Finite Group Databasebeta

← Group #68178

Character table — Group #68178

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size111111112222222222224444444444444444888888888888121212121212121224242424
order1222444434444666121212128888121212122424242424242424246688121224242424244488884488
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
χ511111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i1-11-1ii−i−i1-1i−i
χ101111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i1-111i−i-1-1ii−i−i-11-11−i−iii-11−ii
χ111111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii1-11-1ii−i−i-11−ii
χ121111-1-1-1-1111-1-1111-1-1-1-1ii−i−i11-1-1iiii−i−i−i−i-11-1-1−ii11−i−iii-11-11−i−iii1-1i−i
χ131111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii1-11-1−i−iii1-1−ii
χ141111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii1-111−ii-1-1−i−iii-11-11ii−i−i-11i−i
χ151111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i1-11-1−i−iii-11i−i
χ161111-1-1-1-1111-1-1111-1-1-1-1−i−iii11-1-1−i−i−i−iiiii-11-1-1i−i11ii−i−i-11-11ii−i−i1-1−ii
χ17222222222-2-2-2-222222220000-2-2-2-20000000000000000000022-2-200000000
χ18222222222-2-2-2-222222220000-2-2-2-200000000000000000000-2-22200000000
χ1922222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1000000000000
χ2022222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-211-2-2111111000000000000
χ2122222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-2-2-1-11111000000000000
χ2222222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-111111111-2-2112211-1-1-1-1000000000000
χ232222-2-2-2-22-2-222222-2-2-2-20000-2-222000000000000000000002-2-2200000000
χ242222-2-2-2-22-2-222222-2-2-2-20000-2-22200000000000000000000-222-200000000
χ252222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i-1-111−i−i−i−iiiii2-2-1-12i−2i11−i−iii000000000000
χ262222-2-2-2-2-122-2-2-1-1-111112i2i−2i−2i-1-111−i−i−i−iiiii-2211−2i2i-1-1ii−i−i000000000000
χ272222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i-1-111iiii−i−i−i−i2-2-1-1−2i2i11ii−i−i000000000000
χ282222-2-2-2-2-122-2-2-1-1-11111−2i−2i2i2i-1-111iiii−i−i−i−i-22112i−2i-1-1−i−iii000000000000
χ292-22-22i−2i2i−2i22-22i−2i2-2-22i−2i2i−2i00002-22i−2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ302-22-22i−2i2i−2i22-22i−2i2-2-22i−2i2i−2i00002-22i−2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ312-22-22i−2i2i−2i2-22−2i2i2-2-22i−2i2i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-22−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23000000000000000000000000
χ322-22-22i−2i2i−2i2-22−2i2i2-2-22i−2i2i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-22−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
χ332-22-22i−2i2i−2i-1-22−2i2i-111−ii−ii−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-1i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300−i3i3003−3ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ342-22-22i−2i2i−2i-1-22−2i2i-111−ii−ii−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ231-1i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ2300i3−i300−33−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ352-22-22i−2i2i−2i-1-22−2i2i-111−ii−ii2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-1i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300−i3i3003−3−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000
χ362-22-22i−2i2i−2i-1-22−2i2i-111−ii−ii2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ231-1i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ2300i3−i300−33ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000
χ372-22-2−2i2i−2i2i22-2−2i2i2-2-2−2i2i−2i2i00002-2−2i2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ382-22-2−2i2i−2i2i22-2−2i2i2-2-2−2i2i−2i2i00002-2−2i2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ392-22-2−2i2i−2i2i2-222i−2i2-2-2−2i2i−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13000000000000000000000000
χ402-22-2−2i2i−2i2i2-222i−2i2-2-2−2i2i−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-222i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13000000000000000000000000
χ412-22-2−2i2i−2i2i-1-222i−2i-111i−ii−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-1−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300−i3i300−33ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ422-22-2−2i2i−2i2i-1-222i−2i-111i−ii−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ131-1−ii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300i3−i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ432-22-2−2i2i−2i2i-1-222i−2i-111i−ii−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-1−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300−i3i300−33−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000
χ442-22-2−2i2i−2i2i-1-222i−2i-111i−ii−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ131-1−iiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300i3−i3003−3ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000
χ4544444444-2-4-4-4-4-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ464444-4-4-4-4-2-4-444-2-2-22222000022-2-200000000000000000000000000000000
χ4744-4-444-4-440000-4-4444-4-40000000000000000000000000000000000000000
χ4844-4-444-4-4-2000022-2-2-222000000006−66−66−66−6000000000000000000000000
χ4944-4-444-4-4-2000022-2-2-22200000000−66−66−66−66000000000000000000000000
χ5044-4-4-4-44440000-4-44-4-4440000000000000000000000000000000000000000
χ5144-4-4-4-444-2000022-222-2-200000000i6−i6i6−i6−i6i6−i6i6000000000000000000000000
χ5244-4-4-4-444-2000022-222-2-200000000−i6i6−i6i6i6−i6i6−i6000000000000000000000000
χ534-44-44i−4i4i−4i-24-44i−4i-222−2i2i−2i2i0000-22−2i2i00000000000000000000000000000000
χ544-44-4−4i4i−4i4i-24-4−4i4i-2222i−2i2i−2i0000-222i−2i00000000000000000000000000000000
χ554-4-444i−4i−4i4i40000-44-44i−4i−4i4i0000000000000000000000000000000000000000
χ564-4-444i−4i−4i4i-200002-22−2i2i2i−2i00000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22000000000000000000000000
χ574-4-444i−4i−4i4i-200002-22−2i2i2i−2i00000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22000000000000000000000000
χ584-4-44−4i4i4i−4i40000-44-4−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-44−4i4i4i−4i-200002-222i−2i−2i2i00000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22000000000000000000000000
χ604-4-44−4i4i4i−4i-200002-222i−2i−2i2i00000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22000000000000000000000000

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