Finite Group Databasebeta

← Group #70536

Character table — Group #70536

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order1222444422344666121212126688881212242424242424242444881212121224242424444488882488
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
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111
χ91111-1-1-1-1-1-1111111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−iii−i−i11-1-11-1i−i
χ101111-1-1-1-1-1-1111111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i1-1i−i11-1-1ii−i−i−i−iii-1-111-11−ii
χ111111-1-1-1-1-1-1111111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iiiii−i−i11-1-1-11−ii
χ121111-1-1-1-1-1-1111111-1-1-1-1-1-1ii−i−i11iiii−i−i−i−i-11−ii-1-111−i−iii−i−iii-1-1111-1i−i
χ131111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iiiii−i−i-1-111-11i−i
χ141111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii1-1−ii11-1-1−i−iii−i−iii11-1-11-1−ii
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−iii−i−i-1-1111-1−ii
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−iii11−i−i−i−iiiii-11i−i-1-111ii−i−i−i−iii11-1-1-11i−i
χ172222222222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ182222222222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ192222222222-122-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-2-2-1-1-1-11111000000000000
χ202222222222-122-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2221111-1-1-1-1000000000000
χ2122222222-2-22-2-22222222-2-22-22-2-2-222-2-222-2-2000000000000000000000000
χ2222222222-2-22-2-22222222-2-2-22-22-2-2-2-222-2-222000000000000000000000000
χ2322222222-2-2-1-2-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000−i3i3−i3i3−i3i3−i3i3000000000000
χ2422222222-2-2-1-2-2-1-1-1-1-1-1-1112-22-211-1-111-1-1110000i3−i3i3−i3i3−i3i3−i3000000000000
χ2522222222-2-2-1-2-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000−i3i3−i3i3i3−i3i3−i3000000000000
χ2622222222-2-2-1-2-2-1-1-1-1-1-1-111-22-221111-1-111-1-10000i3−i3i3−i3−i3i3−i3i3000000000000
χ272222-2-2-2-2222-2-2222-2-2-2-2222i−2i−2i2i-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ282222-2-2-2-2222-2-2222-2-2-2-222−2i2i2i−2i-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ292222-2-2-2-222-1-2-2-1-1-11111-1-12i−2i−2i2i11−i−iiiii−i−i0000−i3i3i3−i33−3−33000000000000
χ302222-2-2-2-222-1-2-2-1-1-11111-1-12i−2i−2i2i11−i−iiiii−i−i0000i3−i3−i3i3−333−3000000000000
χ312222-2-2-2-222-1-2-2-1-1-11111-1-1−2i2i2i−2i11ii−i−i−i−iii0000−i3i3i3−i3−333−3000000000000
χ322222-2-2-2-222-1-2-2-1-1-11111-1-1−2i2i2i−2i11ii−i−i−i−iii0000i3−i3−i3i33−3−33000000000000
χ332222-2-2-2-2-2-2-122-1-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii2-22i−2i-1-111−i−iii000000000000
χ342222-2-2-2-2-2-2-122-1-1-11111112i2i−2i−2i-1-1−i−i−i−iiiii-22−2i2i11-1-1ii−i−i000000000000
χ352222-2-2-2-2-2-2-122-1-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i2-2−2i2i-1-111ii−i−i000000000000
χ362222-2-2-2-2-2-2-122-1-1-1111111−2i−2i2i2i-1-1iiii−i−i−i−i-222i−2i11-1-1−i−iii000000000000
χ372-2-2222-2-22-222-22-2-2-2-2222-200002-20000000000000000000000002i−2i2i−2i0000
χ382-2-2222-2-22-222-22-2-2-2-2222-200002-2000000000000000000000000−2i2i−2i2i0000
χ392-2-2222-2-2-222-222-2-2-2-222-220000-22000000000000000000002-22-200000000
χ402-2-2222-2-2-222-222-2-2-2-222-220000-2200000000000000000000-22-2200000000
χ412-2-22-2-2222-22-222-2-222-2-22-20000-22000000000000000000002i−2i−2i2i00000000
χ422-2-22-2-2222-22-222-2-222-2-22-20000-2200000000000000000000−2i2i2i−2i00000000
χ432-2-22-2-222-2222-22-2-222-2-2-2200002-20000000000000000000000002i−2i−2i2i0000
χ442-2-22-2-222-2222-22-2-222-2-2-2200002-2000000000000000000000000−2i2i2i−2i0000
χ4544-4-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000000000000000000000000000000000
χ4644-4-44i−4i4i−4i00-2002-22−2i2i−2i2i00000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000
χ4744-4-44i−4i4i−4i00-2002-22−2i2i−2i2i000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000
χ4844-4-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000000000000000000000000000000000
χ4944-4-4−4i4i−4i4i00-2002-222i−2i2i−2i000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000
χ5044-4-4−4i4i−4i4i00-2002-222i−2i2i−2i00000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000
χ514-44-44i−4i−4i4i00400-4-44−4i4i4i−4i0000000000000000000000000000000000000000
χ524-44-44i−4i−4i4i00-20022-22i−2i−2i2i00000000002ζ5−2ζ13−2ζ5+2ζ1300−2ζ7+2ζ232ζ7−2ζ23000000000000000000000000
χ534-44-44i−4i−4i4i00-20022-22i−2i−2i2i0000000000−2ζ5+2ζ132ζ5−2ζ13002ζ7−2ζ23−2ζ7+2ζ23000000000000000000000000
χ544-44-4−4i4i4i−4i00400-4-444i−4i−4i4i0000000000000000000000000000000000000000
χ554-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i0000000000−2ζ7+2ζ232ζ7−2ζ23002ζ5−2ζ13−2ζ5+2ζ13000000000000000000000000
χ564-44-4−4i4i4i−4i00-20022-2−2i2i2i−2i00000000002ζ7−2ζ23−2ζ7+2ζ2300−2ζ5+2ζ132ζ5−2ζ13000000000000000000000000
χ574-4-4444-4-44-4-24-4-22222-2-2-220000-2200000000000000000000000000000000
χ584-4-4444-4-4-44-2-44-22222-2-22-200002-200000000000000000000000000000000
χ594-4-44-4-4444-4-2-44-222-2-222-2200002-200000000000000000000000000000000
χ604-4-44-4-444-44-24-4-222-2-2222-20000-2200000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.