000000000000000000000000000
χ4844-4-4-4-4444-4-24-422-222-2-20000-222-200000000000000000000000000000000
χ494-44-44i−4i4i−4i004004-4-44i−4i4i−4i0000000000000000000000000000000000000000
χ504-44-44i−4i4i−4i00-200-222−2i2i−2i2i00000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000000000000000
χ514-44-44i−4i4i−4i00-200-222−2i2i−2i2i00000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000000000000000
χ524-44-4−4i4i−4i4i004004-4-4−4i4i−4i4i0000000000000000000000000000000000000000
χ534-44-4−4i4i−4i4i00-200-2222i−2i2i−2i00000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000000000000000
χ544-44-4−4i4i−4i4i00-200-2222i−2i2i−2i00000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000000000000000
χ554-4-444i−4i−4i4i00400-44-44i−4i−4i4i0000000000000000000000000000000000000000
χ564-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000000−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−ζ11000000000000000000000000
χ574-4-444i−4i−4i4i00-2002-22−2i2i2i−2i00000000ζ2−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+ζ11000000000000000000000000
χ584-4-44−4i4i4i−4i00400-44-4−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000000−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+ζ11000000000000000000000000
χ604-4-44−4i4i4i−4i00-2002-222i−2i−2i2i00000000ζ2+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−ζ11000000000000000000000000

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